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PrGns../43c45.. 4.92 barsTMNir../38a48.. negprop ownership controlledby PrCx1.. upto 0TMLFo../d1136.. negprop ownership controlledby PrCx1.. upto 0TMQax../ae809.. negprop ownership controlledby PrCx1.. upto 0TMYyU../de2b7.. negprop ownership controlledby PrCx1.. upto 0TMMyG../b6fff.. negprop ownership controlledby PrCx1.. upto 0TMLzx../807d7.. negprop ownership controlledby PrCx1.. upto 0TMVES../20f9a.. negprop ownership controlledby PrCx1.. upto 0TMbPW../c6bf4.. negprop ownership controlledby PrCx1.. upto 0TMX7y../9abf3.. negprop ownership controlledby PrCx1.. upto 0TMRfd../2740b.. negprop ownership controlledby PrCx1.. upto 0TMXbS../3016b.. negprop ownership controlledby PrCx1.. upto 0TMUba../3f3f9.. negprop ownership controlledby PrCx1.. upto 0TMFFf../10583.. negprop ownership controlledby PrCx1.. upto 0TMKvc../b6446.. negprop ownership controlledby PrCx1.. upto 0TMXbt../40d70.. negprop ownership controlledby PrCx1.. upto 0TMcUE../5f159.. negprop ownership controlledby PrCx1.. upto 0TMW2t../58b0a.. negprop ownership controlledby PrCx1.. upto 0TMUi7../88a9e.. negprop ownership controlledby PrCx1.. upto 0TMMc7../e099c.. negprop ownership controlledby PrCx1.. upto 0TMayo../96831.. negprop ownership controlledby PrCx1.. upto 0TMZwT../351c7.. negprop ownership controlledby PrCx1.. upto 0TMJ2Q../058e1.. negprop ownership controlledby PrCx1.. upto 0TMMGi../1c7aa.. negprop ownership controlledby PrCx1.. upto 0TMJ5c../3f4eb.. negprop ownership controlledby PrCx1.. upto 0TMWvp../7bccf.. negprop ownership controlledby PrCx1.. upto 0TMcQa../f174b.. negprop ownership controlledby PrCx1.. upto 0TMYtU../6e6d5.. negprop ownership controlledby PrCx1.. upto 0TMPNn../c7f02.. negprop ownership controlledby PrCx1.. upto 0TMW2S../947ff.. negprop ownership controlledby PrCx1.. upto 0TMT6B../d3e57.. negprop ownership controlledby PrCx1.. upto 0TMdyL../8fa35.. negprop ownership controlledby PrCx1.. upto 0TMZJk../e60f0.. negprop ownership controlledby PrCx1.. upto 0TMXmu../9b324.. negprop ownership controlledby PrCx1.. upto 0TMRbQ../ccd57.. negprop ownership controlledby PrCx1.. upto 0TMHxj../be754.. negprop ownership controlledby PrCx1.. upto 0TMbdG../51273.. negprop ownership controlledby PrCx1.. upto 0TMUWc../0a409.. negprop ownership controlledby PrCx1.. upto 0TMSfX../d6410.. negprop ownership controlledby PrCx1.. upto 0TMTdm../bbd36.. negprop ownership controlledby PrCx1.. upto 0TMGam../b4f78.. negprop ownership controlledby PrCx1.. upto 0TMdBo../5bd71.. negprop ownership controlledby PrCx1.. upto 0TMchD../801a0.. negprop ownership controlledby PrCx1.. upto 0TMSRk../9e9bd.. negprop ownership controlledby PrCx1.. upto 0TMSFf../17f74.. negprop ownership controlledby PrCx1.. upto 0TMboD../fe526.. negprop ownership controlledby PrCx1.. upto 0TMbbG../f6a48.. negprop ownership controlledby PrCx1.. upto 0TMSVq../48f78.. negprop ownership controlledby PrCx1.. upto 0TMZAY../d40dc.. ownership of aa0b4.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMKxL../22838.. ownership of 0481c.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMb2o../1f659.. ownership of 8d26d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMWUC../b4ab6.. ownership of 49107.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMGfz../b7552.. ownership of 2d23f.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMcN5../dac57.. ownership of 94bca.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMdRX../45a85.. ownership of a40a2.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMG4Y../9e588.. ownership of b6045.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMWvW../b42b0.. ownership of 1bce1.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMdQX../79b68.. ownership of 9ac47.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMcK6../8e088.. ownership of 1fbce.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMJ9G../5e0af.. ownership of d03ed.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMPv7../b94e8.. ownership of 0e27f.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMPiA../6420f.. ownership of df4fd.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMddJ../f17da.. ownership of f1886.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMcZ1../c2e57.. ownership of aba4f.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMNap../4de52.. ownership of 92675.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMEnF../521c7.. ownership of fadb0.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMRpb../35186.. ownership of 96d15.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMZUT../32d70.. ownership of 6515b.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMTzm../10d5a.. ownership of 95ead.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMJKQ../c9600.. ownership of 823a1.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMFij../2997e.. ownership of 5f803.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMbCw../ce029.. ownership of 6c2f3.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMbpu../a6d9c.. ownership of 6292f.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMVbW../70bb9.. ownership of e95d5.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMVP8../f9b3b.. ownership of 03c49.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMaPd../dba19.. ownership of b4239.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMdcX../7193a.. ownership of ca0ea.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMT6j../af01d.. ownership of 2fce8.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMGPw../860f1.. ownership of 74c62.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMLWW../fa2f8.. ownership of a6fa4.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMMCY../b1011.. ownership of cf821.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMUu4../0700f.. ownership of afea9.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMdUa../e8a03.. ownership of 00e43.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMRKu../382ee.. ownership of a489b.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMKHE../e2aeb.. ownership of daf82.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMXae../b2991.. ownership of f7bc0.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMFRm../05520.. ownership of 6100b.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMc23../0ca4d.. ownership of 23a5d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMHjN../8a850.. ownership of c0e2a.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMV69../3cb04.. ownership of 24e5f.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMRQb../0f680.. ownership of d8753.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMXAJ../8fbba.. ownership of e8a7d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMU1z../8686c.. ownership of b1970.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMVB1../4dc1f.. ownership of 7d12e.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMMbe../49a17.. ownership of 08eb8.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMGmb../2ebcd.. ownership of 7d6e5.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMXZo../cb138.. ownership of a600c.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMT8N../7e476.. ownership of 885cd.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMEko../83e02.. ownership of 3851b.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMVv3../0f040.. ownership of f77bb.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMYcP../be282.. ownership of f3196.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMKVP../f9f50.. ownership of 5dc7c.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMbQ7../a06cb.. ownership of 0500c.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMbia../1317e.. ownership of 31c8f.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMZNs../3164a.. ownership of 47606.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMZV6../f1715.. ownership of b4f10.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMU2B../212ea.. ownership of b3a7a.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMauP../3185b.. ownership of 6cf9c.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMUJe../4c215.. ownership of 0e9d4.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMTpD../a7817.. ownership of 64635.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMM6p../cdcc2.. ownership of e3cac.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMVV7../78f36.. ownership of d169f.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMQFp../29873.. ownership of f96b0.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMF1o../18977.. ownership of 45f61.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMGgx../dd5b9.. ownership of a21a5.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMEvR../76c6f.. ownership of 8db14.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMajL../aeaa5.. ownership of ecb34.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMJae../e072c.. ownership of 3eb5b.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMZsK../5130b.. ownership of 6ffc4.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMcY1../df411.. ownership of 3a3be.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMWCx../dbeba.. ownership of 0eba1.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMZ6Q../1d441.. ownership of 5871e.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMRmo../e6b9e.. ownership of 733e1.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMPEa../dbbbe.. ownership of ffb30.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMJST../85fa3.. ownership of 8cb02.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMZNp../d123e.. ownership of acb5f.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMVA5../9e946.. ownership of 5ac76.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMRNY../eeca0.. ownership of c5c7c.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMXYf../bbb3b.. ownership of 36418.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMaoz../22cdc.. ownership of bb858.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMP5w../6fa45.. ownership of bde43.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMLiW../8fd5e.. ownership of 7d435.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMQ57../57f2b.. ownership of 86c6f.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMNH7../c23cd.. ownership of 0060e.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMNyq../b7083.. ownership of a5be8.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMcix../15027.. ownership of 32d89.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMSDN../8bc4f.. ownership of a2b06.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMMhS../f1b8e.. ownership of a5f7c.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMVX9../042fa.. ownership of b7e1c.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMNFu../e845d.. ownership of ad963.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMFYg../d6d2e.. ownership of 8e680.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMNuR../fb839.. ownership of 1144d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0PUSmR../a3806.. 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 x4Known 7c02f..andI : ∀ x0 x1 : ο . x0 ⟶ x1 ⟶ and x0 x1Known 22d81..and4I : ∀ x0 x1 x2 x3 : ο . x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ and (and (and x0 x1) x2) x3Known 9ae18..SingE : ∀ x0 x1 . In x1 (Sing x0) ⟶ x1 = x0Known 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 x1Known 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 x13Known 1bd08..and5I : ∀ x0 x1 x2 x3 x4 : ο . x0 ⟶ x1 ⟶ x2 ⟶ x3 ⟶ x4 ⟶ and (and (and (and x0 x1) x2) x3) x4Theorem 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 x13Known 8106d..notI : ∀ x0 : ο . (x0 ⟶ False) ⟶ not x0Known 2901c..EmptyE : ∀ x0 . In x0 0 ⟶ FalseTheorem 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 x13Theorem 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 . x0Theorem 8e680.. : (∀ 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 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x14 (x8 x15 x16 (x9 x14 x15 (x12 x16 (x13 x14 (x8 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 (x13 x17 x18)) = x7 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 ⟶ 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 ⟶ 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 ⟶ 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 ⟶ x12 x14 (x13 x15 (x7 x16 (x7 x17 x18))) = x7 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 ⟶ x13 x14 (x10 x15 (x7 x16 (x7 x17 x18))) = x7 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 ⟶ ∀ 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 (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 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x10 x16 (x8 x17 x18 (x12 x19 x20))) = x8 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 ⟶ x9 x14 x15 (x10 x16 (x9 x17 x18 (x13 x19 x20))) = x9 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 ⟶ ∀ 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 (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 (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 (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 (x10 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 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 (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 (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 (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 (x12 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem b7e1c.. : (∀ 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 (x7 x14 (x9 x15 x16 (x8 x14 x15 (x10 x16 (x7 x14 (x9 x15 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x10 x14 (x12 x15 (x9 x14 x15 (x10 x14 (x12 x15 (x9 x14 x15 (x10 x14 (x12 x15 (x9 x14 x15 (x10 x14 (x12 x15 (x9 x14 x15 (x10 x14 (x12 x15 x16)))))))))))))) = x16) ⟶ (∀ 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 (x7 x16 (x13 x17 x18)) = x7 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 ⟶ 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 ⟶ 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 ⟶ 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 (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 ⟶ 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 ⟶ 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 ⟶ 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 ⟶ ∀ 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 (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 ⟶ 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 (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 ⟶ 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 (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 (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 (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 ⟶ 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 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 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 (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 a2b06.. : (∀ 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 (x12 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x12 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x12 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 (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 ⟶ 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 (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 ⟶ 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 (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 ⟶ 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 ⟶ x7 x14 (x7 x15 (x7 x16 (x10 x17 x18))) = x7 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 (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 ⟶ ∀ 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 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x7 x18 x19))) = x10 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 (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 ⟶ 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 ⟶ ∀ 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 (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 (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 (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 ⟶ x8 x14 x15 (x13 x16 (x13 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 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 (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))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ 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 (x10 x20 x21)))) = x9 x18 x19 (x10 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 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem a5be8.. : (∀ 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 (x13 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x13 x16 (x8 x14 x15 (x7 x16 x17))))))) = x17) ⟶ (∀ 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 (x7 x16 (x13 x17 x18)) = x7 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 ⟶ 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 ⟶ 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 ⟶ x10 x14 (x7 x15 (x12 x16 (x7 x17 x18))) = x12 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 (x10 x15 (x10 x16 (x10 x17 x18))) = x10 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 ⟶ x10 x14 (x7 x15 (x12 x16 (x7 x17 x18))) = x12 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 ⟶ ∀ 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 ⟶ x9 x14 x15 (x13 x16 (x12 x17 (x10 x18 x19))) = x12 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 ⟶ 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 ⟶ x9 x14 x15 (x10 x16 (x8 x17 x18 (x12 x19 x20))) = x8 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 (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 (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 (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 (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 (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 ⟶ 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 (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 (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 (x12 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 86c6f.. : (∀ 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 (x12 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x12 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x13 x14 (x10 x15 (x9 x14 x15 (x13 x14 (x10 x15 (x9 x14 x15 (x13 x14 (x10 x15 (x9 x14 x15 (x13 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 (x12 x16 x17)) = x7 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 ⟶ 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 ⟶ 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 ⟶ x12 x14 (x10 x15 (x13 x16 (x10 x17 x18))) = x13 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 (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 (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 (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 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x12 x18 x19))) = x12 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 ⟶ 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 ⟶ 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 (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 ⟶ 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 (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 (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 ⟶ 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 (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 ⟶ 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 (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 (x10 x16 (x7 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 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 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem bde43.. : (∀ 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 (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 (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 ⟶ 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 (x12 x16 (x10 x17 x18))) = x12 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 (x12 x15 (x13 x16 (x7 x17 x18))) = x13 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 (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 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x10 x18 x19))) = x7 x17 (x10 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 (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 ⟶ ∀ 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 ⟶ x9 x14 x15 (x13 x16 (x8 x17 x18 (x13 x19 x20))) = x8 x17 x18 (x13 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 ⟶ 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 (x10 x16 (x13 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 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 (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 ⟶ 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 (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 ⟶ 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 (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 (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 ⟶ x8 x14 x15 (x13 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 36418.. : (∀ 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 (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 ⟶ x8 x14 x15 (x7 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x7 x16 (x8 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 (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 ⟶ 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 ⟶ 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 (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 ⟶ 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 ⟶ x10 x14 (x7 x15 (x10 x16 (x12 x17 x18))) = x10 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 (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 ⟶ ∀ 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 (x12 x17 (x10 x18 x19))) = x12 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 ⟶ 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 ⟶ 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 ⟶ 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 (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 (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 (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 (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 (x13 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 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 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 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 (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 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 5ac76.. : (∀ 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 ⟶ x13 x14 (x7 x15 (x13 x16 x17)) = x7 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 (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 (x10 x15 (x10 x16 (x10 x17 x18))) = x10 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 (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 (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 ⟶ 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 ⟶ x10 x14 (x7 x15 (x12 x16 (x7 x17 x18))) = x12 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 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x12 x17 (x7 x18 x19))) = x12 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 (x10 x16 (x10 x17 (x10 x18 x19))) = x10 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 ⟶ 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 ⟶ 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 ⟶ ∀ 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 (x12 x16 (x13 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 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 (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 ⟶ 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 ⟶ 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 ⟶ 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 (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 (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 ⟶ x8 x14 x15 (x13 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 8cb02.. : (∀ 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 ⟶ 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 (x13 x16 (x7 x17 x18)) = x13 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 (x13 x16 (x10 x17 x18))) = x13 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 ⟶ x7 x14 (x7 x15 (x10 x16 (x12 x17 x18))) = x10 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 ⟶ 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 ⟶ 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 ⟶ 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 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x13 x18 x19))) = x7 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 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 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 (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 (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 ⟶ x9 x14 x15 (x10 x16 (x13 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 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 ⟶ 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 (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 (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 (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 (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 ⟶ 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 (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 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 733e1.. : (∀ 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 ⟶ x8 x14 x15 (x10 x14 (x13 x15 (x8 x14 x15 (x10 x14 (x13 x15 (x8 x14 x15 (x10 x14 (x13 x15 (x8 x14 x15 (x10 x14 (x13 x15 (x8 x14 x15 (x10 x14 (x13 x15 x16)))))))))))))) = x16) ⟶ (∀ 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 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x10 x14 (x10 x15 (x7 x16 x17)) = x10 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 (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 ⟶ 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 (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 ⟶ 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 ⟶ 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 ⟶ 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 (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 ⟶ 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 ⟶ 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 ⟶ 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 (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 (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 (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 (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 (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 ⟶ 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 (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 (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 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 0eba1.. : (∀ 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 (x12 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x12 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x12 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x12 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 (x12 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x12 x16 x17))))))))))))))) = x17) ⟶ (∀ 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 (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 (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 (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 (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 (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 (x10 x15 (x13 x16 (x13 x17 x18))) = x13 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 ⟶ ∀ 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 ⟶ 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 (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 ⟶ 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 (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 (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 ⟶ 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 (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 (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 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 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 (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 (x7 x16 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 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 (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 6ffc4.. : (∀ 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 ⟶ 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 (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 ⟶ x10 x14 (x12 x15 (x10 x16 (x13 x17 x18))) = x10 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 ⟶ 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 ⟶ 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 ⟶ x7 x14 (x12 x15 (x13 x16 (x12 x17 x18))) = x13 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 (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 (x12 x16 (x12 x17 (x10 x18 x19))) = x12 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 ⟶ 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 (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 ⟶ 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 (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 (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 (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 (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 (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 (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))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ 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 (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 ecb34.. : (∀ 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 (x7 x15 (x8 x14 x15 (x10 x14 (x7 x15 (x8 x14 x15 (x10 x14 (x7 x15 (x8 x14 x15 (x10 x14 (x7 x15 (x8 x14 x15 (x10 x14 (x7 x15 x16)))))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x14 (x9 x15 x16 (x8 x14 x15 (x10 x16 (x10 x14 (x9 x15 x16 (x8 x14 x15 (x10 x16 (x10 x14 (x9 x15 x16 x17))))))))))) = x17) ⟶ (∀ 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 (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 (x12 x15 (x13 x16 (x12 x17 x18))) = x13 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 (x12 x16 (x12 x17 x18))) = x12 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 ⟶ 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 ⟶ 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 (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 ⟶ ∀ 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 ⟶ 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 (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 ⟶ ∀ 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 (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 (x13 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 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 (x10 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 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 (x10 x16 (x7 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 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 (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 (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 ⟶ 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 (x12 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem a21a5.. : (∀ 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 ⟶ x8 x14 x15 (x12 x14 (x10 x15 (x8 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 (x12 x15 (x7 x16 x17)) = x12 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 ⟶ 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 ⟶ x10 x14 (x13 x15 (x12 x16 (x12 x17 x18))) = x12 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 ⟶ x13 x14 (x10 x15 (x13 x16 (x7 x17 x18))) = x13 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 (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 ⟶ 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 (x13 x15 (x12 x16 (x12 x17 x18))) = x12 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 ⟶ ∀ 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 (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 ⟶ 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 ⟶ x9 x14 x15 (x7 x16 (x9 x17 x18 (x12 x19 x20))) = x9 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 ⟶ 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 (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 (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 (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 (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 (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 (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 ⟶ 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 f96b0.. : (∀ 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 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x13 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x13 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 (x10 x15 (x13 x16 x17)) = x10 x15 (x13 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 (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 ⟶ 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 ⟶ x13 x14 (x7 x15 (x10 x16 (x13 x17 x18))) = x10 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 ⟶ x10 x14 (x7 x15 (x13 x16 (x13 x17 x18))) = x13 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 ⟶ x10 x14 (x10 x15 (x7 x16 (x7 x17 x18))) = x7 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 ⟶ ∀ 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 (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 (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 (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 ⟶ 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 (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 ⟶ 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 (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 (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 (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 (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 (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 ⟶ 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))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem e3cac.. : (∀ 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 ⟶ x13 x14 (x12 x15 (x12 x16 x17)) = x12 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 (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 ⟶ 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 ⟶ 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 (x12 x16 (x12 x17 x18))) = x12 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 (x13 x15 (x13 x16 (x10 x17 x18))) = x13 x16 (x10 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 (x7 x15 (x13 x16 (x10 x17 x18))) = x13 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 (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 ⟶ 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 ⟶ 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 ⟶ x8 x14 x15 (x13 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 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 (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 (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 (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 ⟶ x8 x14 x15 (x13 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 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 (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 (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 (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 ⟶ 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 (x13 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 0e9d4.. : (∀ 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 (x10 x14 (x9 x15 x16 (x8 x14 x15 (x12 x16 (x10 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 (x7 x16 (x7 x14 (x8 x15 x16 (x8 x14 x15 (x7 x16 (x7 x14 (x8 x15 x16 (x8 x14 x15 (x7 x16 (x7 x14 (x8 x15 x16 (x8 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 ⟶ 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 (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 ⟶ x7 x14 (x13 x15 (x12 x16 (x12 x17 x18))) = x12 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 (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 (x7 x15 (x10 x16 (x12 x17 x18))) = x10 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 ⟶ 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 (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 ⟶ ∀ 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 ⟶ 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 (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 (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 (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 ⟶ 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))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ 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 (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 (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 ⟶ 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 (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 (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 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem b3a7a.. : (∀ 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 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x13 x16 (x12 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 (x12 x16 (x13 x14 (x9 x15 x16 (x8 x14 x15 (x12 x16 (x13 x14 (x9 x15 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x13 x14 (x7 x15 (x7 x16 x17)) = x7 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 ⟶ 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 (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 ⟶ x10 x14 (x12 x15 (x13 x16 (x7 x17 x18))) = x13 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 (x13 x15 (x7 x16 (x13 x17 x18))) = x7 x16 (x13 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 (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 (x12 x16 (x10 x17 (x7 x18 x19))) = x10 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 (x10 x16 (x7 x17 (x7 x18 x19))) = x7 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 (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 (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 (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 (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 (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 (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 (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 (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 (x10 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 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 (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 ⟶ 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))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 47606.. : (∀ 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 (x7 x14 (x9 x15 x16 (x8 x14 x15 (x10 x16 (x7 x14 (x9 x15 x16 (x8 x14 x15 (x10 x16 (x7 x14 (x9 x15 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 (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 (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 (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 ⟶ x7 x14 (x13 x15 (x7 x16 (x12 x17 x18))) = x7 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 ⟶ 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 (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 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x12 x18 x19))) = x12 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 (x12 x17 (x7 x18 x19))) = x12 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 (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 (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 ⟶ 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 (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 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 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 (x13 x16 (x10 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 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 (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 ⟶ 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 (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 (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 (x7 x16 (x13 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 0500c.. : (∀ 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 (x7 x14 (x9 x15 x16 (x8 x14 x15 (x12 x16 (x7 x14 (x9 x15 x16 (x8 x14 x15 (x12 x16 (x7 x14 (x9 x15 x16 (x8 x14 x15 (x12 x16 (x7 x14 (x9 x15 x16 (x8 x14 x15 (x12 x16 (x7 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 (x10 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x10 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 ⟶ 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 (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 ⟶ 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 ⟶ 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 (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 (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 (x7 x16 (x7 x17 (x10 x18 x19))) = x7 x17 (x10 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 (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 (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 (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 ⟶ 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 ⟶ 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 (x12 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 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 (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 ⟶ x9 x14 x15 (x10 x16 (x13 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 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 (x7 x20 x21)))) = x9 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 (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 (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 ⟶ 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))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem f3196.. : (∀ 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 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x7 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 (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 (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 (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 ⟶ 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 (x12 x15 (x12 x16 (x7 x17 x18))) = x12 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 ⟶ 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 ⟶ x12 x14 (x12 x15 (x12 x16 (x10 x17 x18))) = x12 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 ⟶ ∀ 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 (x10 x16 (x10 x17 (x12 x18 x19))) = x10 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 ⟶ ∀ 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 ⟶ 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 (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 (x10 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 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 (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 ⟶ 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 (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 (x13 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 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 (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 ⟶ 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 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 3851b.. : (∀ 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 ⟶ 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 ⟶ 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 ⟶ 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 ⟶ x10 x14 (x13 x15 (x7 x16 (x12 x17 x18))) = x7 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 (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 (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 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x12 x18 x19))) = x10 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 (x10 x17 (x10 x18 x19))) = x10 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 ⟶ ∀ 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 (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 ⟶ ∀ 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 ⟶ 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 ⟶ 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 (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 (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 (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 (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 ⟶ 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 (x7 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem a600c.. : (∀ 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 (x13 x16 x17)) = x7 x15 (x13 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 (x7 x16 (x12 x17 x18)) = x7 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 (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 ⟶ 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 ⟶ x7 x14 (x13 x15 (x10 x16 (x7 x17 x18))) = x10 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 ⟶ 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 (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 ⟶ ∀ 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 (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 (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 (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 ⟶ 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 (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 (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 (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 (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 (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 (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 (x13 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 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 ⟶ x9 x14 x15 (x13 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 08eb8.. : (∀ 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 ⟶ x8 x14 x15 (x10 x14 (x7 x15 (x8 x14 x15 (x10 x14 (x7 x15 x16))))) = x16) ⟶ (∀ 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 x16))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x12 x15 (x13 x16 x17)) = x12 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 ⟶ 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 ⟶ 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 ⟶ 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 ⟶ x13 x14 (x13 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 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 (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 ⟶ ∀ 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 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x13 x18 x19))) = x10 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 ⟶ ∀ 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 (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 ⟶ ∀ 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 (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 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 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 (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 (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 (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 (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 (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 (x7 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem b1970.. : (∀ 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 (x13 x16 (x12 x14 (x8 x15 x16 (x8 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 (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 (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 ⟶ 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 ⟶ 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 (x7 x17 x18))) = x12 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 ⟶ 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 (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 ⟶ x10 x14 (x13 x15 (x12 x16 (x12 x17 x18))) = x12 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 ⟶ ∀ 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 ⟶ 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 (x12 x16 (x8 x17 x18 (x13 x19 x20))) = x8 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 ⟶ 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 (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 (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 ⟶ 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 (x13 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 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 (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 (x9 x18 x19 (x7 x20 x21)))) = x9 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 ⟶ 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 (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 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem d8753.. : (∀ 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 (x12 x15 (x13 x16 x17)) = x12 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 ⟶ 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 ⟶ 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 (x13 x15 (x10 x16 (x13 x17 x18))) = x10 x16 (x13 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 (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 ⟶ 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 ⟶ 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 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x10 x18 x19))) = x7 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 ⟶ 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 ⟶ 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 ⟶ ∀ 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 (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 (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 (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 (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 ⟶ 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 (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 (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 (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 c0e2a.. : (∀ 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 (x12 x14 (x7 x15 (x8 x14 x15 (x12 x14 (x7 x15 (x8 x14 x15 (x12 x14 (x7 x15 (x8 x14 x15 (x12 x14 (x7 x15 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x10 x14 (x12 x15 (x9 x14 x15 (x10 x14 (x12 x15 (x9 x14 x15 (x10 x14 (x12 x15 x16)))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x12 x15 (x7 x16 x17)) = x12 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 ⟶ 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 ⟶ x7 x14 (x13 x15 (x12 x16 (x12 x17 x18))) = x12 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 ⟶ x10 x14 (x12 x15 (x13 x16 (x13 x17 x18))) = x13 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 ⟶ x7 x14 (x13 x15 (x10 x16 (x7 x17 x18))) = x10 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 (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 ⟶ x10 x14 (x7 x15 (x12 x16 (x10 x17 x18))) = x12 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 (x7 x16 (x12 x17 (x7 x18 x19))) = x12 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 (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 ⟶ ∀ 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 (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 ⟶ ∀ 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 (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 (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 (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 ⟶ 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))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ 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 (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 ⟶ 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 ⟶ 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))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 6100b.. : (∀ 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 (x12 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x12 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x12 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x12 x16 x17))))))))))))))) = x17) ⟶ (∀ 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 x16)))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x10 x15 (x13 x16 x17)) = x10 x15 (x13 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 ⟶ 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 ⟶ 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 ⟶ x10 x14 (x10 x15 (x7 x16 (x13 x17 x18))) = x7 x16 (x13 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 (x13 x15 (x10 x16 (x10 x17 x18))) = x10 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 ⟶ 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 ⟶ ∀ 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 ⟶ 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 (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 (x13 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 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 (x13 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 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 ⟶ 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 (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 (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 (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 (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 ⟶ 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 ⟶ 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 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem daf82.. : (∀ 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 ⟶ 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 (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 ⟶ 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 ⟶ x12 x14 (x10 x15 (x13 x16 x17)) = x10 x15 (x13 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 (x13 x17 x18)) = x7 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 ⟶ 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 ⟶ x7 x14 (x7 x15 (x7 x16 (x13 x17 x18))) = x7 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 (x10 x17 x18))) = x10 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 ⟶ 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 (x10 x16 (x10 x17 (x13 x18 x19))) = x10 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 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x12 x18 x19))) = x7 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 (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 ⟶ 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 ⟶ ∀ 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 ⟶ 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 (x7 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 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 (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 (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 ⟶ 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 (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 (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 (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 00e43.. : (∀ 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 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x12 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x12 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x12 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x12 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 (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 ⟶ x9 x14 x15 (x10 x16 (x7 x17 x18)) = x10 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 (x13 x15 (x7 x16 (x10 x17 x18))) = x7 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 ⟶ 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 ⟶ 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 ⟶ 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 (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 (x13 x17 (x10 x18 x19))) = x13 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 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x13 x18 x19))) = x10 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 ⟶ ∀ 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 (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 (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 (x13 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 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 (x10 x16 (x10 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 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 (x7 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 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 (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 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 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 (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 (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 (x12 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem cf821.. : (∀ 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 (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 (x8 x14 x15 (x12 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x10 x16 (x13 x14 (x9 x15 x16 (x9 x14 x15 (x10 x16 (x13 x14 (x9 x15 x16 (x9 x14 x15 (x10 x16 (x13 x14 (x9 x15 x16 (x9 x14 x15 (x10 x16 (x13 x14 (x9 x15 x16 x17))))))))))))))) = x17) ⟶ (∀ 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 ⟶ 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 ⟶ 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 (x13 x15 (x12 x16 (x12 x17 x18))) = x12 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 (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 (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 ⟶ 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 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x10 x18 x19))) = x10 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 (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 (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 (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 (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 (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 (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 ⟶ x9 x14 x15 (x13 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 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 ⟶ 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 (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 (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 (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 ⟶ 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))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 74c62.. : (∀ 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 (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 ⟶ x9 x14 x15 (x13 x16 (x9 x14 x15 (x13 x16 (x9 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 ⟶ 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 (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 (x13 x15 (x13 x16 (x7 x17 x18))) = x13 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 ⟶ 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 ⟶ 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 ⟶ 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 ⟶ x10 x14 (x7 x15 (x12 x16 (x10 x17 x18))) = x12 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 (x13 x16 (x12 x17 (x10 x18 x19))) = x12 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 (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 (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 ⟶ x8 x14 x15 (x13 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 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 (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 (x13 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 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 (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 (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 (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 (x13 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 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 ⟶ 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 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 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 ⟶ 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))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem ca0ea.. : (∀ 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 (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 ⟶ 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 ⟶ 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 ⟶ 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 ⟶ 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 ⟶ x10 x14 (x7 x15 (x13 x16 (x12 x17 x18))) = x13 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 (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 ⟶ x12 x14 (x10 x15 (x10 x16 (x10 x17 x18))) = x10 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 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x10 x18 x19))) = x7 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 ⟶ 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 ⟶ ∀ 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 ⟶ 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 (x12 x16 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 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 (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 (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 ⟶ 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 (x13 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 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 ⟶ 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 (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 (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 (x12 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 03c49.. : (∀ 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 (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 (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 ⟶ x12 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 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 (x10 x17 x18))) = x7 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 (x10 x15 (x7 x16 (x7 x17 x18))) = x7 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 (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 (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 ⟶ ∀ 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 (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 ⟶ ∀ 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 (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 (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 (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 (x7 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 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 ⟶ 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 (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 (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 (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 (x13 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 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 (x12 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 6292f.. : (∀ 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 (x8 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x8 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x8 x15 x16 (x9 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 ⟶ 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 ⟶ x9 x14 x15 (x7 x16 (x12 x17 x18)) = x7 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 (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 (x12 x15 (x12 x16 (x10 x17 x18))) = x12 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 ⟶ 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 (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 ⟶ 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 (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 ⟶ x8 x14 x15 (x7 x16 (x9 x17 x18 (x13 x19 x20))) = x9 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 (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 ⟶ 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 (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 (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 (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 (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 (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 (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 (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 (x12 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 5f803.. : (∀ 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 (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 (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 (x13 x15 (x7 x16 x17)) = x13 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 (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 ⟶ 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 ⟶ 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 (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 (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 (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 ⟶ ∀ 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 (x12 x16 (x10 x17 (x7 x18 x19))) = x10 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 (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 ⟶ 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 (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 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 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 ⟶ 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 ⟶ 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 (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 (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 (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 (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 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 95ead.. : (∀ 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 (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 ⟶ 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 ⟶ 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 ⟶ x10 x14 (x10 x15 (x12 x16 (x10 x17 x18))) = x12 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 ⟶ 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 (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 ⟶ ∀ 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 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x10 x18 x19))) = x10 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 (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 (x7 x16 (x9 x17 x18 (x12 x19 x20))) = x9 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 ⟶ 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 (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 (x13 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 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 (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 (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 (x10 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 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 (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 (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 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 96d15.. : (∀ 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 (x7 x14 (x8 x15 x16 (x8 x14 x15 (x10 x16 (x7 x14 (x8 x15 x16 (x8 x14 x15 (x10 x16 (x7 x14 (x8 x15 x16 (x8 x14 x15 (x10 x16 (x7 x14 (x8 x15 x16 (x8 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 ⟶ 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 ⟶ x10 x14 (x13 x15 (x10 x16 x17)) = x13 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 ⟶ 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 (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 ⟶ 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 (x7 x15 (x13 x16 (x10 x17 x18))) = x13 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 (x13 x15 (x7 x16 (x13 x17 x18))) = x7 x16 (x13 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 (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 ⟶ 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 (x13 x16 (x13 x17 (x12 x18 x19))) = x13 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 (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 ⟶ 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 (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 ⟶ 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))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ 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 (x12 x20 x21)))) = x9 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 ⟶ 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 (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 (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 ⟶ 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 (x12 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 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 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 92675.. : (∀ 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 (x7 x15 (x9 x14 x15 (x12 x14 (x7 x15 (x9 x14 x15 (x12 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 ⟶ 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 ⟶ 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 ⟶ 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 ⟶ x12 x14 (x12 x15 (x13 x16 (x13 x17 x18))) = x13 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 (x13 x15 (x7 x16 (x10 x17 x18))) = x7 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 (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 ⟶ ∀ 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 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x7 x18 x19))) = x10 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 (x13 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 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 (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 ⟶ 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))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ 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 (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 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 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 (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 ⟶ x9 x14 x15 (x13 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 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 (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 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 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 ⟶ 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))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem f1886.. : (∀ 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 ⟶ 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 ⟶ 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 ⟶ 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 (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 (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 (x7 x16 (x7 x17 x18))) = x7 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 (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 (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 ⟶ x7 x14 (x10 x15 (x10 x16 (x10 x17 x18))) = x10 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 (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 (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 ⟶ 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 (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 (x7 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 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 (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 (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 (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 (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 (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 (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 (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 (x13 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 0e27f.. : (∀ 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 (x7 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x7 x16 x17))))))))))))))) = x17) ⟶ (∀ 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 (x7 x16 (x13 x17 x18)) = x7 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 ⟶ 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 ⟶ 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 (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 (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 ⟶ x7 x14 (x10 x15 (x10 x16 (x13 x17 x18))) = x10 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 ⟶ ∀ 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 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x7 x18 x19))) = x12 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 (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 (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 (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 (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 (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 ⟶ 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 (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 (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 ⟶ 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 (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 (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 1fbce.. : (∀ 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 (x13 x14 (x12 x15 (x9 x14 x15 (x13 x14 (x12 x15 (x9 x14 x15 (x13 x14 (x12 x15 (x9 x14 x15 (x13 x14 (x12 x15 (x9 x14 x15 (x13 x14 (x12 x15 x16)))))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x10 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x10 x16 (x9 x14 x15 (x12 x16 x17))))))) = x17) ⟶ (∀ 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 ⟶ 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 (x10 x15 (x10 x16 (x10 x17 x18))) = x10 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 (x7 x15 (x10 x16 (x13 x17 x18))) = x10 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 ⟶ x12 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 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 (x13 x15 (x13 x16 (x12 x17 x18))) = x13 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 (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 (x13 x16 (x7 x17 (x12 x18 x19))) = x7 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 ⟶ 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 ⟶ ∀ 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 (x8 x17 x18 (x12 x19 x20))) = x8 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 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 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 ⟶ 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 ⟶ 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 ⟶ 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 (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 (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 (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 (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 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 1bce1.. : (∀ 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 ⟶ x10 x14 (x10 x15 (x10 x16 x17)) = x10 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 (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 ⟶ x12 x14 (x7 x15 (x7 x16 (x7 x17 x18))) = x7 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 (x10 x15 (x13 x16 (x7 x17 x18))) = x13 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 (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 ⟶ 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 (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 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x13 x17 (x12 x18 x19))) = x13 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 ⟶ 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 ⟶ ∀ 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 (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 ⟶ ∀ 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 (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 (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 (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 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 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 (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 (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 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 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 ⟶ 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))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem a40a2.. : (∀ 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 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x14 (x8 x15 x16 (x9 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 ⟶ x12 x14 (x10 x15 (x10 x16 x17)) = x10 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 (x13 x16 (x13 x17 x18)) = x13 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 ⟶ 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 (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 (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 ⟶ 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 ⟶ x10 x14 (x10 x15 (x10 x16 (x13 x17 x18))) = x10 x16 (x13 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 ⟶ 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 (x12 x16 (x10 x17 (x13 x18 x19))) = x10 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 ⟶ 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 (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 ⟶ ∀ 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 (x13 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 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 (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 (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 (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 (x13 x16 (x7 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 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 (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 (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 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 2d23f.. : (∀ 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 ⟶ x8 x14 x15 (x13 x14 (x7 x15 (x8 x14 x15 (x13 x14 (x7 x15 (x8 x14 x15 (x13 x14 (x7 x15 (x8 x14 x15 (x13 x14 (x7 x15 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 (x7 x14 (x13 x15 (x8 x14 x15 (x7 x14 (x13 x15 (x8 x14 x15 (x7 x14 (x13 x15 (x8 x14 x15 (x7 x14 (x13 x15 x16))))))))))) = x16) ⟶ (∀ 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 ⟶ 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 ⟶ x10 x14 (x10 x15 (x13 x16 (x7 x17 x18))) = x13 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 (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 (x12 x15 (x12 x16 (x7 x17 x18))) = x12 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 ⟶ 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 (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 (x12 x16 (x12 x17 (x12 x18 x19))) = x12 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 ⟶ 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 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x10 x16 (x9 x17 x18 (x13 x19 x20))) = x9 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 ⟶ x8 x14 x15 (x13 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 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 (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 (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 ⟶ 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 ⟶ 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 (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 (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 (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 ⟶ 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 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 8d26d.. : (∀ 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 (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 (x7 x16 (x13 x17 x18)) = x7 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 ⟶ x12 x14 (x12 x15 (x12 x16 (x10 x17 x18))) = x12 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 (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 (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 ⟶ 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 ⟶ 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 ⟶ 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 ⟶ 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 (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 ⟶ x9 x14 x15 (x7 x16 (x8 x17 x18 (x7 x19 x20))) = x8 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 ⟶ x9 x14 x15 (x10 x16 (x13 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 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 ⟶ 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 ⟶ 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 (x7 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 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 (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 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 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 ⟶ 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 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem aa0b4.. : (∀ 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 ⟶ 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 (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 (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 (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 ⟶ x12 x14 (x12 x15 (x12 x16 (x10 x17 x18))) = x12 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 (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 (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 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x10 x18 x19))) = x12 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 ⟶ 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 ⟶ ∀ 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 (x10 x16 (x8 x17 x18 (x12 x19 x20))) = x8 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 (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 (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 (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 ⟶ 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 ⟶ 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 (x8 x18 x19 (x7 x20 x21)))) = x8 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 (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 (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 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof) |
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