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PrPyv../8c560.. 24.97 barsTMKvT../d20e9.. negprop ownership controlledby PrCx1.. upto 0TMSe8../6435b.. negprop ownership controlledby PrCx1.. upto 0TMXoX../8710f.. negprop ownership controlledby PrCx1.. upto 0TMJjK../20a46.. negprop ownership controlledby PrCx1.. upto 0TMHgH../87ab7.. negprop ownership controlledby PrCx1.. upto 0TMLpp../d9aa5.. negprop ownership controlledby PrCx1.. upto 0TMFYv../523d3.. negprop ownership controlledby PrCx1.. upto 0TMWnS../8e887.. negprop ownership controlledby PrCx1.. upto 0TMViZ../e8fcb.. negprop ownership controlledby PrCx1.. upto 0TMUJU../d9f3f.. negprop ownership controlledby PrCx1.. upto 0TMVjT../6c9a7.. negprop ownership controlledby PrCx1.. upto 0TMXgq../c365c.. negprop ownership controlledby PrCx1.. upto 0TMHNS../99a8e.. negprop ownership controlledby PrCx1.. upto 0TMShs../c0ca8.. negprop ownership controlledby PrCx1.. upto 0TMZs9../ecc94.. negprop ownership controlledby PrCx1.. upto 0TMKUJ../023d4.. negprop ownership controlledby PrCx1.. upto 0TMFRk../30335.. negprop ownership controlledby PrCx1.. upto 0TMNQM../ef6c2.. negprop ownership controlledby PrCx1.. upto 0TMdW5../ce1bb.. negprop ownership controlledby PrCx1.. upto 0TMRzN../8b720.. negprop ownership controlledby PrCx1.. upto 0TMdJ4../dcc26.. negprop ownership controlledby PrCx1.. upto 0TMXG6../5dfc9.. negprop ownership controlledby PrCx1.. upto 0TMd7j../d8491.. negprop ownership controlledby PrCx1.. upto 0TMVH3../15d61.. negprop ownership controlledby PrCx1.. upto 0TMXod../1b223.. negprop ownership controlledby PrCx1.. upto 0TMNcM../58b92.. negprop ownership controlledby PrCx1.. upto 0TMchp../4231e.. negprop ownership controlledby PrCx1.. upto 0TMQh1../3e0a6.. negprop ownership controlledby PrCx1.. upto 0TMWDr../0122a.. negprop ownership controlledby PrCx1.. upto 0TMGUD../441bb.. negprop ownership controlledby PrCx1.. upto 0TMXpY../c6118.. negprop ownership controlledby PrCx1.. upto 0TMQL8../ab7b6.. negprop ownership controlledby PrCx1.. upto 0TML7k../06755.. negprop ownership controlledby PrCx1.. upto 0TMbUv../65e9c.. negprop ownership controlledby PrCx1.. upto 0TMHKT../8295f.. negprop ownership controlledby PrCx1.. upto 0TMGRp../30858.. negprop ownership controlledby PrCx1.. upto 0TMZiL../0a18f.. negprop ownership controlledby PrCx1.. upto 0TMLYj../503fd.. negprop ownership controlledby PrCx1.. upto 0TMJCC../8e756.. negprop ownership controlledby PrCx1.. upto 0TMNdr../4eaff.. negprop ownership controlledby PrCx1.. upto 0TMUtX../b9fac.. negprop ownership controlledby PrCx1.. upto 0TMZEH../90f05.. negprop ownership controlledby PrCx1.. upto 0TMQte../62415.. negprop ownership controlledby PrCx1.. upto 0TMUr9../a04a5.. negprop ownership controlledby PrCx1.. upto 0TMKBw../53c04.. negprop ownership controlledby PrCx1.. upto 0TMSZ2../c098f.. negprop ownership controlledby PrCx1.. upto 0TMbwQ../facf9.. negprop ownership controlledby PrCx1.. upto 0TMNDf../68db2.. ownership of 02e64.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMNrL../b899e.. ownership of fbf53.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMXo3../6fe2d.. ownership of 695d7.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMch8../5724a.. ownership of fe950.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMVJs../90aae.. ownership of 850cf.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMTHS../16207.. ownership of d27c3.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMMAC../27a2e.. ownership of 7c049.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMNP2../0ba77.. ownership of e3adf.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMYKJ../40099.. ownership of 4c0df.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMLLE../62974.. ownership of 298f3.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMRUU../91d0b.. ownership of b7862.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMcvo../06567.. ownership of c7fe8.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMXan../0197f.. ownership of b6e10.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMKXF../625f5.. ownership of ddd50.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMPgi../88dfe.. ownership of 9c627.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMTZ2../53148.. ownership of e836d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMRxM../a2815.. ownership of 09cc2.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMRdE../c282d.. ownership of 72a6e.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMSHv../44262.. ownership of bf8e8.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMZ8K../dd7a5.. ownership of b4882.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMYT9../dbfbf.. ownership of a6dd3.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMV8v../c8370.. ownership of f337b.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMW1U../821fa.. ownership of 40de5.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMUNQ../9222f.. ownership of bf68d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMHcJ../868c9.. ownership of 9a1bf.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMFNj../c3145.. ownership of 9682d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMLDh../557ab.. ownership of 03fc5.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMKKF../40c31.. ownership of 6713a.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMJGf../5291d.. ownership of 3e19a.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMces../cfd05.. ownership of c14b0.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMHSX../ad132.. ownership of b37f1.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMFdp../e43ea.. ownership of 84976.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMbB2../ca723.. ownership of 5a6ae.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMFLu../787bf.. ownership of 394f4.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMR92../c12a9.. ownership of 9038d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMU25../36956.. ownership of 12202.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMcg9../bd6c5.. ownership of db85e.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMZcA../b5bd7.. ownership of 7d87d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMUVX../f4654.. ownership of 716ff.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMRyD../63b2a.. ownership of 87a64.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMYK4../2f4d2.. ownership of 7585d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMVWH../818f6.. ownership of 1bbd9.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMQ7Z../84682.. ownership of 57314.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMJLC../d6e84.. ownership of aec11.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMWeL../a3f32.. ownership of 36a63.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMaN9../be324.. ownership of 246c5.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMYai../2ec17.. ownership of 6f748.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMa3K../05376.. ownership of 9fbcb.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMLN9../4e928.. ownership of 71c25.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMYvj../2662a.. ownership of 2e6af.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMF4L../19d1c.. ownership of 82f4b.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMPs4../983ec.. ownership of ce55d.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMMtB../d57fb.. ownership of 4e482.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMVg3../cf355.. ownership of b5784.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMGPy../e45ea.. ownership of 4fa0a.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMWkL../1adab.. ownership of 6713a.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMKdz../44c03.. ownership of 4d769.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMQQg../312b9.. ownership of 45e60.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMcv9../faa3f.. ownership of cdf7b.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMSWs../6f79f.. ownership of 692ef.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMRtt../b0ce0.. ownership of f28c4.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMa3q../dc5a7.. ownership of 00b6e.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMTgh../e20a8.. ownership of 6464f.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMXem../88f35.. ownership of f2b30.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMK7E../ca121.. ownership of 830aa.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMLZb../7778d.. ownership of 50eaa.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMFBu../612f1.. ownership of a8630.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMVo8../2133e.. ownership of a3c63.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMTLp../a1890.. ownership of e1d01.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMT4v../bcbda.. ownership of 30ac0.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMavb../d0443.. ownership of a454e.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMamH../5f65f.. ownership of 9cb9a.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMFMf../f9417.. ownership of ccfbe.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMavN../85f7d.. ownership of 8dba4.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMWdT../da363.. ownership of 8db65.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMGpq../e1aff.. ownership of b4dac.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMTTs../af40b.. ownership of b3c5c.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMdLt../6bd99.. ownership of 09bc1.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMbsp../4d64f.. ownership of 77a24.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMM8M../856db.. ownership of de524.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMR5W../ba200.. ownership of 73bca.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMcx9../c8026.. ownership of 8be80.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMXZX../0ad29.. ownership of 13105.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMRfM../d08d0.. ownership of 44897.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMMH7../41ff7.. ownership of ed741.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMGyq../5e68e.. ownership of 05349.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMRVh../f6a9e.. ownership of 9e519.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMMUY../d352d.. ownership of 2b079.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMWWs../ffbfa.. ownership of 01b15.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMXez../bd309.. ownership of 9d16e.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMF1y../6e975.. ownership of bfdc7.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMXCN../42951.. ownership of b2c06.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMLTC../ad8a1.. ownership of b6ecd.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0TMLJ9../23509.. ownership of 54fe1.. as prop with payaddr PrCx1.. rights free controlledby PrCx1.. upto 0PUgX9../6e628.. 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 b6ecd.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x14 (x9 x15 x16 (x8 x14 x15 (x10 x16 (x12 x14 (x9 x15 x16 (x8 x14 x15 (x10 x16 (x12 x14 (x9 x15 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ 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 ⟶ x10 x14 (x12 x15 (x12 x16 x17)) = x12 x15 (x12 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (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 (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 (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 ⟶ x10 x14 (x12 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x13 x15 (x12 x16 (x13 x17 x18))) = x12 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 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x10 x17 (x7 x18 x19))) = x10 x17 (x7 x18 (x8 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ 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 ⟶ 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 (x12 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 (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 (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 ⟶ 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 (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 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem bfdc7.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 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 x16)))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x12 x15 (x10 x16 x17)) = x12 x15 (x10 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x17 x18)) = x13 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 (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 ⟶ 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 (x10 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (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 (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 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x7 x18 x19))) = x10 x17 (x7 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ 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 (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 ⟶ 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 (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 ⟶ 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 (x10 x16 (x7 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (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 (x7 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 (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 01b15.. : (∀ 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 ⟶ 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 ⟶ 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 (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 ⟶ x10 x14 (x12 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (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 (x12 x16 (x12 x17 (x7 x18 x19))) = x12 x17 (x7 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x13 x18 x19))) = x12 x17 (x13 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x8 x17 x18 (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 (x12 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 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 (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 (x10 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 (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 ⟶ 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 (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 (x10 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 9e519.. : (∀ 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 x16)))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x10 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x10 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x10 x16 (x12 x14 (x9 x15 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x10 x14 (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 (x10 x17 x18)) = x7 x16 (x10 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x12 x16 (x13 x17 x18))) = x12 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 (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 ⟶ 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 ⟶ x12 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x13 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x7 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x13 x18 x19))) = x7 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 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x10 x18 x19))) = x13 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 (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 (x13 x16 (x9 x17 x18 (x13 x19 x20))) = x9 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 (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 (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 (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 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (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 (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 (x7 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem ed741.. : (∀ 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 (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 ⟶ 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 ⟶ 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 ⟶ 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 (x13 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x10 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ 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 (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 ⟶ x7 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (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 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x7 x18 x19))) = x13 x17 (x7 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (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 ⟶ 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 (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 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (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 (x12 x16 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 ⟶ x8 x14 x15 (x13 x16 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 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 (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 (x7 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 13105.. : (∀ 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 (x7 x15 (x10 x16 x17)) = x7 x15 (x10 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 x18)) = x12 x16 (x13 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x10 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x13 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (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 (x10 x15 (x13 x16 (x13 x17 x18))) = x13 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 ⟶ 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 ⟶ 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 ⟶ 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 ⟶ x8 x14 x15 (x7 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 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 (x9 x18 x19 (x13 x20 x21)))) = x9 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 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (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 (x13 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (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 (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 (x10 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 73bca.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x13 x16 (x8 x14 x15 (x13 x16 (x9 x14 x15 (x13 x16 (x8 x14 x15 (x13 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 (x13 x17 x18)) = x12 x16 (x13 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x7 x15 (x7 x16 (x13 x17 x18))) = x7 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 (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 (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 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x10 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (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 ⟶ 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 (x12 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x10 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x9 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 (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 (x10 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (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 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 (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 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 77a24.. : (∀ 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 (x10 x15 (x8 x14 x15 (x10 x14 (x10 x15 (x8 x14 x15 (x10 x14 (x10 x15 x16)))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ 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 (x12 x16 (x13 x17 x18)) = x12 x16 (x13 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x10 x15 (x7 x16 (x13 x17 x18))) = x7 x16 (x13 x17 (x13 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (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 (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 ⟶ 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 ⟶ x13 x14 (x12 x15 (x13 x16 (x12 x17 x18))) = x13 x16 (x12 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x10 x17 (x10 x18 x19))) = x10 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 ⟶ 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 (x12 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (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 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 (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 (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 (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 (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 (x7 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (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 (x10 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem b3c5c.. : (∀ 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 (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 ⟶ x8 x14 x15 (x12 x14 (x10 x15 (x8 x14 x15 (x12 x14 (x10 x15 (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 ⟶ x12 x14 (x10 x15 (x7 x16 x17)) = x10 x15 (x7 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (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 (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 (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 (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 (x10 x15 (x13 x16 (x7 x17 x18))) = x13 x16 (x7 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ 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 ⟶ ∀ 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 (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 ⟶ x8 x14 x15 (x7 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 (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 (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 (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 (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 (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 (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 (x7 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 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))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 8db65.. : (∀ 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 (x10 x14 (x8 x15 x16 (x8 x14 x15 (x13 x16 (x10 x14 (x8 x15 x16 (x8 x14 x15 (x13 x16 (x10 x14 (x8 x15 x16 (x8 x14 x15 (x13 x16 (x10 x14 (x8 x15 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x12 x14 (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 ⟶ x13 x14 (x10 x15 (x7 x16 x17)) = x10 x15 (x7 x16 (x13 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 x18)) = x7 x16 (x10 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x12 x15 (x7 x16 (x7 x17 x18))) = x7 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 ⟶ x7 x14 (x12 x15 (x10 x16 (x13 x17 x18))) = x10 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 ⟶ x12 x14 (x7 x15 (x13 x16 (x7 x17 x18))) = x13 x16 (x7 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (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 (x10 x16 (x9 x17 x18 (x13 x19 x20))) = x9 x17 x18 (x13 x19 (x8 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (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 (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 (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 (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 (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 ⟶ 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 (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 (x10 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem ccfbe.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x14 x15 (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 ⟶ x9 x14 x15 (x12 x14 (x7 x15 (x9 x14 x15 (x12 x14 (x7 x15 (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 ⟶ 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 (x7 x16 (x7 x17 x18)) = x7 x16 (x7 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (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 ⟶ 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 ⟶ x12 x14 (x12 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (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 ⟶ 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 (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 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x10 x18 x19))) = x7 x17 (x10 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ 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 ⟶ 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 ⟶ ∀ 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 (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 (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 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem a454e.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x7 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x12 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x7 x16 (x13 x14 (x9 x15 x16 (x8 x14 x15 (x7 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 (x13 x15 (x10 x16 x17)) = x13 x15 (x10 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 x18)) = x12 x16 (x13 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x10 x15 (x13 x16 (x12 x17 x18))) = x13 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 ⟶ 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 ⟶ x10 x14 (x10 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ 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 (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 ⟶ 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 ⟶ 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 ⟶ ∀ 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 ⟶ x8 x14 x15 (x13 x16 (x9 x17 x18 (x7 x19 x20))) = x9 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 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (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 (x13 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (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 ⟶ 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 (x7 x16 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (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 ⟶ 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 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem e1d01.. : (∀ 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 (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 ⟶ x7 x14 (x7 x15 (x7 x16 (x12 x17 x18))) = x7 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 (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 ⟶ x10 x14 (x13 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x10 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (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 (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 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ 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 (x12 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (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 (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 (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 (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 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (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 (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 ⟶ 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 (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 a8630.. : (∀ 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 ⟶ 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 (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 (x13 x17 x18))) = x10 x16 (x13 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (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 ⟶ 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 ⟶ x10 x14 (x7 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x10 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x7 x18 x19))) = x12 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 (x7 x16 (x13 x17 (x10 x18 x19))) = x13 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 ⟶ 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 ⟶ x8 x14 x15 (x7 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 (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 (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 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (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 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 830aa.. : (∀ 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 ⟶ x10 x14 (x12 x15 (x12 x16 x17)) = x12 x15 (x12 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 x18)) = x10 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x7 x16 (x13 x17 x18))) = x7 x16 (x13 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (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 ⟶ 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 (x7 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x10 x16 (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 (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 (x7 x17 (x10 x18 x19))) = x7 x17 (x10 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ 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 (x9 x17 x18 (x13 x19 x20))) = x9 x17 x18 (x13 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (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 (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 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (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 (x7 x16 (x10 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (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 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 6464f.. : (∀ 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 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x7 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 (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 (x7 x16 (x7 x17 x18)) = x7 x16 (x7 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x13 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (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 (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 ⟶ x13 x14 (x7 x15 (x7 x16 (x7 x17 x18))) = x7 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 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x10 x16 (x8 x17 x18 (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 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 (x12 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x13 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x13 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 (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 (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))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem f28c4.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 x17))))))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ 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 ⟶ x12 x14 (x12 x15 (x12 x16 x17)) = x12 x15 (x12 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 x18)) = x10 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x13 x16 (x12 x17 x18))) = x13 x16 (x12 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x7 x15 (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 ⟶ 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 (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 (x7 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ 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 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x7 x18 x19))) = x12 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 (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 (x7 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 (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 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (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 (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 (x13 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (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 (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 (x12 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem cdf7b.. : (∀ 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 ⟶ x9 x14 x15 (x7 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x7 x16 x17))))))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ 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 ⟶ 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 (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 ⟶ x10 x14 (x12 x15 (x13 x16 (x10 x17 x18))) = x13 x16 (x10 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x7 x16 (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 ⟶ x7 x14 (x12 x15 (x7 x16 (x13 x17 x18))) = x7 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 ⟶ 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 ⟶ ∀ 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 (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 (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 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 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 (x7 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (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 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (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 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 4d769.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x14 (x9 x15 x16 (x8 x14 x15 (x7 x16 (x12 x14 (x9 x15 x16 (x8 x14 x15 (x7 x16 (x12 x14 (x9 x15 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x14 (x8 x15 x16 (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 ⟶ x7 x14 (x7 x15 (x13 x16 x17)) = x7 x15 (x13 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ 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 (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 ⟶ x10 x14 (x10 x15 (x13 x16 (x10 x17 x18))) = x13 x16 (x10 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ 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 ⟶ 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 (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 ⟶ ∀ 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 (x12 x16 (x12 x17 (x7 x18 x19))) = x12 x17 (x7 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (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 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (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 (x7 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 (x7 x16 (x10 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 (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 4fa0a.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x14 (x9 x15 x16 (x9 x14 x15 (x10 x16 (x7 x14 (x9 x15 x16 (x9 x14 x15 (x10 x16 (x7 x14 (x9 x15 x16 (x9 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 (x10 x16 (x7 x17 x18)) = x10 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (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 (x12 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x13 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x10 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x13 x16 (x12 x17 x18))) = x13 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x13 x17 (x10 x18 x19))) = x13 x17 (x10 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ 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 ⟶ x8 x14 x15 (x13 x16 (x9 x17 x18 (x10 x19 x20))) = x9 x17 x18 (x10 x19 (x8 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (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 (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 (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 (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 (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 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (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 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 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 (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 ⟶ 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))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 4e482.. : (∀ 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 (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 (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 ⟶ 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 ⟶ 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 (x13 x17 x18))) = x12 x16 (x13 x17 (x10 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (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 (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 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x10 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x8 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ 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 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (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 ⟶ x8 x14 x15 (x7 x16 (x13 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x10 x17 (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 (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 ⟶ 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 (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 (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 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 82f4b.. : (∀ 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 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x12 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x12 x16 x17))))))))))))))) = x17) ⟶ (∀ 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 ⟶ x12 x14 (x7 x15 (x12 x16 x17)) = x7 x15 (x12 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 x18)) = x12 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (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 ⟶ 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 ⟶ 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 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (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 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x13 x18 x19))) = x12 x17 (x13 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ 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 ⟶ ∀ 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 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (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 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 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 (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 (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 (x10 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 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))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 71c25.. : (∀ 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 (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 (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 ⟶ 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 ⟶ 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 ⟶ 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 (x7 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (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 (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 (x7 x17 (x13 x18 x19))) = x7 x17 (x13 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 ⟶ 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 (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 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (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 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 (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 6f748.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 (x9 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ 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 ⟶ x10 x14 (x10 x15 (x12 x16 x17)) = x10 x15 (x12 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x10 x16 (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 ⟶ 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 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x13 x15 (x13 x16 (x13 x17 x18))) = x13 x16 (x13 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 (x7 x16 (x13 x17 x18))) = x7 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 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x13 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x10 x16 (x13 x17 (x12 x18 x19))) = x13 x17 (x12 x18 (x8 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (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 ⟶ ∀ 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 (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 (x12 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (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 ⟶ 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 (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 (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 ⟶ 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 (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 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (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 36a63.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x13 x14 (x7 x15 (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 (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 ⟶ 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 (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 (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 ⟶ x12 x14 (x13 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x12 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (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 (x7 x16 (x10 x17 (x13 x18 x19))) = x10 x17 (x13 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x10 x18 x19))) = x10 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 (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 (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 (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 (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 (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 (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 (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 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 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))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 57314.. : (∀ 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 (x7 x14 (x10 x15 (x9 x14 x15 (x7 x14 (x10 x15 (x9 x14 x15 (x7 x14 (x10 x15 (x9 x14 x15 (x7 x14 (x10 x15 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ 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 (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 (x10 x15 (x13 x16 x17)) = x10 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 (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 (x7 x15 (x13 x16 (x12 x17 x18))) = x13 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 (x12 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x13 x15 (x10 x16 (x10 x17 x18))) = x10 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 ⟶ 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 (x10 x15 (x13 x16 (x7 x17 x18))) = x13 x16 (x7 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ 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 ⟶ 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 ⟶ ∀ 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 (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 (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 (x12 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (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 (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 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x13 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 7585d.. : (∀ 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 ⟶ x10 x14 (x10 x15 (x12 x16 x17)) = x10 x15 (x12 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x7 x16 (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 (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 ⟶ 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 (x7 x15 (x10 x16 (x13 x17 x18))) = x10 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 ⟶ x13 x14 (x10 x15 (x10 x16 (x12 x17 x18))) = x10 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 (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 ⟶ ∀ 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 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x7 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x9 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ 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 (x12 x16 (x10 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 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 (x12 x16 (x13 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (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 (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 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (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 (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 (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 (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 716ff.. : (∀ 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 (x7 x16 x17)) = x10 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 ⟶ 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 (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 (x12 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x13 x15 (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 ⟶ 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 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x8 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ 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 ⟶ x8 x14 x15 (x7 x16 (x8 x17 x18 (x12 x19 x20))) = x8 x17 x18 (x12 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (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 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 (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 (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 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x13 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem db85e.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x12 x16 (x8 x14 x15 (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 ⟶ x9 x14 x15 (x12 x16 (x10 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x10 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x10 x14 (x9 x15 x16 (x9 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 ⟶ x10 x14 (x7 x15 (x7 x16 x17)) = x7 x15 (x7 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 x18)) = x7 x16 (x12 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ 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 ⟶ x10 x14 (x13 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x10 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x10 x15 (x7 x16 (x13 x17 x18))) = x7 x16 (x13 x17 (x7 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ 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 (x12 x15 (x10 x16 (x7 x17 x18))) = x10 x16 (x7 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (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 (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 (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 ⟶ x8 x14 x15 (x12 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 (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 ⟶ 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 ⟶ 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 ⟶ 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 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 9038d.. : (∀ 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 (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 (x7 x17 x18)) = x12 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (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 (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 ⟶ x13 x14 (x12 x15 (x12 x16 (x7 x17 x18))) = x12 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 ⟶ 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 ⟶ 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 ⟶ ∀ 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 ⟶ 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 (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 ⟶ x9 x14 x15 (x10 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x9 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (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 (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 (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 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 (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 5a6ae.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 (x10 x14 (x12 x15 (x8 x14 x15 (x10 x14 (x12 x15 (x8 x14 x15 (x10 x14 (x12 x15 (x8 x14 x15 (x10 x14 (x12 x15 (x8 x14 x15 (x10 x14 (x12 x15 x16)))))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x8 x14 x15 (x10 x14 (x12 x15 (x8 x14 x15 (x10 x14 (x12 x15 (x8 x14 x15 (x10 x14 (x12 x15 (x8 x14 x15 (x10 x14 (x12 x15 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ 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 (x7 x16 (x7 x17 x18)) = x7 x16 (x7 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ 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 ⟶ 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 ⟶ x12 x14 (x12 x15 (x10 x16 (x13 x17 x18))) = x10 x16 (x13 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ 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 (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 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x10 x18 x19))) = x7 x17 (x10 x18 (x8 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ 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 (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 ⟶ 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 (x10 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 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 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (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 (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 (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 (x10 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (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 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem b37f1.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x10 x16 (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 ⟶ x9 x14 x15 (x13 x16 (x10 x14 (x8 x15 x16 (x9 x14 x15 (x13 x16 (x10 x14 (x8 x15 x16 (x9 x14 x15 (x13 x16 (x10 x14 (x8 x15 x16 x17))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ 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 (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 ⟶ x7 x14 (x7 x15 (x7 x16 (x12 x17 x18))) = x7 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 (x13 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x12 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x10 x16 (x13 x17 x18))) = x10 x16 (x13 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ 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 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x7 x18 x19))) = x7 x17 (x7 x18 (x8 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x13 x16 (x13 x17 (x10 x18 x19))) = x13 x17 (x10 x18 (x9 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x10 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x8 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (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 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 (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 (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 (x10 x16 (x7 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 3e19a.. : (∀ 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 (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 (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 ⟶ 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 (x12 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ 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 (x7 x17 x18))) = x12 x16 (x7 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (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 (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 ⟶ ∀ 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 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x9 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 (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 ⟶ 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 (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 (x7 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (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 (x12 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 03fc5.. : (∀ 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 (x10 x15 (x8 x14 x15 (x10 x14 (x10 x15 x16))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x12 x14 (x10 x15 (x9 x14 x15 (x12 x14 (x10 x15 (x9 x14 x15 (x12 x14 (x10 x15 (x9 x14 x15 (x12 x14 (x10 x15 (x9 x14 x15 (x12 x14 (x10 x15 x16)))))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x7 x15 (x10 x16 x17)) = x7 x15 (x10 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 x18)) = x7 x16 (x7 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x12 x15 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x10 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x12 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (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 ⟶ 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 ⟶ x10 x14 (x13 x15 (x10 x16 (x13 x17 x18))) = x10 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 ⟶ ∀ 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 ⟶ x9 x14 x15 (x10 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ 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 (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 (x7 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (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 (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 ⟶ 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 (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 (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 (x7 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 9a1bf.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x7 x16 (x9 x14 x15 (x12 x16 (x9 x14 x15 (x7 x16 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 (x12 x16 (x7 x17 x18)) = x12 x16 (x7 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (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 (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 ⟶ 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 ⟶ 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 (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 (x10 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (x13 x17 (x12 x18 x19))) = x13 x17 (x12 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x7 x16 (x8 x17 x18 (x13 x19 x20))) = x8 x17 x18 (x13 x19 (x9 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x12 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x9 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (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 (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 (x13 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (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 (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 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 40de5.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x14 (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 ⟶ x9 x14 x15 (x10 x16 (x13 x14 (x8 x15 x16 (x9 x14 x15 (x10 x16 (x13 x14 (x8 x15 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x10 x14 (x7 x15 (x12 x16 x17)) = x7 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 (x7 x16 (x7 x17 x18)) = x7 x16 (x7 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x7 x16 (x12 x17 x18))) = x7 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 (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 (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 (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 ⟶ ∀ 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 (x13 x18 x19))) = x12 x17 (x13 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 (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 (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 ⟶ ∀ 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 (x12 x16 (x10 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (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 (x13 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 (x12 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x10 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem a6dd3.. : (∀ 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 ⟶ x8 x14 x15 (x12 x14 (x12 x15 (x8 x14 x15 (x12 x14 (x12 x15 x16))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x12 x14 (x7 x15 (x12 x16 x17)) = x7 x15 (x12 x16 (x12 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (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 (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 ⟶ x7 x14 (x12 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (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 (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 (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 (x10 x18 x19))) = x12 x17 (x10 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (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 ⟶ 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 (x12 x16 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x10 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 (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 (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 (x7 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem bf8e8.. : (∀ 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 (x7 x15 (x12 x16 x17)) = x7 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 (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 (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 (x13 x16 (x10 x17 x18))) = x13 x16 (x10 x17 (x10 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ 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 ⟶ 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 ⟶ 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 (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 ⟶ 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 (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 (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 (x7 x16 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 ⟶ 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 (x12 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x8 x18 x19 (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 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x8 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x13 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x9 x14 x15 (x13 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 09cc2.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x12 x16 (x12 x14 (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 ⟶ x9 x14 x15 (x7 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x7 x16 (x12 x14 (x9 x15 x16 x17))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x10 x14 (x12 x15 (x10 x16 x17)) = x12 x15 (x10 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x7 x16 (x7 x17 x18)) = x7 x16 (x7 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ 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 (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 (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 ⟶ x7 x14 (x7 x15 (x13 x16 (x7 x17 x18))) = x13 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 ⟶ 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 (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 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x12 x18 x19))) = x10 x17 (x12 x18 (x8 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x9 x17 x18 (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 (x7 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ 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 (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 (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 (x13 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (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 (x13 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x7 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 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 ⟶ 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 9c627.. : (∀ 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 (x13 x15 (x12 x16 x17)) = x13 x15 (x12 x16 (x13 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x17 x18)) = x12 x16 (x10 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ 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 ⟶ 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 ⟶ 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 ⟶ 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 ⟶ 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 (x10 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ 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 (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 ⟶ 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 (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 (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 (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 (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 (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 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (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 (x12 x16 (x12 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem b6e10.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x10 x16 (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 (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 ⟶ x8 x14 x15 (x10 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x7 x16 x17))))))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x7 x14 (x13 x15 (x12 x16 x17)) = x13 x15 (x12 x16 (x7 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 x18)) = x7 x16 (x10 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x7 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x12 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (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 (x12 x15 (x10 x16 (x10 x17 x18))) = x10 x16 (x10 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x10 x15 (x7 x16 (x12 x17 x18))) = x7 x16 (x12 x17 (x13 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x10 x15 (x7 x16 (x10 x17 x18))) = x7 x16 (x10 x17 (x10 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x12 x18 x19))) = x12 x17 (x12 x18 (x9 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x9 x14 x15 (x12 x16 (x7 x17 (x12 x18 x19))) = x7 x17 (x12 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x12 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x8 x14 x15 (x12 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (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 (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 (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 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x7 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 (x12 x16 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (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 (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 (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 ⟶ 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))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem b7862.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x13 x14 (x12 x15 (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 (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 ⟶ x13 x14 (x10 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x13 x14 (x10 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ 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 (x13 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x12 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x13 x14 (x7 x15 (x7 x16 (x7 x17 x18))) = x7 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 ⟶ x13 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x13 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x12 x16 (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 ⟶ 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 ⟶ ∀ 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 ⟶ x8 x14 x15 (x7 x16 (x9 x17 x18 (x7 x19 x20))) = x9 x17 x18 (x7 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ 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 (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 (x13 x16 (x10 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x12 x20 x21)))) = x9 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x7 x16 (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 ⟶ 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 ⟶ 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 (x13 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x13 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 4c0df.. : (∀ 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 ⟶ 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 ⟶ x10 x14 (x13 x15 (x12 x16 (x10 x17 x18))) = x12 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 ⟶ x12 x14 (x13 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x12 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (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 ⟶ x7 x14 (x10 x15 (x12 x16 (x13 x17 x18))) = x12 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 ⟶ 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 (x7 x16 (x10 x17 (x7 x18 x19))) = x10 x17 (x7 x18 (x8 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ 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 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x10 x16 (x9 x17 x18 (x13 x19 x20))) = x9 x17 x18 (x13 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 (x13 x16 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x9 x14 x15 (x13 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x10 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x7 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x13 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (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 (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 (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 (x7 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 (x13 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x13 x16 (x13 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 7c049.. : (∀ 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 (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 ⟶ x8 x14 x15 (x7 x14 (x10 x15 (x8 x14 x15 (x7 x14 (x10 x15 (x8 x14 x15 (x7 x14 (x10 x15 (x8 x14 x15 (x7 x14 (x10 x15 x16))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x13 x14 (x7 x15 (x12 x16 x17)) = x7 x15 (x12 x16 (x13 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x12 x16 (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 (x12 x16 (x13 x17 x18))) = x12 x16 (x13 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (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 (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 ⟶ x7 x14 (x7 x15 (x12 x16 (x10 x17 x18))) = x12 x16 (x10 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (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 (x12 x16 (x12 x17 (x10 x18 x19))) = x12 x17 (x10 x18 (x9 x14 x15 (x12 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x7 x16 (x9 x17 x18 (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 ⟶ 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 (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 (x13 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 (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 (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 (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 (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 (x10 x17 (x8 x18 x19 (x7 x20 x21)))) = x8 x18 x19 (x7 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 850cf.. : (∀ 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 (x10 x15 (x8 x14 x15 (x10 x14 (x10 x15 (x8 x14 x15 (x10 x14 (x10 x15 x16)))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x8 x14 x15 (x10 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x7 x16 (x8 x14 x15 (x10 x16 (x8 x14 x15 (x7 x16 x17))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x10 x14 (x13 x15 (x13 x16 x17)) = x13 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 ⟶ x9 x14 x15 (x12 x16 (x12 x17 x18)) = x12 x16 (x12 x17 (x9 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x7 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x7 x14 (x7 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x7 x16 (x13 x17 x18))) = x7 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 ⟶ 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 ⟶ x13 x14 (x13 x15 (x10 x16 (x12 x17 x18))) = x10 x16 (x12 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 (x7 x17 x18))) = x13 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 (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 (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 ⟶ 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 ⟶ 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 (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 (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 (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 (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 (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 (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 ⟶ 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 (x13 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x7 x16 (x13 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 695d7.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 (x9 x14 x15 (x12 x16 (x12 x14 (x9 x15 x16 x17))))))))))))))))))) = x17) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x10 x16 (x12 x14 (x8 x15 x16 (x9 x14 x15 (x10 x16 (x12 x14 (x8 x15 x16 (x9 x14 x15 (x10 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 (x12 x15 (x12 x16 x17)) = x12 x15 (x12 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 x18)) = x10 x16 (x7 x17 (x8 x14 x15 x18))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x12 x15 (x7 x16 (x7 x17 x18))) = x7 x16 (x7 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x7 x14 (x12 x15 (x12 x16 (x12 x17 x18))) = x12 x16 (x12 x17 (x7 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x10 x14 (x13 x15 (x7 x16 (x10 x17 x18))) = x7 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 ⟶ x10 x14 (x13 x15 (x12 x16 (x7 x17 x18))) = x12 x16 (x7 x17 (x10 x14 (x13 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x10 x16 (x7 x17 (x10 x18 x19))) = x7 x17 (x10 x18 (x8 x14 x15 (x10 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ x8 x14 x15 (x13 x16 (x7 x17 (x10 x18 x19))) = x7 x17 (x10 x18 (x8 x14 x15 (x13 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x8 x14 x15 (x7 x16 (x8 x17 x18 (x7 x19 x20))) = x8 x17 x18 (x7 x19 (x8 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (x10 x16 (x9 x17 x18 (x12 x19 x20))) = x9 x17 x18 (x12 x19 (x9 x14 x15 (x10 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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 (x12 x17 (x8 x18 x19 (x13 x20 x21)))) = x8 x18 x19 (x13 x20 (x9 x14 x15 (x13 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x10 x16 (x12 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x8 x14 x15 (x10 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 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 (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 (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 ⟶ 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 (x13 x16 (x10 x17 (x9 x18 x19 (x13 x20 x21)))) = x9 x18 x19 (x13 x20 (x9 x14 x15 (x13 x16 (x10 x17 x21))))) ⟶ False) ⟶ ∀ x0 : ο . x0 (proof)Theorem 02e64.. : (∀ x0 . ∀ x1 x2 x3 : ι → ι → ι . ∀ x4 . ∀ x5 : ι → ι → ι . ∀ x6 : ι → ι → ι → ι . ∀ x7 : ι → ι → ι . ∀ x8 x9 : ι → ι → ι → ι . ∀ x10 x11 x12 x13 : ι → ι → ι . Loop_with_defs_cex1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ x9 x14 x15 (x7 x14 (x7 x15 (x9 x14 x15 (x7 x14 (x7 x15 (x9 x14 x15 (x7 x14 (x7 x15 (x9 x14 x15 (x7 x14 (x7 x15 (x9 x14 x15 (x7 x14 (x7 x15 x16)))))))))))))) = x16) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ x9 x14 x15 (x12 x16 (x10 x14 (x9 x15 x16 (x9 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 ⟶ x10 x14 (x12 x15 (x10 x16 x17)) = x12 x15 (x10 x16 (x10 x14 x17))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x8 x14 x15 (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 (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 (x12 x15 (x13 x16 (x10 x17 x18))) = x13 x16 (x10 x17 (x12 x14 (x12 x15 x18)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ x12 x14 (x10 x15 (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 (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 (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 (x12 x16 (x12 x17 (x7 x18 x19))) = x12 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 (x7 x16 (x13 x17 (x13 x18 x19))) = x13 x17 (x13 x18 (x9 x14 x15 (x7 x16 x19)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ x9 x14 x15 (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 (x8 x17 x18 (x10 x19 x20))) = x8 x17 x18 (x10 x19 (x9 x14 x15 (x7 x16 x20)))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x9 x18 x19 (x10 x20 x21)))) = x9 x18 x19 (x10 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (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 (x13 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x13 x16 (x13 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x9 x18 x19 (x7 x20 x21)))) = x9 x18 x19 (x7 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (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 ⟶ x9 x14 x15 (x12 x16 (x12 x17 (x8 x18 x19 (x10 x20 x21)))) = x8 x18 x19 (x10 x20 (x9 x14 x15 (x12 x16 (x12 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x12 x16 (x10 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x12 x16 (x10 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ x8 x14 x15 (x7 x16 (x7 x17 (x8 x18 x19 (x12 x20 x21)))) = x8 x18 x19 (x12 x20 (x8 x14 x15 (x7 x16 (x7 x17 x21))))) ⟶ (∀ x14 . In x14 x0 ⟶ ∀ x15 . In x15 x0 ⟶ ∀ x16 . In x16 x0 ⟶ ∀ x17 . In x17 x0 ⟶ ∀ x18 . In x18 x0 ⟶ ∀ x19 . In x19 x0 ⟶ ∀ x20 . In x20 x0 ⟶ ∀ x21 . In x21 x0 ⟶ 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) |
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