%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET714+4 : TPTP v8.1.2. Bugfixed v2.2.1. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n022.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Thu Aug 31 15:26:06 EDT 2023 % Result : Theorem 14.41s 2.74s % Output : Proof 18.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET714+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.16/0.35 % Computer : n022.cluster.edu % 0.16/0.35 % Model : x86_64 x86_64 % 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.16/0.35 % Memory : 8042.1875MB % 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.16/0.35 % CPULimit : 300 % 0.16/0.35 % WCLimit : 300 % 0.16/0.35 % DateTime : Sat Aug 26 15:13:40 EDT 2023 % 0.16/0.35 % CPUTime : % 0.20/0.57 ________ _____ % 0.20/0.57 ___ __ \_________(_)________________________________ % 0.20/0.57 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.57 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.57 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.57 % 0.20/0.57 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.57 (2023-06-19) % 0.20/0.57 % 0.20/0.57 (c) Philipp Rümmer, 2009-2023 % 0.20/0.57 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.57 Amanda Stjerna. % 0.20/0.57 Free software under BSD-3-Clause. % 0.20/0.57 % 0.20/0.57 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.57 % 0.20/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.58 Running up to 7 provers in parallel. % 0.20/0.60 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.60 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.60 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.60 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.60 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.60 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.60 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.25/1.18 Prover 1: Preprocessing ... % 3.94/1.19 Prover 4: Preprocessing ... % 4.00/1.23 Prover 5: Preprocessing ... % 4.00/1.23 Prover 2: Preprocessing ... % 4.00/1.23 Prover 3: Preprocessing ... % 4.00/1.23 Prover 6: Preprocessing ... % 4.00/1.24 Prover 0: Preprocessing ... % 9.01/1.91 Prover 5: Proving ... % 9.01/1.94 Prover 2: Proving ... % 9.51/2.05 Prover 6: Proving ... % 9.51/2.09 Prover 1: Constructing countermodel ... % 9.51/2.10 Prover 3: Constructing countermodel ... % 11.52/2.26 Prover 3: gave up % 11.52/2.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 11.52/2.27 Prover 1: gave up % 11.52/2.27 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.11/2.35 Prover 8: Preprocessing ... % 12.11/2.38 Prover 7: Preprocessing ... % 12.59/2.43 Prover 0: Proving ... % 13.35/2.50 Prover 4: Constructing countermodel ... % 13.64/2.53 Prover 7: Warning: ignoring some quantifiers % 13.78/2.58 Prover 7: Constructing countermodel ... % 13.78/2.58 Prover 8: Warning: ignoring some quantifiers % 13.78/2.60 Prover 8: Constructing countermodel ... % 14.41/2.74 Prover 0: proved (2151ms) % 14.41/2.74 % 14.41/2.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 14.41/2.74 % 14.41/2.75 Prover 2: stopped % 14.41/2.76 Prover 5: stopped % 14.41/2.76 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 14.41/2.76 Prover 6: stopped % 14.41/2.77 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 14.41/2.77 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 14.41/2.77 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 15.69/2.82 Prover 8: gave up % 15.69/2.82 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 15.69/2.85 Prover 16: Preprocessing ... % 15.69/2.85 Prover 10: Preprocessing ... % 15.69/2.87 Prover 11: Preprocessing ... % 15.69/2.87 Prover 13: Preprocessing ... % 16.53/2.92 Prover 19: Preprocessing ... % 16.53/2.94 Prover 4: Found proof (size 83) % 16.53/2.94 Prover 4: proved (2339ms) % 16.53/2.94 Prover 13: stopped % 16.53/2.94 Prover 7: stopped % 16.53/2.94 Prover 16: Warning: ignoring some quantifiers % 16.53/2.96 Prover 10: Warning: ignoring some quantifiers % 16.53/2.97 Prover 16: Constructing countermodel ... % 16.53/2.97 Prover 11: stopped % 16.53/2.97 Prover 10: Constructing countermodel ... % 16.53/2.98 Prover 10: stopped % 16.53/2.98 Prover 16: stopped % 17.52/3.10 Prover 19: Warning: ignoring some quantifiers % 17.52/3.12 Prover 19: Constructing countermodel ... % 17.52/3.13 Prover 19: stopped % 17.52/3.13 % 17.52/3.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 17.52/3.13 % 17.52/3.14 % SZS output start Proof for theBenchmark % 17.52/3.14 Assumptions after simplification: % 17.52/3.14 --------------------------------- % 17.52/3.14 % 17.52/3.14 (compose_function) % 17.52/3.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 17.52/3.17 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 17.52/3.17 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 17.52/3.17 ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | % 17.52/3.17 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] % 17.52/3.17 : ((apply(v0, v9, v6) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 % 17.52/3.17 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = % 17.52/3.17 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 17.52/3.17 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 17.52/3.17 int] : ! [v9: $i] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = % 17.52/3.17 v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) % 17.52/3.17 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 17.52/3.17 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v11 & % 17.52/3.17 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) % 17.52/3.17 = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! % 17.52/3.17 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 17.52/3.17 : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 17.52/3.17 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 17.52/3.17 ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ % 17.52/3.17 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] : % 17.52/3.17 ((apply(v1, v5, v9) = v10 & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~ % 17.52/3.17 (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 % 17.52/3.17 = 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 17.52/3.17 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 17.52/3.17 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | % 17.52/3.17 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 17.52/3.17 $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ? % 17.52/3.17 [v12: int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 & % 17.52/3.17 apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, v3) = 0) % 17.52/3.17 | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 = % 17.52/3.17 0)))))) % 17.52/3.17 % 17.52/3.17 (identity) % 17.52/3.17 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 17.52/3.17 (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 17.52/3.17 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0: % 17.52/3.17 $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ~ % 17.52/3.17 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & apply(v0, % 17.52/3.17 v3, v3) = v4 & member(v3, v1) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] % 17.52/3.17 : ! [v2: $i] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ~ % 17.52/3.17 $i(v2) | ~ $i(v1) | ~ $i(v0) | apply(v0, v2, v2) = 0) % 17.52/3.17 % 17.52/3.17 (inverse_function) % 17.52/3.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 17.52/3.18 $i] : ! [v6: any] : ( ~ (inverse_function(v0, v1, v2) = v5) | ~ (apply(v5, % 17.52/3.18 v4, v3) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 17.52/3.18 $i(v0) | ? [v7: any] : ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) = % 17.52/3.18 v9 & member(v4, v2) = v8 & member(v3, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 = % 17.52/3.18 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0))))) % 17.52/3.18 % 17.52/3.18 (maps) % 17.95/3.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 17.95/3.18 $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ % 17.95/3.18 (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 17.95/3.18 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 17.95/3.18 (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = % 17.95/3.18 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 17.95/3.18 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, % 17.95/3.18 v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ~ % 17.95/3.18 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 17.95/3.18 any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, % 17.95/3.18 v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 17.95/3.18 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 17.95/3.18 [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, % 17.95/3.18 v3, v4) = 0) | ~ (member(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 17.95/3.18 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 17.95/3.18 ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v4, v2) = v7 & member(v3, v1) % 17.95/3.18 = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: % 17.95/3.18 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ % 17.95/3.18 (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) | % 17.95/3.18 ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 17.95/3.18 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & % 17.95/3.18 apply(v0, v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! % 17.95/3.18 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) | % 17.95/3.18 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 17.95/3.18 : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] % 17.95/3.18 : ? [v12: $i] : ? [v13: int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13 % 17.95/3.18 = 0 & member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) = % 17.95/3.18 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & member(v14, v2) % 17.95/3.18 = v15)) & ! [v14: $i] : ( ~ (member(v14, v2) = 0) | ~ $i(v14) | % 17.95/3.18 ? [v15: int] : ( ~ (v15 = 0) & apply(v0, v12, v14) = v15))) | (v11 = % 17.95/3.18 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, % 17.95/3.18 v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, % 17.95/3.18 v2) = 0 & member(v4, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 17.95/3.18 [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) % 17.95/3.18 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, % 17.95/3.18 v3, v4) = 0 & member(v4, v2) = 0 & $i(v4))) % 17.95/3.18 % 17.95/3.18 (thII05) % 17.95/3.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 17.95/3.19 int] : ( ~ (v5 = 0) & inverse_function(v0, v1, v2) = v3 & one_to_one(v0, v1, % 17.95/3.19 v2) = 0 & identity(v4, v1) = v5 & compose_function(v3, v0, v1, v2, v1) = % 17.95/3.19 v4 & maps(v0, v1, v2) = 0 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 17.95/3.19 % 17.95/3.19 (function-axioms) % 17.95/3.20 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 17.95/3.20 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 17.95/3.20 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 17.95/3.20 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 17.95/3.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.95/3.20 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 17.95/3.20 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 17.95/3.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.95/3.20 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 17.95/3.20 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 17.95/3.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.95/3.20 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 17.95/3.20 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 17.95/3.20 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 17.95/3.20 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 17.95/3.20 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 17.95/3.20 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 17.95/3.20 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 17.95/3.20 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 17.95/3.20 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 17.95/3.20 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 17.95/3.20 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 17.95/3.20 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 17.95/3.20 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 17.95/3.20 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 17.95/3.20 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 17.95/3.20 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 17.95/3.20 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 17.95/3.20 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 17.95/3.20 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 17.95/3.20 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 17.95/3.20 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 17.95/3.20 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.95/3.20 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 17.95/3.20 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 17.95/3.20 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 17.95/3.20 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 17.95/3.20 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 17.95/3.20 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 17.95/3.20 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 17.95/3.20 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 17.95/3.20 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 17.95/3.20 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 17.95/3.20 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 17.95/3.20 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 17.95/3.20 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.95/3.20 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 17.95/3.20 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.95/3.20 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 17.95/3.20 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 17.95/3.20 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 17.95/3.20 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 17.95/3.20 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 17.95/3.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 17.95/3.20 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 17.95/3.20 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 17.95/3.20 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 17.95/3.20 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 17.95/3.20 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 17.95/3.20 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 17.95/3.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 17.95/3.20 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 17.95/3.20 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 17.95/3.20 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 17.95/3.20 (power_set(v2) = v0)) % 17.95/3.20 % 17.95/3.20 Further assumptions not needed in the proof: % 17.95/3.20 -------------------------------------------- % 17.95/3.20 compose_predicate, decreasing_function, difference, empty_set, equal_maps, % 17.95/3.20 equal_set, image2, image3, increasing_function, injective, intersection, % 17.95/3.20 inverse_image2, inverse_image3, inverse_predicate, isomorphism, one_to_one, % 17.95/3.20 power_set, product, singleton, subset, sum, surjective, union, unordered_pair % 17.95/3.20 % 17.95/3.20 Those formulas are unsatisfiable: % 17.95/3.20 --------------------------------- % 17.95/3.20 % 17.95/3.20 Begin of proof % 17.95/3.20 | % 17.95/3.20 | ALPHA: (maps) implies: % 18.04/3.20 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, % 18.04/3.20 | v1, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) | % 18.04/3.20 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & % 18.04/3.20 | member(v4, v2) = 0 & $i(v4))) % 18.04/3.20 | % 18.04/3.20 | ALPHA: (compose_function) implies: % 18.04/3.20 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 18.04/3.20 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : % 18.04/3.20 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ % 18.04/3.20 | (apply(v7, v5, v6) = v8) | ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ % 18.04/3.20 | $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 18.04/3.20 | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v10 % 18.04/3.20 | & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 18.04/3.20 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 18.04/3.20 | (v10 = 0))))) % 18.04/3.21 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 18.04/3.21 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : % 18.04/3.21 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ % 18.04/3.21 | (apply(v7, v5, v6) = v8) | ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | % 18.04/3.21 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 18.04/3.21 | | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v0, v9, v6) = % 18.04/3.21 | v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 18.04/3.21 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 18.04/3.21 | (v10 = 0))))) % 18.04/3.21 | % 18.04/3.21 | ALPHA: (identity) implies: % 18.04/3.21 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (identity(v0, % 18.04/3.21 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : % 18.04/3.21 | ( ~ (v4 = 0) & apply(v0, v3, v3) = v4 & member(v3, v1) = 0 & $i(v3))) % 18.04/3.21 | % 18.04/3.21 | ALPHA: (function-axioms) implies: % 18.04/3.21 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 18.04/3.21 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 18.04/3.21 | = v0)) % 18.04/3.21 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 18.04/3.21 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ % 18.04/3.21 | (apply(v4, v3, v2) = v0)) % 18.04/3.21 | % 18.04/3.21 | DELTA: instantiating (thII05) with fresh symbols all_32_0, all_32_1, all_32_2, % 18.04/3.21 | all_32_3, all_32_4, all_32_5 gives: % 18.04/3.21 | (7) ~ (all_32_0 = 0) & inverse_function(all_32_5, all_32_4, all_32_3) = % 18.04/3.21 | all_32_2 & one_to_one(all_32_5, all_32_4, all_32_3) = 0 & % 18.04/3.21 | identity(all_32_1, all_32_4) = all_32_0 & compose_function(all_32_2, % 18.04/3.21 | all_32_5, all_32_4, all_32_3, all_32_4) = all_32_1 & maps(all_32_5, % 18.04/3.21 | all_32_4, all_32_3) = 0 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3) % 18.04/3.21 | & $i(all_32_4) & $i(all_32_5) % 18.04/3.21 | % 18.04/3.21 | ALPHA: (7) implies: % 18.04/3.21 | (8) ~ (all_32_0 = 0) % 18.04/3.21 | (9) $i(all_32_5) % 18.04/3.21 | (10) $i(all_32_4) % 18.04/3.21 | (11) $i(all_32_3) % 18.04/3.21 | (12) $i(all_32_2) % 18.04/3.21 | (13) $i(all_32_1) % 18.04/3.21 | (14) maps(all_32_5, all_32_4, all_32_3) = 0 % 18.04/3.21 | (15) compose_function(all_32_2, all_32_5, all_32_4, all_32_3, all_32_4) = % 18.04/3.21 | all_32_1 % 18.04/3.21 | (16) identity(all_32_1, all_32_4) = all_32_0 % 18.04/3.21 | (17) inverse_function(all_32_5, all_32_4, all_32_3) = all_32_2 % 18.04/3.21 | % 18.10/3.22 | GROUND_INST: instantiating (4) with all_32_1, all_32_4, all_32_0, simplifying % 18.10/3.22 | with (10), (13), (16) gives: % 18.10/3.22 | (18) all_32_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 18.10/3.22 | apply(all_32_1, v0, v0) = v1 & member(v0, all_32_4) = 0 & $i(v0)) % 18.10/3.22 | % 18.10/3.22 | BETA: splitting (18) gives: % 18.10/3.22 | % 18.10/3.22 | Case 1: % 18.10/3.22 | | % 18.10/3.22 | | (19) all_32_0 = 0 % 18.10/3.22 | | % 18.10/3.22 | | REDUCE: (8), (19) imply: % 18.10/3.22 | | (20) $false % 18.10/3.22 | | % 18.10/3.22 | | CLOSE: (20) is inconsistent. % 18.10/3.22 | | % 18.10/3.22 | Case 2: % 18.10/3.22 | | % 18.10/3.22 | | (21) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & apply(all_32_1, v0, v0) % 18.10/3.22 | | = v1 & member(v0, all_32_4) = 0 & $i(v0)) % 18.10/3.22 | | % 18.10/3.22 | | DELTA: instantiating (21) with fresh symbols all_44_0, all_44_1 gives: % 18.10/3.22 | | (22) ~ (all_44_0 = 0) & apply(all_32_1, all_44_1, all_44_1) = all_44_0 & % 18.10/3.22 | | member(all_44_1, all_32_4) = 0 & $i(all_44_1) % 18.10/3.22 | | % 18.10/3.22 | | ALPHA: (22) implies: % 18.10/3.22 | | (23) ~ (all_44_0 = 0) % 18.10/3.22 | | (24) $i(all_44_1) % 18.10/3.22 | | (25) member(all_44_1, all_32_4) = 0 % 18.10/3.22 | | (26) apply(all_32_1, all_44_1, all_44_1) = all_44_0 % 18.10/3.22 | | % 18.10/3.22 | | GROUND_INST: instantiating (1) with all_32_5, all_32_4, all_32_3, all_44_1, % 18.10/3.22 | | simplifying with (9), (10), (11), (14), (24), (25) gives: % 18.10/3.22 | | (27) ? [v0: $i] : (apply(all_32_5, all_44_1, v0) = 0 & member(v0, % 18.10/3.22 | | all_32_3) = 0 & $i(v0)) % 18.10/3.22 | | % 18.10/3.22 | | DELTA: instantiating (27) with fresh symbol all_51_0 gives: % 18.10/3.22 | | (28) apply(all_32_5, all_44_1, all_51_0) = 0 & member(all_51_0, all_32_3) % 18.10/3.22 | | = 0 & $i(all_51_0) % 18.10/3.22 | | % 18.10/3.22 | | ALPHA: (28) implies: % 18.10/3.22 | | (29) $i(all_51_0) % 18.10/3.22 | | (30) member(all_51_0, all_32_3) = 0 % 18.10/3.22 | | (31) apply(all_32_5, all_44_1, all_51_0) = 0 % 18.10/3.22 | | % 18.10/3.22 | | GROUND_INST: instantiating (2) with all_32_2, all_32_5, all_32_4, all_32_3, % 18.10/3.22 | | all_32_4, all_44_1, all_44_1, all_32_1, all_44_0, all_51_0, % 18.10/3.22 | | simplifying with (9), (10), (11), (12), (15), (24), (26), (29), % 18.10/3.22 | | (30) gives: % 18.10/3.23 | | (32) all_44_0 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_2, % 18.10/3.23 | | all_51_0, all_44_1) = v1 & apply(all_32_5, all_44_1, all_51_0) % 18.10/3.23 | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_44_1, % 18.10/3.23 | | all_32_4) = v1 & member(all_44_1, all_32_4) = v0 & ( ~ (v1 = % 18.10/3.23 | | 0) | ~ (v0 = 0)))) % 18.10/3.23 | | % 18.10/3.23 | | GROUND_INST: instantiating (3) with all_32_2, all_32_5, all_32_4, all_32_3, % 18.10/3.23 | | all_32_4, all_44_1, all_44_1, all_32_1, all_44_0, all_51_0, % 18.10/3.23 | | simplifying with (9), (10), (11), (12), (15), (24), (26), (29), % 18.10/3.23 | | (31) gives: % 18.10/3.23 | | (33) all_44_0 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_2, % 18.10/3.23 | | all_51_0, all_44_1) = v1 & member(all_51_0, all_32_3) = v0 & ( % 18.10/3.23 | | ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_44_1, all_32_4) = v1 % 18.10/3.23 | | & member(all_44_1, all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 18.10/3.23 | | 0)))) % 18.10/3.23 | | % 18.10/3.23 | | BETA: splitting (33) gives: % 18.10/3.23 | | % 18.10/3.23 | | Case 1: % 18.10/3.23 | | | % 18.10/3.23 | | | (34) all_44_0 = 0 % 18.10/3.23 | | | % 18.10/3.23 | | | REDUCE: (23), (34) imply: % 18.10/3.23 | | | (35) $false % 18.10/3.23 | | | % 18.10/3.23 | | | CLOSE: (35) is inconsistent. % 18.10/3.23 | | | % 18.10/3.23 | | Case 2: % 18.10/3.23 | | | % 18.10/3.23 | | | (36) ? [v0: any] : ? [v1: any] : ((apply(all_32_2, all_51_0, % 18.10/3.23 | | | all_44_1) = v1 & member(all_51_0, all_32_3) = v0 & ( ~ (v1 = % 18.10/3.23 | | | 0) | ~ (v0 = 0))) | (member(all_44_1, all_32_4) = v1 & % 18.10/3.23 | | | member(all_44_1, all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 18.10/3.23 | | | 0)))) % 18.10/3.23 | | | % 18.10/3.23 | | | DELTA: instantiating (36) with fresh symbols all_64_0, all_64_1 gives: % 18.10/3.23 | | | (37) (apply(all_32_2, all_51_0, all_44_1) = all_64_0 & member(all_51_0, % 18.10/3.23 | | | all_32_3) = all_64_1 & ( ~ (all_64_0 = 0) | ~ (all_64_1 = % 18.10/3.23 | | | 0))) | (member(all_44_1, all_32_4) = all_64_0 & % 18.10/3.23 | | | member(all_44_1, all_32_4) = all_64_1 & ( ~ (all_64_0 = 0) | ~ % 18.10/3.23 | | | (all_64_1 = 0))) % 18.10/3.23 | | | % 18.10/3.23 | | | BETA: splitting (32) gives: % 18.10/3.23 | | | % 18.10/3.23 | | | Case 1: % 18.10/3.23 | | | | % 18.10/3.23 | | | | (38) all_44_0 = 0 % 18.10/3.23 | | | | % 18.10/3.23 | | | | REDUCE: (23), (38) imply: % 18.10/3.23 | | | | (39) $false % 18.10/3.23 | | | | % 18.10/3.23 | | | | CLOSE: (39) is inconsistent. % 18.10/3.23 | | | | % 18.10/3.23 | | | Case 2: % 18.10/3.23 | | | | % 18.10/3.23 | | | | (40) ? [v0: any] : ? [v1: any] : ((apply(all_32_2, all_51_0, % 18.10/3.23 | | | | all_44_1) = v1 & apply(all_32_5, all_44_1, all_51_0) = v0 % 18.10/3.23 | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_44_1, all_32_4) % 18.10/3.23 | | | | = v1 & member(all_44_1, all_32_4) = v0 & ( ~ (v1 = 0) | ~ % 18.10/3.23 | | | | (v0 = 0)))) % 18.10/3.23 | | | | % 18.10/3.23 | | | | DELTA: instantiating (40) with fresh symbols all_68_0, all_68_1 gives: % 18.10/3.23 | | | | (41) (apply(all_32_2, all_51_0, all_44_1) = all_68_0 & % 18.10/3.23 | | | | apply(all_32_5, all_44_1, all_51_0) = all_68_1 & ( ~ (all_68_0 % 18.10/3.23 | | | | = 0) | ~ (all_68_1 = 0))) | (member(all_44_1, all_32_4) = % 18.10/3.23 | | | | all_68_0 & member(all_44_1, all_32_4) = all_68_1 & ( ~ % 18.10/3.23 | | | | (all_68_0 = 0) | ~ (all_68_1 = 0))) % 18.10/3.23 | | | | % 18.10/3.23 | | | | BETA: splitting (41) gives: % 18.10/3.23 | | | | % 18.10/3.23 | | | | Case 1: % 18.10/3.23 | | | | | % 18.10/3.23 | | | | | (42) apply(all_32_2, all_51_0, all_44_1) = all_68_0 & % 18.10/3.23 | | | | | apply(all_32_5, all_44_1, all_51_0) = all_68_1 & ( ~ (all_68_0 % 18.10/3.23 | | | | | = 0) | ~ (all_68_1 = 0)) % 18.10/3.23 | | | | | % 18.10/3.23 | | | | | ALPHA: (42) implies: % 18.10/3.23 | | | | | (43) apply(all_32_5, all_44_1, all_51_0) = all_68_1 % 18.10/3.23 | | | | | (44) apply(all_32_2, all_51_0, all_44_1) = all_68_0 % 18.10/3.23 | | | | | (45) ~ (all_68_0 = 0) | ~ (all_68_1 = 0) % 18.10/3.23 | | | | | % 18.10/3.23 | | | | | BETA: splitting (37) gives: % 18.10/3.23 | | | | | % 18.10/3.23 | | | | | Case 1: % 18.10/3.23 | | | | | | % 18.10/3.24 | | | | | | (46) apply(all_32_2, all_51_0, all_44_1) = all_64_0 & % 18.10/3.24 | | | | | | member(all_51_0, all_32_3) = all_64_1 & ( ~ (all_64_0 = 0) | % 18.10/3.24 | | | | | | ~ (all_64_1 = 0)) % 18.10/3.24 | | | | | | % 18.10/3.24 | | | | | | ALPHA: (46) implies: % 18.10/3.24 | | | | | | (47) member(all_51_0, all_32_3) = all_64_1 % 18.10/3.24 | | | | | | (48) apply(all_32_2, all_51_0, all_44_1) = all_64_0 % 18.10/3.24 | | | | | | (49) ~ (all_64_0 = 0) | ~ (all_64_1 = 0) % 18.10/3.24 | | | | | | % 18.10/3.24 | | | | | | GROUND_INST: instantiating (5) with 0, all_64_1, all_32_3, all_51_0, % 18.10/3.24 | | | | | | simplifying with (30), (47) gives: % 18.10/3.24 | | | | | | (50) all_64_1 = 0 % 18.10/3.24 | | | | | | % 18.10/3.24 | | | | | | GROUND_INST: instantiating (6) with 0, all_68_1, all_51_0, all_44_1, % 18.10/3.24 | | | | | | all_32_5, simplifying with (31), (43) gives: % 18.10/3.24 | | | | | | (51) all_68_1 = 0 % 18.10/3.24 | | | | | | % 18.10/3.24 | | | | | | GROUND_INST: instantiating (6) with all_64_0, all_68_0, all_44_1, % 18.10/3.24 | | | | | | all_51_0, all_32_2, simplifying with (44), (48) gives: % 18.10/3.24 | | | | | | (52) all_68_0 = all_64_0 % 18.10/3.24 | | | | | | % 18.10/3.24 | | | | | | BETA: splitting (49) gives: % 18.10/3.24 | | | | | | % 18.10/3.24 | | | | | | Case 1: % 18.10/3.24 | | | | | | | % 18.10/3.24 | | | | | | | (53) ~ (all_64_0 = 0) % 18.10/3.24 | | | | | | | % 18.10/3.24 | | | | | | | GROUND_INST: instantiating (inverse_function) with all_32_5, % 18.10/3.24 | | | | | | | all_32_4, all_32_3, all_44_1, all_51_0, all_32_2, % 18.10/3.24 | | | | | | | all_64_0, simplifying with (9), (10), (11), (17), % 18.10/3.24 | | | | | | | (24), (29), (48) gives: % 18.10/3.24 | | | | | | | (54) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 18.10/3.24 | | | | | | | (apply(all_32_5, all_44_1, all_51_0) = v2 & % 18.10/3.24 | | | | | | | member(all_51_0, all_32_3) = v1 & member(all_44_1, % 18.10/3.24 | | | | | | | all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0) | (( ~ (v2 % 18.10/3.24 | | | | | | | = 0) | all_64_0 = 0) & ( ~ (all_64_0 = 0) | v2 = % 18.10/3.24 | | | | | | | 0)))) % 18.10/3.24 | | | | | | | % 18.10/3.24 | | | | | | | DELTA: instantiating (54) with fresh symbols all_92_0, all_92_1, % 18.10/3.24 | | | | | | | all_92_2 gives: % 18.10/3.24 | | | | | | | (55) apply(all_32_5, all_44_1, all_51_0) = all_92_0 & % 18.10/3.24 | | | | | | | member(all_51_0, all_32_3) = all_92_1 & member(all_44_1, % 18.10/3.24 | | | | | | | all_32_4) = all_92_2 & ( ~ (all_92_1 = 0) | ~ (all_92_2 % 18.10/3.24 | | | | | | | = 0) | (( ~ (all_92_0 = 0) | all_64_0 = 0) & ( ~ % 18.10/3.24 | | | | | | | (all_64_0 = 0) | all_92_0 = 0))) % 18.10/3.24 | | | | | | | % 18.10/3.24 | | | | | | | ALPHA: (55) implies: % 18.10/3.24 | | | | | | | (56) member(all_44_1, all_32_4) = all_92_2 % 18.10/3.24 | | | | | | | (57) member(all_51_0, all_32_3) = all_92_1 % 18.10/3.24 | | | | | | | (58) apply(all_32_5, all_44_1, all_51_0) = all_92_0 % 18.10/3.24 | | | | | | | (59) ~ (all_92_1 = 0) | ~ (all_92_2 = 0) | (( ~ (all_92_0 = % 18.10/3.24 | | | | | | | 0) | all_64_0 = 0) & ( ~ (all_64_0 = 0) | all_92_0 = % 18.10/3.24 | | | | | | | 0)) % 18.10/3.24 | | | | | | | % 18.10/3.24 | | | | | | | GROUND_INST: instantiating (5) with 0, all_92_2, all_32_4, % 18.10/3.24 | | | | | | | all_44_1, simplifying with (25), (56) gives: % 18.10/3.24 | | | | | | | (60) all_92_2 = 0 % 18.10/3.24 | | | | | | | % 18.10/3.24 | | | | | | | GROUND_INST: instantiating (5) with 0, all_92_1, all_32_3, % 18.10/3.24 | | | | | | | all_51_0, simplifying with (30), (57) gives: % 18.10/3.24 | | | | | | | (61) all_92_1 = 0 % 18.10/3.24 | | | | | | | % 18.10/3.24 | | | | | | | GROUND_INST: instantiating (6) with 0, all_92_0, all_51_0, % 18.10/3.24 | | | | | | | all_44_1, all_32_5, simplifying with (31), (58) % 18.10/3.24 | | | | | | | gives: % 18.10/3.24 | | | | | | | (62) all_92_0 = 0 % 18.10/3.24 | | | | | | | % 18.10/3.24 | | | | | | | BETA: splitting (59) gives: % 18.10/3.24 | | | | | | | % 18.10/3.24 | | | | | | | Case 1: % 18.10/3.24 | | | | | | | | % 18.10/3.24 | | | | | | | | (63) ~ (all_92_1 = 0) % 18.10/3.24 | | | | | | | | % 18.10/3.24 | | | | | | | | REDUCE: (61), (63) imply: % 18.10/3.24 | | | | | | | | (64) $false % 18.10/3.24 | | | | | | | | % 18.10/3.24 | | | | | | | | CLOSE: (64) is inconsistent. % 18.10/3.24 | | | | | | | | % 18.10/3.24 | | | | | | | Case 2: % 18.10/3.24 | | | | | | | | % 18.10/3.25 | | | | | | | | (65) ~ (all_92_2 = 0) | (( ~ (all_92_0 = 0) | all_64_0 = 0) % 18.10/3.25 | | | | | | | | & ( ~ (all_64_0 = 0) | all_92_0 = 0)) % 18.10/3.25 | | | | | | | | % 18.10/3.25 | | | | | | | | BETA: splitting (65) gives: % 18.10/3.25 | | | | | | | | % 18.10/3.25 | | | | | | | | Case 1: % 18.10/3.25 | | | | | | | | | % 18.10/3.25 | | | | | | | | | (66) ~ (all_92_2 = 0) % 18.10/3.25 | | | | | | | | | % 18.10/3.25 | | | | | | | | | REDUCE: (60), (66) imply: % 18.10/3.25 | | | | | | | | | (67) $false % 18.10/3.25 | | | | | | | | | % 18.10/3.25 | | | | | | | | | CLOSE: (67) is inconsistent. % 18.10/3.25 | | | | | | | | | % 18.10/3.25 | | | | | | | | Case 2: % 18.10/3.25 | | | | | | | | | % 18.10/3.25 | | | | | | | | | (68) ( ~ (all_92_0 = 0) | all_64_0 = 0) & ( ~ (all_64_0 = % 18.10/3.25 | | | | | | | | | 0) | all_92_0 = 0) % 18.10/3.25 | | | | | | | | | % 18.10/3.25 | | | | | | | | | ALPHA: (68) implies: % 18.10/3.25 | | | | | | | | | (69) ~ (all_92_0 = 0) | all_64_0 = 0 % 18.10/3.25 | | | | | | | | | % 18.10/3.25 | | | | | | | | | BETA: splitting (69) gives: % 18.10/3.25 | | | | | | | | | % 18.10/3.25 | | | | | | | | | Case 1: % 18.10/3.25 | | | | | | | | | | % 18.10/3.25 | | | | | | | | | | (70) ~ (all_92_0 = 0) % 18.10/3.25 | | | | | | | | | | % 18.10/3.25 | | | | | | | | | | REDUCE: (62), (70) imply: % 18.10/3.25 | | | | | | | | | | (71) $false % 18.10/3.25 | | | | | | | | | | % 18.10/3.25 | | | | | | | | | | CLOSE: (71) is inconsistent. % 18.10/3.25 | | | | | | | | | | % 18.10/3.25 | | | | | | | | | Case 2: % 18.10/3.25 | | | | | | | | | | % 18.10/3.25 | | | | | | | | | | (72) all_64_0 = 0 % 18.10/3.25 | | | | | | | | | | % 18.10/3.25 | | | | | | | | | | REDUCE: (53), (72) imply: % 18.10/3.25 | | | | | | | | | | (73) $false % 18.10/3.25 | | | | | | | | | | % 18.10/3.25 | | | | | | | | | | CLOSE: (73) is inconsistent. % 18.10/3.25 | | | | | | | | | | % 18.10/3.25 | | | | | | | | | End of split % 18.10/3.25 | | | | | | | | | % 18.10/3.25 | | | | | | | | End of split % 18.10/3.25 | | | | | | | | % 18.10/3.25 | | | | | | | End of split % 18.10/3.25 | | | | | | | % 18.10/3.25 | | | | | | Case 2: % 18.10/3.25 | | | | | | | % 18.10/3.25 | | | | | | | (74) all_64_0 = 0 % 18.10/3.25 | | | | | | | % 18.10/3.25 | | | | | | | COMBINE_EQS: (52), (74) imply: % 18.10/3.25 | | | | | | | (75) all_68_0 = 0 % 18.10/3.25 | | | | | | | % 18.10/3.25 | | | | | | | REF_CLOSE: (45), (51), (75) are inconsistent by sub-proof #1. % 18.10/3.25 | | | | | | | % 18.10/3.25 | | | | | | End of split % 18.10/3.25 | | | | | | % 18.10/3.25 | | | | | Case 2: % 18.10/3.25 | | | | | | % 18.10/3.25 | | | | | | (76) member(all_44_1, all_32_4) = all_64_0 & member(all_44_1, % 18.10/3.25 | | | | | | all_32_4) = all_64_1 & ( ~ (all_64_0 = 0) | ~ (all_64_1 = % 18.10/3.25 | | | | | | 0)) % 18.10/3.25 | | | | | | % 18.10/3.25 | | | | | | ALPHA: (76) implies: % 18.10/3.25 | | | | | | (77) member(all_44_1, all_32_4) = all_64_1 % 18.10/3.25 | | | | | | (78) member(all_44_1, all_32_4) = all_64_0 % 18.10/3.25 | | | | | | (79) ~ (all_64_0 = 0) | ~ (all_64_1 = 0) % 18.10/3.25 | | | | | | % 18.10/3.25 | | | | | | GROUND_INST: instantiating (5) with 0, all_64_0, all_32_4, all_44_1, % 18.10/3.25 | | | | | | simplifying with (25), (78) gives: % 18.10/3.25 | | | | | | (80) all_64_0 = 0 % 18.10/3.25 | | | | | | % 18.10/3.25 | | | | | | GROUND_INST: instantiating (5) with all_64_1, all_64_0, all_32_4, % 18.10/3.25 | | | | | | all_44_1, simplifying with (77), (78) gives: % 18.10/3.25 | | | | | | (81) all_64_0 = all_64_1 % 18.10/3.25 | | | | | | % 18.10/3.25 | | | | | | COMBINE_EQS: (80), (81) imply: % 18.10/3.25 | | | | | | (82) all_64_1 = 0 % 18.10/3.25 | | | | | | % 18.10/3.25 | | | | | | BETA: splitting (79) gives: % 18.10/3.25 | | | | | | % 18.10/3.25 | | | | | | Case 1: % 18.10/3.25 | | | | | | | % 18.10/3.25 | | | | | | | (83) ~ (all_64_0 = 0) % 18.10/3.25 | | | | | | | % 18.10/3.25 | | | | | | | REDUCE: (80), (83) imply: % 18.10/3.25 | | | | | | | (84) $false % 18.10/3.25 | | | | | | | % 18.10/3.25 | | | | | | | CLOSE: (84) is inconsistent. % 18.10/3.25 | | | | | | | % 18.10/3.25 | | | | | | Case 2: % 18.10/3.25 | | | | | | | % 18.10/3.25 | | | | | | | (85) ~ (all_64_1 = 0) % 18.10/3.25 | | | | | | | % 18.10/3.25 | | | | | | | REDUCE: (82), (85) imply: % 18.10/3.25 | | | | | | | (86) $false % 18.10/3.25 | | | | | | | % 18.10/3.25 | | | | | | | CLOSE: (86) is inconsistent. % 18.10/3.25 | | | | | | | % 18.10/3.25 | | | | | | End of split % 18.10/3.25 | | | | | | % 18.10/3.25 | | | | | End of split % 18.10/3.25 | | | | | % 18.10/3.25 | | | | Case 2: % 18.10/3.25 | | | | | % 18.10/3.25 | | | | | (87) member(all_44_1, all_32_4) = all_68_0 & member(all_44_1, % 18.10/3.25 | | | | | all_32_4) = all_68_1 & ( ~ (all_68_0 = 0) | ~ (all_68_1 = % 18.10/3.25 | | | | | 0)) % 18.10/3.25 | | | | | % 18.10/3.25 | | | | | ALPHA: (87) implies: % 18.10/3.25 | | | | | (88) member(all_44_1, all_32_4) = all_68_1 % 18.10/3.25 | | | | | (89) member(all_44_1, all_32_4) = all_68_0 % 18.10/3.25 | | | | | (90) ~ (all_68_0 = 0) | ~ (all_68_1 = 0) % 18.10/3.25 | | | | | % 18.10/3.25 | | | | | GROUND_INST: instantiating (5) with 0, all_68_0, all_32_4, all_44_1, % 18.10/3.25 | | | | | simplifying with (25), (89) gives: % 18.10/3.25 | | | | | (91) all_68_0 = 0 % 18.10/3.25 | | | | | % 18.10/3.25 | | | | | GROUND_INST: instantiating (5) with all_68_1, all_68_0, all_32_4, % 18.10/3.25 | | | | | all_44_1, simplifying with (88), (89) gives: % 18.10/3.25 | | | | | (92) all_68_0 = all_68_1 % 18.10/3.25 | | | | | % 18.10/3.25 | | | | | COMBINE_EQS: (91), (92) imply: % 18.10/3.25 | | | | | (93) all_68_1 = 0 % 18.10/3.25 | | | | | % 18.10/3.25 | | | | | REF_CLOSE: (90), (91), (93) are inconsistent by sub-proof #1. % 18.10/3.25 | | | | | % 18.10/3.25 | | | | End of split % 18.10/3.25 | | | | % 18.10/3.25 | | | End of split % 18.10/3.25 | | | % 18.10/3.25 | | End of split % 18.10/3.25 | | % 18.10/3.25 | End of split % 18.10/3.25 | % 18.10/3.25 End of proof % 18.10/3.26 % 18.10/3.26 Sub-proof #1 shows that the following formulas are inconsistent: % 18.10/3.26 ---------------------------------------------------------------- % 18.10/3.26 (1) ~ (all_68_0 = 0) | ~ (all_68_1 = 0) % 18.10/3.26 (2) all_68_0 = 0 % 18.10/3.26 (3) all_68_1 = 0 % 18.10/3.26 % 18.10/3.26 Begin of proof % 18.10/3.26 | % 18.10/3.26 | BETA: splitting (1) gives: % 18.10/3.26 | % 18.10/3.26 | Case 1: % 18.10/3.26 | | % 18.10/3.26 | | (4) ~ (all_68_0 = 0) % 18.10/3.26 | | % 18.10/3.26 | | REDUCE: (2), (4) imply: % 18.10/3.26 | | (5) $false % 18.10/3.26 | | % 18.10/3.26 | | CLOSE: (5) is inconsistent. % 18.10/3.26 | | % 18.10/3.26 | Case 2: % 18.10/3.26 | | % 18.10/3.26 | | (6) ~ (all_68_1 = 0) % 18.10/3.26 | | % 18.10/3.26 | | REDUCE: (3), (6) imply: % 18.10/3.26 | | (7) $false % 18.10/3.26 | | % 18.10/3.26 | | CLOSE: (7) is inconsistent. % 18.10/3.26 | | % 18.10/3.26 | End of split % 18.10/3.26 | % 18.10/3.26 End of proof % 18.10/3.26 % SZS output end Proof for theBenchmark % 18.10/3.26 % 18.10/3.26 2683ms %------------------------------------------------------------------------------