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Proofgold Signed Transaction

vin
PrGns../43c45..
PUTMr../f61ab..
vout
PrGns../9565c.. 4.90 bars
TMKwS../8d698.. negprop ownership controlledby PrCx1.. upto 0
TMS5v../165e7.. negprop ownership controlledby PrCx1.. upto 0
TMMJo../62afd.. negprop ownership controlledby PrCx1.. upto 0
TMVUD../1f3b2.. negprop ownership controlledby PrCx1.. upto 0
TMFTX../2578a.. negprop ownership controlledby PrCx1.. upto 0
TMKhs../c438e.. negprop ownership controlledby PrCx1.. upto 0
TML9v../38a61.. negprop ownership controlledby PrCx1.. upto 0
TMboW../2c99f.. negprop ownership controlledby PrCx1.. upto 0
TMPQS../3dc0d.. negprop ownership controlledby PrCx1.. upto 0
TMLW9../291e4.. negprop ownership controlledby PrCx1.. upto 0
TMckj../2aa4b.. negprop ownership controlledby PrCx1.. upto 0
TMbYC../49bd6.. negprop ownership controlledby PrCx1.. upto 0
TMdbY../cdf7a.. negprop ownership controlledby PrCx1.. upto 0
TMLiP../29c2b.. negprop ownership controlledby PrCx1.. upto 0
TMFj8../487ee.. negprop ownership controlledby PrCx1.. upto 0
TMP3k../a231a.. negprop ownership controlledby PrCx1.. upto 0
TMG8q../7780d.. negprop ownership controlledby PrCx1.. upto 0
TMcZE../175a0.. negprop ownership controlledby PrCx1.. upto 0
TMFPm../f4bad.. negprop ownership controlledby PrCx1.. upto 0
TMP5D../4d469.. negprop ownership controlledby PrCx1.. upto 0
TMTsP../713d9.. negprop ownership controlledby PrCx1.. upto 0
TMKfi../d4dcd.. negprop ownership controlledby PrCx1.. upto 0
TMKdd../306d3.. negprop ownership controlledby PrCx1.. upto 0
TMXk3../60f57.. negprop ownership controlledby PrCx1.. upto 0
TMb3i../6d8c3.. negprop ownership controlledby PrCx1.. upto 0
TMF23../37ae8.. negprop ownership controlledby PrCx1.. upto 0
TMbRn../93f43.. negprop ownership controlledby PrCx1.. upto 0
TMJz9../02dd8.. negprop ownership controlledby PrCx1.. upto 0
TMHFc../67e96.. negprop ownership controlledby PrCx1.. upto 0
TMWez../3a49c.. negprop ownership controlledby PrCx1.. upto 0
TMcvJ../dfc7f.. negprop ownership controlledby PrCx1.. upto 0
TML6L../49c3f.. negprop ownership controlledby PrCx1.. upto 0
TMYZ1../a0df4.. negprop ownership controlledby PrCx1.. upto 0
TMcqh../a390a.. negprop ownership controlledby PrCx1.. upto 0
TMYrB../7d94b.. negprop ownership controlledby PrCx1.. upto 0
TMQMM../fb750.. negprop ownership controlledby PrCx1.. upto 0
TMaiR../45fdf.. negprop ownership controlledby PrCx1.. upto 0
TMdjp../a28b0.. negprop ownership controlledby PrCx1.. upto 0
TMYoa../19a31.. negprop ownership controlledby PrCx1.. upto 0
TMWYK../e9d2b.. negprop ownership controlledby PrCx1.. upto 0
TMN4s../fcb37.. negprop ownership controlledby PrCx1.. upto 0
TMNPK../4edf6.. negprop ownership controlledby PrCx1.. upto 0
TMUDX../e3f7c.. negprop ownership controlledby PrCx1.. upto 0
TMHw4../681ab.. negprop ownership controlledby PrCx1.. upto 0
TMH1u../bdb68.. negprop ownership controlledby PrCx1.. upto 0
TMYw6../3264e.. negprop ownership controlledby PrCx1.. upto 0
TMZjf../f4921.. negprop ownership controlledby PrCx1.. upto 0
TMMAQ../dcae0.. ownership of 2641e.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMNFi../30961.. ownership of f1074.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMRZS../16ac5.. ownership of d7d2d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMZ7Y../9e863.. ownership of f9114.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMcwL../94ce4.. ownership of dc60c.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMF47../fee16.. ownership of fff8d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMaXv../a1777.. ownership of 27eb8.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMV8f../8013b.. ownership of ebff1.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMTEp../ea1b7.. ownership of 67030.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMce2../8f377.. ownership of bbfec.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMQ9q../7e2b6.. ownership of c3545.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMXyd../2be36.. ownership of 2ef28.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMcV3../c69a8.. ownership of eb403.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMN36../c4d85.. ownership of f0de0.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMbQA../beb73.. ownership of d5a6e.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMatB../33838.. ownership of ef94c.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMHE7../2aa29.. ownership of d8355.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMVBB../3c803.. ownership of 31629.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMVgV../ad7b7.. ownership of 5c322.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMLTy../6ec6a.. ownership of 2ac2e.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMMxq../96ee8.. ownership of 53cb6.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMdZx../5990a.. ownership of b0f4f.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMbWw../dee9e.. ownership of 045e9.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMWfU../ea3d7.. ownership of ce1c8.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMQUg../6d979.. ownership of 3c5d6.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMbGr../a5274.. ownership of dd4f3.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMX9Q../f2497.. ownership of cda45.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMMkt../e786a.. ownership of 0fea1.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMdge../532c6.. ownership of 0c054.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMVtt../02209.. ownership of 53802.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMYae../4022b.. ownership of 95678.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMK62../73e90.. ownership of 3ecb4.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMamZ../6ecfd.. ownership of c94e6.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMchn../b797d.. ownership of 83f90.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMbQ3../62153.. ownership of a2ce8.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMTa4../9923b.. ownership of 30697.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMPFq../5a4ca.. ownership of 116ab.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMEzr../3f302.. ownership of 27f27.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMYXh../33ce3.. ownership of 9f67b.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMNrg../09a44.. ownership of e37b7.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMFuY../2a536.. ownership of c4f39.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMaCf../76c61.. ownership of d4c91.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMH3y../8fa92.. ownership of 41f1d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMWwn../0f0ba.. ownership of 5ac8e.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMSFh../b9168.. ownership of 38e04.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMT3Z../257a9.. ownership of 06d83.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMavQ../6211c.. ownership of 07f21.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMQPX../2143d.. ownership of 6f5ae.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMMLe../75055.. ownership of 99d41.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMaEU../38f57.. ownership of 84454.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMMat../85775.. ownership of 42ea4.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMaZr../ca6e7.. ownership of a5858.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMRJ5../08447.. ownership of 4fcd2.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMZh9../dea94.. ownership of a5136.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMWgt../facef.. ownership of 9afec.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMNSA../4b0b0.. ownership of 9d231.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMTss../6b0bb.. ownership of 24cb9.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMdD7../ef32f.. ownership of acc1f.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMdmy../7e0c6.. ownership of 46424.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMT1G../d3e85.. ownership of 191de.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMVdM../c31ed.. ownership of 468a8.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMQSa../fd572.. ownership of 020eb.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMJug../0be9c.. ownership of 39a62.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMdrn../7f81e.. ownership of 51646.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMM2y../521d7.. ownership of d8cf4.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMdkQ../15911.. ownership of 4382e.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMNWY../dd82d.. ownership of aa851.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMLsJ../30c6e.. ownership of 6073f.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMcfk../5f4f9.. ownership of c6dcd.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMXM1../add08.. ownership of e425e.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMQhY../54c03.. ownership of 37787.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMTSH../39473.. ownership of 83524.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMT1X../6918b.. ownership of 00f54.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMHfh../7723d.. ownership of c2a06.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMduU../ce560.. ownership of 5b61b.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMN1R../2f81b.. ownership of e8a3a.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMVVK../3578a.. ownership of a800b.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMUXs../5130f.. ownership of 2dc08.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMbk7../7d01f.. ownership of f649b.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMczD../d5b93.. ownership of 0ca8d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMF7o../a4bfa.. ownership of eb0c8.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMc4A../04f8f.. ownership of 73494.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMYCZ../b7c69.. ownership of 2dc4f.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMWKi../f998a.. ownership of 966d8.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMT3e../d158b.. ownership of 989cb.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMGMM../e6268.. ownership of 6dfff.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMJRp../bf554.. ownership of dae89.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMPVA../3e00b.. ownership of 209f2.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMUsP../95ae4.. ownership of 8d336.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMcCz../f8946.. ownership of e3da8.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMNFj../ef92e.. ownership of d9582.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMajT../e8528.. ownership of 7894d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMWdR../385da.. ownership of 0859d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
TMKW9../0cc7a.. ownership of dc75c.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0
PUhzW../56c83.. doc published by PrCx1..
Known 46237..LoopI : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . binop_on x0 x1 ⟶ binop_on x0 x2 ⟶ binop_on x0 x3 ⟶ (∀ x5 . In x5 x0 ⟶ and (x1 x4 x5 = x5) (x1 x5 x4 = x5)) ⟶ (∀ x5 . In x5 x0 ⟶ ∀ x6 . In x6 x0 ⟶ and (and (and (x2 x5 (x1 x5 x6) = x6) (x1 x5 (x2 x5 x6) = x6)) (x3 (x1 x5 x6) x6 = x5)) (x1 (x3 x5 x6) x6 = x5)) ⟶ Loop x0 x1 x2 x3 x4
Known 7c02f..andI : ∀ x0 x1 : ο . x0 ⟶ x1 ⟶ and x0 x1
Known 22d81..and4I : ∀ x0 x1 x2 x3 : ο . x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ and (and (and x0 x1) x2) x3
Known 9ae18..SingE : ∀ x0 x1 . In x1 (Sing x0) ⟶ x1 = x0
Known 86824..binop_on_I : ∀ x0 . ∀ x1 : ι → ι → ι . (∀ x2 . In x2 x0 ⟶ ∀ x3 . In x3 x0 ⟶ In (x1 x2 x3) x0) ⟶ binop_on x0 x1
Known 1f15b..SingI : ∀ x0 . In x0 (Sing x0)
Theorem f3ad1.. : Loop (Sing 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (Sing 0) (proof)
Known 20499..Loop_with_defs_I : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop x0 x1 x2 x3 x4 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ x5 x14 x15 = x2 (x1 x15 x14) (x1 x14 x15)) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x6 x14 x15 x16 = x2 (x1 x14 (x1 x15 x16)) (x1 (x1 x14 x15) x16)) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ and (and (and (and (x7 x14 x15 = x2 x14 (x1 x15 x14)) (x10 x14 x15 = x1 x14 (x1 x15 (x2 x14 x4)))) (x11 x14 x15 = x1 (x1 (x3 x4 x14) x15) x14)) (x12 x14 x15 = x1 (x2 x14 x15) (x2 (x2 x14 x4) x4))) (x13 x14 x15 = x1 (x3 x4 (x3 x4 x14)) (x3 x15 x14))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ and (x8 x14 x15 x16 = x2 (x1 x15 x14) (x1 x15 (x1 x14 x16))) (x9 x14 x15 x16 = x3 (x1 (x1 x16 x14) x15) (x1 x14 x15))) ⟶ Loop_with_defs x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13
Known 1bd08..and5I : ∀ x0 x1 x2 x3 x4 : ο . x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ and (and (and (and x0 x1) x2) x3) x4
Theorem 6e0b2.. : Loop_with_defs (Sing 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (Sing 0) (λ x0 x1 . 0) (λ x0 x1 x2 . 0) (λ x0 x1 . 0) (λ x0 x1 x2 . 0) (λ x0 x1 x2 . 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (proof)
Known 9d0a4..Loop_with_defs_cex1_I : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . ∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ Loop_with_defs x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ not (x5 (x1 (x2 (x8 x15 x16 x14) x4) x14) x17 = x4) ⟶ Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13
Known 8106d..notI : ∀ x0 : ο . (x0 ⟶ False) ⟶ not x0
Known 2901c..EmptyE : ∀ x0 . In x0 0 ⟶ False
Theorem bc517.. : Loop_with_defs_cex1 (Sing 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (Sing 0) (λ x0 x1 . 0) (λ x0 x1 x2 . 0) (λ x0 x1 . 0) (λ x0 x1 x2 . 0) (λ x0 x1 x2 . 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (proof)
Known 7054a..Loop_with_defs_cex2_I : ∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . ∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ Loop_with_defs x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ not (x6 x18 (x1 (x3 x4 x14) (x9 x15 x16 x14)) x17 = x4) ⟶ Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13
Theorem 8fd72.. : Loop_with_defs_cex2 (Sing 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (Sing 0) (λ x0 x1 . 0) (λ x0 x1 x2 . 0) (λ x0 x1 . 0) (λ x0 x1 x2 . 0) (λ x0 x1 x2 . 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (λ x0 x1 . 0) (proof)
Known FalseEFalseE : False ⟶ ∀ x0 : ο . x0
Theorem 0859d.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x12 x16 (x9 x14 x15 (x7 x16 (x8 x14 x15 (x12 x16 (x9 x14 x15 (x7 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x7 x15 (x12 x16 x17)) = x7 x15 (x12 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 x18)) = x10 x16 (x12 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x13 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x13 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x10 x16 (x13 x17 x18))) = x10 x16 (x13 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x13 x16 (x12 x17 x18))) = x13 x16 (x12 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x7 x18 x19))) = x13 x17 (x7 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x7 x18 x19))) = x10 x17 (x7 x18 (x9 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x17 x18 (x13 x19 x20))) = x9 x17 x18 (x13 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem d9582.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x10 x14 (x12 x15 (x10 x16 x17)) = x12 x15 (x10 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 x18)) = x10 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x13 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x10 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x13 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x10 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x13 x16 (x12 x17 x18))) = x13 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x8 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x8 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x13 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x8 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 8d336.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x12 x14 (x12 x15 (x9 x14 x15 (x12 x14 (x12 x15 (x9 x14 x15 (x12 x14 (x12 x15 (x9 x14 x15 (x12 x14 (x12 x15 (x9 x14 x15 (x12 x14 (x12 x15 x16)))))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x8 x14 x15 (x13 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x13 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x13 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x13 x14 (x12 x15 (x10 x16 x17)) = x12 x15 (x10 x16 (x13 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 x18)) = x12 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x7 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x10 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x7 x18 x19))) = x12 x17 (x7 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem dae89.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x7 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x7 x14 (x9 x15 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 (x10 x14 (x10 x15 (x8 x14 x15 (x10 x14 (x10 x15 (x8 x14 x15 (x10 x14 (x10 x15 (x8 x14 x15 (x10 x14 (x10 x15 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x12 x15 (x10 x16 x17)) = x12 x15 (x10 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x10 x16 (x13 x17 x18)) = x10 x16 (x13 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x10 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x13 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x7 x18 x19))) = x10 x17 (x7 x18 (x9 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x7 x16 (x9 x17 x18 (x13 x19 x20))) = x9 x17 x18 (x13 x19 (x9 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x7 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x9 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 989cb.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x13 x14 (x7 x15 (x12 x16 x17)) = x7 x15 (x12 x16 (x13 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 x18)) = x12 x16 (x12 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x7 x16 (x13 x17 x18))) = x7 x16 (x13 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x7 x16 (x13 x17 x18))) = x7 x16 (x13 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x7 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x13 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x13 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x10 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x7 x18 x19))) = x12 x17 (x7 x18 (x8 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x13 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x8 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x7 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x9 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 2dc4f.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x13 x14 (x12 x15 (x13 x16 x17)) = x12 x15 (x13 x16 (x13 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 x18)) = x12 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x13 x16 (x7 x17 x18))) = x13 x16 (x7 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x17 (x13 x18 x19))) = x12 x17 (x13 x18 (x9 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x13 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x8 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem eb0c8.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x12 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x12 x16 (x8 x14 x15 (x10 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x10 x15 (x10 x16 x17)) = x10 x15 (x10 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 x18)) = x7 x16 (x10 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x13 x16 (x12 x17 x18))) = x13 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x7 x18 x19))) = x7 x17 (x7 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem f649b.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x14 (x8 x15 x16 (x9 x14 x15 (x13 x16 (x12 x14 (x8 x15 x16 (x9 x14 x15 (x13 x16 (x12 x14 (x8 x15 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x13 x16 (x9 x14 x15 (x13 x16 (x8 x14 x15 (x13 x16 (x9 x14 x15 (x13 x16 (x8 x14 x15 (x13 x16 (x9 x14 x15 (x13 x16 (x8 x14 x15 (x13 x16 (x9 x14 x15 (x13 x16 (x8 x14 x15 (x13 x16 (x9 x14 x15 (x13 x16 x17))))))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x10 x14 (x13 x15 (x12 x16 x17)) = x13 x15 (x12 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 x18)) = x12 x16 (x12 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x13 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x7 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x9 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x13 x17 (x10 x18 x19))) = x13 x17 (x10 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x10 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x9 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x10 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x9 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem a800b.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x13 x15 (x10 x16 x17)) = x13 x15 (x10 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x13 x16 (x7 x17 x18)) = x13 x16 (x7 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x13 x16 (x10 x17 x18))) = x13 x16 (x10 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x10 x18 x19))) = x7 x17 (x10 x18 (x8 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x10 x18 x19))) = x10 x17 (x10 x18 (x8 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x13 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x8 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x10 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x8 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 5b61b.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 x17))))))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x10 x14 (x12 x15 (x12 x16 x17)) = x12 x15 (x12 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 x18)) = x10 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x13 x16 (x13 x17 x18))) = x13 x16 (x13 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x13 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x10 x18 x19))) = x7 x17 (x10 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x10 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x8 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x17 x18 (x13 x19 x20))) = x9 x17 x18 (x13 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x13 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 00f54.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x14 (x8 x15 x16 (x9 x14 x15 (x10 x16 (x10 x14 (x8 x15 x16 (x9 x14 x15 (x10 x16 (x10 x14 (x8 x15 x16 (x9 x14 x15 (x10 x16 (x10 x14 (x8 x15 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x12 x14 (x10 x15 (x9 x14 x15 (x12 x14 (x10 x15 x16))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x7 x15 (x10 x16 x17)) = x7 x15 (x10 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 x18)) = x7 x16 (x10 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x13 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x13 x16 (x12 x17 x18))) = x13 x16 (x12 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x17 (x7 x18 x19))) = x12 x17 (x7 x18 (x9 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x13 x17 (x12 x18 x19))) = x13 x17 (x12 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x7 x16 (x8 x17 x18 (x13 x19 x20))) = x8 x17 x18 (x13 x19 (x9 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 37787.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x13 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x13 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x13 x16 (x9 x14 x15 (x10 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 (x12 x14 (x12 x15 (x8 x14 x15 (x12 x14 (x12 x15 (x8 x14 x15 (x12 x14 (x12 x15 (x8 x14 x15 (x12 x14 (x12 x15 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x10 x15 (x12 x16 x17)) = x10 x15 (x12 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 x18)) = x12 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x13 x18 x19))) = x12 x17 (x13 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x13 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x9 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x13 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x9 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem c6dcd.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 (x10 x14 (x12 x15 (x8 x14 x15 (x10 x14 (x12 x15 (x8 x14 x15 (x10 x14 (x12 x15 (x8 x14 x15 (x10 x14 (x12 x15 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x14 (x9 x15 x16 (x8 x14 x15 (x10 x16 (x12 x14 (x9 x15 x16 (x8 x14 x15 (x10 x16 (x12 x14 (x9 x15 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x12 x15 (x10 x16 x17)) = x12 x15 (x10 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 x18)) = x12 x16 (x10 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x13 x16 (x13 x17 x18))) = x13 x16 (x13 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x7 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x13 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x10 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x13 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x7 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x13 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x9 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x10 x18 x19))) = x7 x17 (x10 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x13 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x9 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x13 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x9 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x13 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem aa851.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x14 (x8 x15 x16 (x9 x14 x15 (x7 x16 (x7 x14 (x8 x15 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x12 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x12 x16 (x8 x14 x15 (x10 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x12 x15 (x7 x16 x17)) = x12 x15 (x7 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 x18)) = x12 x16 (x10 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x13 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x7 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x13 x16 (x12 x17 x18))) = x13 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x8 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x9 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x13 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x9 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem d8cf4.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x7 x16 x17))))))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x14 (x8 x15 x16 (x9 x14 x15 (x10 x16 (x7 x14 (x8 x15 x16 (x9 x14 x15 (x10 x16 (x7 x14 (x8 x15 x16 (x9 x14 x15 (x10 x16 (x7 x14 (x8 x15 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x13 x14 (x13 x15 (x7 x16 x17)) = x13 x15 (x7 x16 (x13 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 x18)) = x12 x16 (x10 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x10 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x13 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x7 x18 x19))) = x10 x17 (x7 x18 (x9 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x10 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 x19 (x8 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x10 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x8 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 39a62.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x14 (x9 x15 x16 (x8 x14 x15 (x7 x16 (x7 x14 (x9 x15 x16 (x8 x14 x15 (x7 x16 (x7 x14 (x9 x15 x16 (x8 x14 x15 (x7 x16 (x7 x14 (x9 x15 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x10 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x10 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x10 x14 (x12 x15 (x12 x16 x17)) = x12 x15 (x12 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 x18)) = x7 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x7 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x10 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x7 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x10 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x10 x16 (x13 x17 x18))) = x10 x16 (x13 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x10 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x9 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 468a8.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x7 x15 (x10 x16 x17)) = x7 x15 (x10 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 x18)) = x12 x16 (x12 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x13 x16 (x10 x17 x18))) = x13 x16 (x10 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x7 x18 x19))) = x7 x17 (x7 x18 (x9 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x10 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x9 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x7 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x9 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x13 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 46424.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x14 (x8 x15 x16 (x8 x14 x15 (x7 x16 (x12 x14 (x8 x15 x16 (x8 x14 x15 (x7 x16 (x12 x14 (x8 x15 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 (x10 x14 (x10 x15 (x8 x14 x15 (x10 x14 (x10 x15 (x8 x14 x15 (x10 x14 (x10 x15 x16)))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x10 x14 (x12 x15 (x7 x16 x17)) = x12 x15 (x7 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 x18)) = x12 x16 (x10 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x13 x16 (x12 x17 x18))) = x13 x16 (x12 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x13 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x12 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x10 x18 x19))) = x7 x17 (x10 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x13 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x8 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x9 x17 x18 (x13 x19 x20))) = x9 x17 x18 (x13 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 24cb9.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x7 x14 (x12 x15 (x9 x14 x15 (x7 x14 (x12 x15 (x9 x14 x15 (x7 x14 (x12 x15 (x9 x14 x15 (x7 x14 (x12 x15 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x7 x14 (x10 x15 (x9 x14 x15 (x7 x14 (x10 x15 x16))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x12 x15 (x10 x16 x17)) = x12 x15 (x10 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 x18)) = x10 x16 (x10 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x10 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x13 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x7 x18 x19))) = x12 x17 (x7 x18 (x8 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x7 x18 x19))) = x10 x17 (x7 x18 (x8 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x13 x16 (x9 x17 x18 (x13 x19 x20))) = x9 x17 x18 (x13 x19 (x8 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 9afec.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x14 (x8 x15 x16 (x8 x14 x15 (x7 x16 (x12 x14 (x8 x15 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x13 x14 (x7 x15 (x9 x14 x15 (x13 x14 (x7 x15 x16))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x12 x15 (x12 x16 x17)) = x12 x15 (x12 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 x18)) = x10 x16 (x10 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x13 x16 (x7 x17 x18))) = x13 x16 (x7 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x13 x18 x19))) = x7 x17 (x13 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x7 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x9 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 4fcd2.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x8 x14 x15 (x7 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x7 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x7 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 (x12 x14 (x13 x15 (x8 x14 x15 (x12 x14 (x13 x15 x16))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x13 x15 (x10 x16 x17)) = x13 x15 (x10 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 x18)) = x10 x16 (x12 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x13 x16 (x10 x17 x18))) = x13 x16 (x10 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x10 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x9 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 42ea4.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x7 x14 (x10 x15 (x9 x14 x15 (x7 x14 (x10 x15 (x9 x14 x15 (x7 x14 (x10 x15 x16)))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x14 (x8 x15 x16 (x9 x14 x15 (x13 x16 (x10 x14 (x8 x15 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x13 x14 (x7 x15 (x12 x16 x17)) = x7 x15 (x12 x16 (x13 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 x18)) = x7 x16 (x7 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x13 x16 (x10 x17 x18))) = x13 x16 (x10 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x13 x18 x19))) = x7 x17 (x13 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x13 x18 x19))) = x7 x17 (x13 x18 (x9 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x13 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x9 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x9 x17 x18 (x13 x19 x20))) = x9 x17 x18 (x13 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 99d41.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 (x10 x14 (x10 x15 (x8 x14 x15 (x10 x14 (x10 x15 (x8 x14 x15 (x10 x14 (x10 x15 (x8 x14 x15 (x10 x14 (x10 x15 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 (x7 x14 (x12 x15 (x8 x14 x15 (x7 x14 (x12 x15 (x8 x14 x15 (x7 x14 (x12 x15 (x8 x14 x15 (x7 x14 (x12 x15 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x7 x15 (x12 x16 x17)) = x7 x15 (x12 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 x18)) = x10 x16 (x12 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x12 x18 x19))) = x13 x17 (x12 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x7 x18 x19))) = x12 x17 (x7 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 07f21.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x10 x15 (x12 x16 x17)) = x10 x15 (x12 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 x18)) = x7 x16 (x10 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x13 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x12 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x7 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x10 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x13 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x7 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x13 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x12 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x13 x16 (x7 x17 x18))) = x13 x16 (x7 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x10 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x9 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 38e04.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x14 (x9 x15 x16 (x8 x14 x15 (x10 x16 (x12 x14 (x9 x15 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x10 x14 (x7 x15 (x13 x16 x17)) = x7 x15 (x13 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 x18)) = x12 x16 (x12 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x13 x16 (x12 x17 x18))) = x13 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x13 x16 (x10 x17 x18))) = x13 x16 (x10 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x7 x18 x19))) = x12 x17 (x7 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x13 x17 (x10 x18 x19))) = x13 x17 (x10 x18 (x8 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x10 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x8 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x10 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 41f1d.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x10 x15 (x7 x16 x17)) = x10 x15 (x7 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 x18)) = x12 x16 (x7 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x13 x15 (x13 x16 (x12 x17 x18))) = x13 x16 (x12 x17 (x12 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x13 x16 (x7 x17 x18))) = x13 x16 (x7 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x8 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x13 x18 x19))) = x7 x17 (x13 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x10 x16 (x8 x17 x18 (x13 x19 x20))) = x8 x17 x18 (x13 x19 (x9 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x10 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x9 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem c4f39.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x7 x15 (x7 x16 x17)) = x7 x15 (x7 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 x18)) = x12 x16 (x10 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x13 x16 (x13 x17 x18))) = x13 x16 (x13 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x10 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x8 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x13 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 9f67b.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x12 x14 (x13 x15 (x9 x14 x15 (x12 x14 (x13 x15 (x9 x14 x15 (x12 x14 (x13 x15 (x9 x14 x15 (x12 x14 (x13 x15 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x14 x15 (x13 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x13 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x13 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x13 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x12 x15 (x12 x16 x17)) = x12 x15 (x12 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 x18)) = x12 x16 (x13 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x7 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x13 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x7 x16 (x13 x17 x18))) = x7 x16 (x13 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x9 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x13 x18 x19))) = x7 x17 (x13 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x8 x17 x18 (x13 x19 x20))) = x8 x17 x18 (x13 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x13 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x13 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 116ab.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x7 x16 (x13 x14 (x8 x15 x16 (x8 x14 x15 (x7 x16 (x13 x14 (x8 x15 x16 (x8 x14 x15 (x7 x16 (x13 x14 (x8 x15 x16 (x8 x14 x15 (x7 x16 (x13 x14 (x8 x15 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x10 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x7 x16 x17))))))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x10 x14 (x7 x15 (x7 x16 x17)) = x7 x15 (x7 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 x18)) = x7 x16 (x12 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x13 x16 (x7 x17 x18))) = x13 x16 (x7 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x13 x16 (x10 x17 x18))) = x13 x16 (x10 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x7 x18 x19))) = x10 x17 (x7 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x9 x17 x18 (x13 x19 x20))) = x9 x17 x18 (x13 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem a2ce8.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x12 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x12 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x12 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x12 x14 (x8 x15 x16 x17))))))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x8 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x8 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x13 x14 (x12 x15 (x10 x16 x17)) = x12 x15 (x10 x16 (x13 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 x18)) = x7 x16 (x12 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x13 x16 (x13 x17 x18))) = x13 x16 (x13 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x13 x17 (x7 x18 x19))) = x13 x17 (x7 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x13 x17 (x13 x18 x19))) = x13 x17 (x13 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x13 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x9 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem c94e6.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x13 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x13 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x13 x16 (x8 x14 x15 (x10 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x12 x15 (x12 x16 x17)) = x12 x15 (x12 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 x18)) = x7 x16 (x10 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x13 x16 (x12 x17 x18))) = x13 x16 (x12 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x10 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x13 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x13 x18 x19))) = x10 x17 (x13 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x13 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x9 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 95678.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x7 x16 (x8 x14 x15 (x13 x16 (x9 x14 x15 (x7 x16 (x8 x14 x15 (x13 x16 (x9 x14 x15 (x7 x16 (x8 x14 x15 (x13 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x10 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x13 x14 (x10 x15 (x7 x16 x17)) = x10 x15 (x7 x16 (x13 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 x18)) = x10 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x13 x16 (x12 x17 x18))) = x13 x16 (x12 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x10 x16 (x13 x17 x18))) = x10 x16 (x13 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x10 x18 x19))) = x7 x17 (x10 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x7 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 0c054.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x10 x16 (x9 x14 x15 (x13 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x13 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x12 x16 (x9 x14 x15 (x10 x16 (x8 x14 x15 (x12 x16 (x9 x14 x15 (x10 x16 (x8 x14 x15 (x12 x16 (x9 x14 x15 (x10 x16 (x8 x14 x15 (x12 x16 (x9 x14 x15 (x10 x16 (x8 x14 x15 (x12 x16 (x9 x14 x15 (x10 x16 x17))))))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x7 x15 (x10 x16 x17)) = x7 x15 (x10 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 x18)) = x10 x16 (x12 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x13 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x10 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x7 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x13 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x13 x16 (x13 x17 (x10 x18 x19))) = x13 x17 (x10 x18 (x9 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x10 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x8 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x7 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 x19 (x9 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x13 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x13 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem cda45.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x10 x16 (x13 x14 (x8 x15 x16 (x9 x14 x15 (x10 x16 (x13 x14 (x8 x15 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 (x10 x14 (x10 x15 (x8 x14 x15 (x10 x14 (x10 x15 x16))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x12 x15 (x10 x16 x17)) = x12 x15 (x10 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 x18)) = x12 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x13 x15 (x13 x16 (x10 x17 x18))) = x13 x16 (x10 x17 (x12 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x9 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x10 x17 (x7 x18 x19))) = x10 x17 (x7 x18 (x8 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x8 x17 x18 (x13 x19 x20))) = x8 x17 x18 (x13 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x7 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x13 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x13 x16 (x13 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 3c5d6.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x10 x16 (x8 x14 x15 (x13 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x13 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x13 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x13 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x10 x15 (x7 x16 x17)) = x10 x15 (x7 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 x18)) = x7 x16 (x12 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x7 x16 (x13 x17 x18))) = x7 x16 (x13 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x10 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x13 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x13 x17 (x12 x18 x19))) = x13 x17 (x12 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x10 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x8 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 045e9.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x10 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x10 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x10 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x10 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x10 x16 (x8 x14 x15 (x10 x16 x17))))))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x10 x15 (x7 x16 x17)) = x10 x15 (x7 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 x18)) = x7 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x13 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x13 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x7 x18 x19))) = x13 x17 (x7 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x10 x18 x19))) = x7 x17 (x10 x18 (x8 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x10 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x8 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x10 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x9 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x13 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x13 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 53cb6.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 (x8 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 x17))))))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x12 x15 (x12 x16 x17)) = x12 x15 (x12 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x13 x16 (x10 x17 x18)) = x13 x16 (x10 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x9 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x13 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 5c322.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x7 x15 (x10 x16 x17)) = x7 x15 (x10 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 x18)) = x12 x16 (x10 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x7 x18 x19))) = x10 x17 (x7 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x10 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x9 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem d8355.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x12 x16 (x9 x14 x15 (x7 x16 (x8 x14 x15 (x12 x16 (x9 x14 x15 (x7 x16 (x8 x14 x15 (x12 x16 (x9 x14 x15 (x7 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x10 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x10 x16 (x8 x14 x15 (x10 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x10 x15 (x12 x16 x17)) = x10 x15 (x12 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 x18)) = x7 x16 (x10 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x7 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x10 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x10 x18 x19))) = x13 x17 (x10 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x13 x18 x19))) = x12 x17 (x13 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x10 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x9 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem d5a6e.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x8 x14 x15 (x13 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x13 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x10 x14 (x7 x15 (x9 x14 x15 (x10 x14 (x7 x15 (x9 x14 x15 (x10 x14 (x7 x15 (x9 x14 x15 (x10 x14 (x7 x15 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x7 x15 (x13 x16 x17)) = x7 x15 (x13 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 x18)) = x12 x16 (x13 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x7 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x13 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x13 x16 (x13 x17 x18))) = x13 x16 (x13 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x7 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x10 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x8 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x13 x17 (x12 x18 x19))) = x13 x17 (x12 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x8 x17 x18 (x13 x19 x20))) = x8 x17 x18 (x13 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem eb403.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x13 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x13 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x13 x16 (x8 x14 x15 (x10 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x14 (x8 x15 x16 (x8 x14 x15 (x7 x16 (x10 x14 (x8 x15 x16 (x8 x14 x15 (x7 x16 (x10 x14 (x8 x15 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x10 x15 (x12 x16 x17)) = x10 x15 (x12 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 x18)) = x12 x16 (x10 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x10 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x13 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x7 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x13 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x10 x16 (x13 x17 (x12 x18 x19))) = x13 x17 (x12 x18 (x8 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x7 x18 x19))) = x10 x17 (x7 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x13 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x9 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x13 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem c3545.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x13 x15 (x12 x16 x17)) = x13 x15 (x12 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 x18)) = x12 x16 (x12 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x13 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x12 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x10 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 x19 (x8 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x10 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x8 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 67030.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x7 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x7 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x13 x14 (x12 x15 (x10 x16 x17)) = x12 x15 (x10 x16 (x13 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 x18)) = x12 x16 (x12 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x13 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x12 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x13 x15 (x13 x16 (x7 x17 x18))) = x13 x16 (x7 x17 (x7 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x7 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x10 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x7 x18 x19))) = x7 x17 (x7 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x13 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 27eb8.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x8 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x8 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x8 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x14 (x8 x15 x16 (x9 x14 x15 (x7 x16 (x12 x14 (x8 x15 x16 (x9 x14 x15 (x7 x16 (x12 x14 (x8 x15 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x13 x14 (x10 x15 (x7 x16 x17)) = x10 x15 (x7 x16 (x13 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 x18)) = x13 x16 (x10 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x13 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x13 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x8 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem dc60c.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x12 x15 (x12 x16 x17)) = x12 x15 (x12 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 x18)) = x10 x16 (x10 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x13 x16 (x12 x17 x18))) = x13 x16 (x12 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x7 x18 x19))) = x7 x17 (x7 x18 (x8 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x7 x18 x19))) = x13 x17 (x7 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x13 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x9 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem d7d2d.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x7 x16 (x8 x14 x15 (x13 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x13 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x13 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x13 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x10 x16 x17))))))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x12 x15 (x12 x16 x17)) = x12 x15 (x12 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x13 x16 (x12 x17 x18)) = x13 x16 (x12 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x7 x15 (x13 x16 (x10 x17 x18))) = x13 x16 (x10 x17 (x10 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x13 x16 (x13 x17 x18))) = x13 x16 (x13 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x10 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x13 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x10 x16 (x13 x17 x18))) = x10 x16 (x13 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x10 x17 (x13 x18 x19))) = x10 x17 (x13 x18 (x8 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)
Theorem 2641e.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x13 x14 (x10 x15 (x12 x16 x17)) = x10 x15 (x12 x16 (x13 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 x18)) = x12 x16 (x10 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x13 x16 (x10 x17 x18))) = x13 x16 (x10 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x7 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x9 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)