%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET743+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 : n019.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 15:26:14 EDT 2023 % Result : Theorem 77.85s 11.15s % Output : Proof 79.48s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET743+4 : TPTP v8.1.2. Bugfixed v2.2.1. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n019.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 12:06:43 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.62 Running up to 7 provers in parallel. % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.58/1.24 Prover 1: Preprocessing ... % 3.58/1.24 Prover 4: Preprocessing ... % 3.58/1.34 Prover 6: Preprocessing ... % 3.58/1.34 Prover 3: Preprocessing ... % 3.58/1.34 Prover 5: Preprocessing ... % 3.58/1.35 Prover 0: Preprocessing ... % 4.28/1.35 Prover 2: Preprocessing ... % 9.70/2.12 Prover 2: Proving ... % 9.70/2.13 Prover 6: Proving ... % 9.70/2.13 Prover 5: Proving ... % 10.34/2.18 Prover 1: Constructing countermodel ... % 10.34/2.21 Prover 3: Constructing countermodel ... % 10.98/2.30 Prover 3: gave up % 10.98/2.30 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.98/2.31 Prover 1: gave up % 10.98/2.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.61/2.36 Prover 7: Preprocessing ... % 11.98/2.39 Prover 8: Preprocessing ... % 12.62/2.48 Prover 4: Constructing countermodel ... % 12.99/2.52 Prover 0: Proving ... % 12.99/2.53 Prover 7: Warning: ignoring some quantifiers % 13.27/2.58 Prover 7: Constructing countermodel ... % 13.27/2.70 Prover 8: Warning: ignoring some quantifiers % 13.27/2.71 Prover 8: Constructing countermodel ... % 15.21/2.88 Prover 8: gave up % 15.21/2.88 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 15.71/2.92 Prover 9: Preprocessing ... % 19.79/3.45 Prover 9: Constructing countermodel ... % 62.05/9.05 Prover 2: stopped % 62.05/9.06 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 62.87/9.13 Prover 10: Preprocessing ... % 63.87/9.24 Prover 10: Warning: ignoring some quantifiers % 63.87/9.26 Prover 10: Constructing countermodel ... % 64.90/9.37 Prover 10: gave up % 65.20/9.39 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 65.62/9.45 Prover 11: Preprocessing ... % 66.57/9.85 Prover 11: Constructing countermodel ... % 77.85/11.14 Prover 4: Found proof (size 390) % 77.85/11.14 Prover 4: proved (10500ms) % 77.85/11.14 Prover 6: stopped % 77.85/11.14 Prover 5: stopped % 77.85/11.14 Prover 11: stopped % 77.85/11.15 Prover 0: stopped % 77.85/11.15 Prover 9: stopped % 77.85/11.15 Prover 7: stopped % 77.85/11.15 % 77.85/11.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 77.85/11.15 % 77.85/11.16 % SZS output start Proof for theBenchmark % 77.85/11.16 Assumptions after simplification: % 77.85/11.16 --------------------------------- % 77.85/11.16 % 77.85/11.16 (compose_function) % 78.79/11.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 78.79/11.20 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 78.79/11.20 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 78.79/11.20 ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | % 78.79/11.20 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] % 78.79/11.20 : ((apply(v0, v9, v6) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 % 78.79/11.20 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = % 78.79/11.20 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 78.79/11.20 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: % 78.79/11.20 int] : ! [v9: $i] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = % 78.79/11.20 v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) % 78.79/11.20 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 78.79/11.20 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v11 & % 78.79/11.20 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4) % 78.79/11.20 = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & ! % 78.79/11.20 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 78.79/11.20 : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~ % 78.79/11.20 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) | % 78.79/11.20 ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ % 78.79/11.20 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] : % 78.79/11.20 ((apply(v1, v5, v9) = v10 & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~ % 78.79/11.20 (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 % 78.79/11.20 = 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 78.79/11.20 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ % 78.79/11.20 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | % 78.79/11.20 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 78.79/11.20 $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ? % 78.79/11.20 [v12: int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 & % 78.79/11.20 apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, v3) = 0) % 78.79/11.20 | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 = % 78.79/11.20 0)))))) % 78.79/11.20 % 78.79/11.20 (injective) % 78.79/11.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 78.79/11.21 $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) % 78.79/11.21 | ~ (apply(v0, v3, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) % 78.79/11.21 | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 78.79/11.21 (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = % 78.79/11.21 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 78.79/11.21 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ % 78.79/11.21 (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3, % 78.79/11.21 v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 78.79/11.21 ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v5) = % 78.79/11.21 v8 & member(v5, v2) = v7 & member(v4, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = % 78.79/11.21 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 78.79/11.21 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = % 78.79/11.21 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ~ $i(v5) | ~ % 78.79/11.21 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? % 78.79/11.21 [v7: any] : ? [v8: any] : (apply(v0, v4, v5) = v8 & member(v5, v2) = v7 & % 78.79/11.21 member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! % 78.79/11.21 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] % 78.79/11.21 : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ % 78.79/11.21 (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 78.79/11.21 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 78.79/11.21 (apply(v0, v4, v5) = v7 & apply(v0, v3, v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = % 78.79/11.21 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = % 78.79/11.21 0 | ~ (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 78.79/11.21 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0 % 78.79/11.21 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 & % 78.79/11.21 member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4))) % 78.79/11.21 % 78.79/11.21 (maps) % 78.79/11.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 78.79/11.22 $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ % 78.79/11.22 (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 78.79/11.22 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : % 78.79/11.22 (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = % 78.79/11.22 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 78.79/11.22 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, % 78.79/11.22 v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ~ % 78.79/11.22 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: % 78.79/11.22 any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, % 78.79/11.22 v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = % 78.79/11.22 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 78.79/11.22 [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, % 78.79/11.22 v3, v4) = 0) | ~ (member(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ % 78.79/11.22 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : % 78.79/11.22 ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v4, v2) = v7 & member(v3, v1) % 78.79/11.22 = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: % 78.79/11.22 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ % 78.79/11.22 (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) | % 78.79/11.22 ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ % 78.79/11.22 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & % 78.79/11.22 apply(v0, v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! % 78.79/11.22 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) | % 78.79/11.22 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i] % 78.79/11.22 : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int] % 78.79/11.22 : ? [v12: $i] : ? [v13: int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13 % 78.79/11.22 = 0 & member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) = % 78.79/11.22 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & member(v14, v2) % 78.79/11.22 = v15)) & ! [v14: $i] : ( ~ (member(v14, v2) = 0) | ~ $i(v14) | % 78.79/11.22 ? [v15: int] : ( ~ (v15 = 0) & apply(v0, v12, v14) = v15))) | (v11 = % 78.79/11.22 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, % 78.79/11.22 v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, % 78.79/11.22 v2) = 0 & member(v4, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : ! % 78.79/11.22 [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0) % 78.79/11.22 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, % 78.79/11.22 v3, v4) = 0 & member(v4, v2) = 0 & $i(v4))) % 78.79/11.22 % 78.79/11.22 (one_to_one) % 78.79/11.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 78.79/11.22 (one_to_one(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 78.79/11.22 any] : ? [v5: any] : (surjective(v0, v1, v2) = v5 & injective(v0, v1, v2) % 78.79/11.22 = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 78.79/11.22 $i] : ! [v3: any] : ( ~ (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ % 78.79/11.22 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (one_to_one(v0, v1, v2) = % 78.79/11.22 v4 & injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! % 78.79/11.22 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (injective(v0, v1, % 78.79/11.22 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: % 78.79/11.22 any] : (one_to_one(v0, v1, v2) = v4 & surjective(v0, v1, v2) = v5 & ( ~ % 78.79/11.22 (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 78.79/11.22 $i] : ( ~ (one_to_one(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 78.79/11.22 (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0)) & ! [v0: $i] : ! % 78.79/11.22 [v1: $i] : ! [v2: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ $i(v2) | ~ % 78.79/11.22 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) = % 78.79/11.22 v4 & injective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] : % 78.79/11.22 ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = 0) | ~ $i(v2) | ~ % 78.79/11.22 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) = % 78.79/11.22 v4 & surjective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) % 78.79/11.22 % 78.79/11.22 (surjective) % 78.79/11.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 78.79/11.22 (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: % 78.79/11.22 $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ (apply(v0, v5, v4) % 78.79/11.22 = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6)) % 78.79/11.22 & ! [v5: $i] : ( ~ (member(v5, v1) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ % 78.79/11.22 (v6 = 0) & apply(v0, v5, v4) = v6)))) & ! [v0: $i] : ! [v1: $i] : ! % 78.79/11.22 [v2: $i] : ! [v3: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) % 78.79/11.23 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : % 78.79/11.23 (apply(v0, v4, v3) = 0 & member(v4, v1) = 0 & $i(v4))) % 78.79/11.23 % 78.79/11.23 (thII34) % 78.79/11.23 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 78.79/11.23 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & % 78.79/11.23 one_to_one(v7, v4, v3) = 0 & one_to_one(v6, v3, v5) = 0 & one_to_one(v1, v4, % 78.79/11.23 v5) = v8 & compose_function(v2, v1, v4, v5, v3) = v7 & % 78.79/11.23 compose_function(v1, v0, v3, v4, v5) = v6 & maps(v2, v5, v3) = 0 & maps(v1, % 78.79/11.23 v4, v5) = 0 & maps(v0, v3, v4) = 0 & $i(v7) & $i(v6) & $i(v5) & $i(v4) & % 78.79/11.23 $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 78.79/11.23 % 78.79/11.23 (function-axioms) % 78.79/11.24 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 78.79/11.24 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 | % 78.79/11.24 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~ % 78.79/11.24 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0: % 78.79/11.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 78.79/11.24 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5, % 78.79/11.24 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 78.79/11.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 78.79/11.24 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5, % 78.79/11.24 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 78.79/11.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 78.79/11.24 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5, % 78.79/11.24 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0: % 78.79/11.24 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : % 78.79/11.24 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~ % 78.79/11.24 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : % 78.79/11.24 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 78.79/11.24 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~ % 78.79/11.24 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 78.79/11.24 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 78.79/11.24 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5, % 78.79/11.24 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 78.79/11.24 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~ % 78.79/11.24 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 78.79/11.24 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~ % 78.79/11.24 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 78.79/11.24 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) | % 78.79/11.24 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 78.79/11.24 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | % 78.79/11.24 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & ! % 78.79/11.24 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 78.79/11.24 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~ % 78.79/11.24 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 78.79/11.24 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ % 78.79/11.24 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0: % 78.79/11.24 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 78.79/11.24 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) = % 78.79/11.24 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 78.79/11.24 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 78.79/11.24 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! % 78.79/11.24 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~ % 78.79/11.24 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 78.79/11.24 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) & % 78.79/11.24 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 78.79/11.24 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0)) % 78.79/11.24 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 78.79/11.24 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 78.79/11.24 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 78.79/11.24 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 78.79/11.24 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 78.79/11.24 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 78.79/11.24 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 78.79/11.24 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 78.79/11.24 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 78.79/11.24 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 78.79/11.24 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 78.79/11.24 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 78.79/11.24 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 78.79/11.24 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 78.79/11.24 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 78.79/11.24 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 78.79/11.24 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 78.79/11.24 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 78.79/11.24 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 78.79/11.24 (power_set(v2) = v0)) % 78.79/11.24 % 78.79/11.24 Further assumptions not needed in the proof: % 78.79/11.24 -------------------------------------------- % 78.79/11.24 compose_predicate, decreasing_function, difference, empty_set, equal_maps, % 78.79/11.24 equal_set, identity, image2, image3, increasing_function, intersection, % 78.79/11.24 inverse_function, inverse_image2, inverse_image3, inverse_predicate, % 78.79/11.24 isomorphism, power_set, product, singleton, subset, sum, union, unordered_pair % 78.79/11.24 % 78.79/11.24 Those formulas are unsatisfiable: % 78.79/11.24 --------------------------------- % 78.79/11.24 % 78.79/11.24 Begin of proof % 78.79/11.24 | % 78.79/11.24 | ALPHA: (maps) implies: % 78.79/11.24 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, % 78.79/11.24 | v1, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) | % 78.79/11.24 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v3, v4) = 0 & % 78.79/11.24 | member(v4, v2) = 0 & $i(v4))) % 78.79/11.24 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 78.79/11.24 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) % 78.79/11.24 | = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~ % 78.79/11.24 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 78.79/11.24 | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & apply(v0, v3, % 78.79/11.24 | v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 78.79/11.24 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 78.79/11.24 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, % 78.79/11.24 | v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | % 78.79/11.24 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: % 78.79/11.24 | any] : ? [v8: any] : (member(v5, v2) = v8 & member(v4, v2) = v7 & % 78.79/11.24 | member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) % 78.79/11.24 | % 78.79/11.24 | ALPHA: (compose_function) implies: % 78.79/11.24 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 78.79/11.24 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (compose_function(v0, v1, % 78.79/11.24 | v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | ~ $i(v6) | ~ % 78.79/11.24 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 78.79/11.24 | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ? [v12: % 78.79/11.24 | int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 & % 78.79/11.24 | apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, % 78.79/11.24 | v3) = 0) | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ % 78.79/11.24 | (v9 = 0) | ~ (v8 = 0)))))) % 78.79/11.25 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 78.79/11.25 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : % 78.79/11.25 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ % 78.79/11.25 | (apply(v7, v5, v6) = v8) | ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ % 78.79/11.25 | $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | % 78.79/11.25 | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v10 % 78.79/11.25 | & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 78.79/11.25 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 78.79/11.25 | (v10 = 0))))) % 78.79/11.25 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 78.79/11.25 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : % 78.79/11.25 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~ % 78.79/11.25 | (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) | % 78.79/11.25 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) % 78.79/11.25 | | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = % 78.79/11.25 | v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | % 78.79/11.25 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ % 78.79/11.25 | (v10 = 0))))) % 78.79/11.25 | % 78.79/11.25 | ALPHA: (injective) implies: % 79.26/11.25 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 79.26/11.25 | (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 79.26/11.25 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, % 79.26/11.25 | v6) = 0 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, % 79.26/11.25 | v1) = 0 & member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4))) % 79.26/11.25 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : % 79.26/11.25 | ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, % 79.26/11.25 | v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ % 79.26/11.25 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 79.26/11.25 | ? [v6: any] : ? [v7: any] : (apply(v0, v4, v5) = v7 & apply(v0, v3, % 79.26/11.25 | v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) % 79.26/11.25 | % 79.26/11.25 | ALPHA: (surjective) implies: % 79.26/11.25 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 79.26/11.25 | (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ~ $i(v3) | % 79.26/11.25 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v4, v3) = % 79.26/11.25 | 0 & member(v4, v1) = 0 & $i(v4))) % 79.26/11.25 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 79.26/11.25 | (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 79.26/11.25 | ? [v4: $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ % 79.26/11.25 | (apply(v0, v5, v4) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = % 79.26/11.25 | 0) & member(v5, v1) = v6)) & ! [v5: $i] : ( ~ (member(v5, % 79.26/11.25 | v1) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & % 79.26/11.25 | apply(v0, v5, v4) = v6)))) % 79.26/11.25 | % 79.26/11.25 | ALPHA: (one_to_one) implies: % 79.26/11.26 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (one_to_one(v0, v1, v2) % 79.26/11.26 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (surjective(v0, v1, v2) % 79.26/11.26 | = 0 & injective(v0, v1, v2) = 0)) % 79.26/11.26 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 79.26/11.26 | (one_to_one(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 79.26/11.26 | ? [v4: any] : ? [v5: any] : (surjective(v0, v1, v2) = v5 & % 79.26/11.26 | injective(v0, v1, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) % 79.26/11.26 | % 79.26/11.26 | ALPHA: (function-axioms) implies: % 79.26/11.26 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 79.26/11.26 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, % 79.26/11.26 | v2) = v0)) % 79.26/11.26 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 79.26/11.26 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | % 79.26/11.26 | ~ (apply(v4, v3, v2) = v0)) % 79.26/11.26 | % 79.26/11.26 | DELTA: instantiating (thII34) with fresh symbols all_32_0, all_32_1, all_32_2, % 79.26/11.26 | all_32_3, all_32_4, all_32_5, all_32_6, all_32_7, all_32_8 gives: % 79.26/11.26 | (15) ~ (all_32_0 = 0) & one_to_one(all_32_1, all_32_4, all_32_5) = 0 & % 79.26/11.26 | one_to_one(all_32_2, all_32_5, all_32_3) = 0 & one_to_one(all_32_7, % 79.26/11.26 | all_32_4, all_32_3) = all_32_0 & compose_function(all_32_6, % 79.26/11.26 | all_32_7, all_32_4, all_32_3, all_32_5) = all_32_1 & % 79.26/11.26 | compose_function(all_32_7, all_32_8, all_32_5, all_32_4, all_32_3) = % 79.26/11.26 | all_32_2 & maps(all_32_6, all_32_3, all_32_5) = 0 & maps(all_32_7, % 79.26/11.26 | all_32_4, all_32_3) = 0 & maps(all_32_8, all_32_5, all_32_4) = 0 & % 79.26/11.26 | $i(all_32_1) & $i(all_32_2) & $i(all_32_3) & $i(all_32_4) & % 79.26/11.26 | $i(all_32_5) & $i(all_32_6) & $i(all_32_7) & $i(all_32_8) % 79.26/11.26 | % 79.26/11.26 | ALPHA: (15) implies: % 79.26/11.26 | (16) ~ (all_32_0 = 0) % 79.26/11.26 | (17) $i(all_32_8) % 79.26/11.26 | (18) $i(all_32_7) % 79.26/11.26 | (19) $i(all_32_6) % 79.26/11.26 | (20) $i(all_32_5) % 79.26/11.26 | (21) $i(all_32_4) % 79.26/11.26 | (22) $i(all_32_3) % 79.26/11.26 | (23) $i(all_32_2) % 79.26/11.26 | (24) $i(all_32_1) % 79.26/11.26 | (25) maps(all_32_8, all_32_5, all_32_4) = 0 % 79.26/11.26 | (26) maps(all_32_7, all_32_4, all_32_3) = 0 % 79.26/11.26 | (27) maps(all_32_6, all_32_3, all_32_5) = 0 % 79.26/11.26 | (28) compose_function(all_32_7, all_32_8, all_32_5, all_32_4, all_32_3) = % 79.26/11.26 | all_32_2 % 79.26/11.26 | (29) compose_function(all_32_6, all_32_7, all_32_4, all_32_3, all_32_5) = % 79.26/11.26 | all_32_1 % 79.26/11.26 | (30) one_to_one(all_32_7, all_32_4, all_32_3) = all_32_0 % 79.26/11.26 | (31) one_to_one(all_32_2, all_32_5, all_32_3) = 0 % 79.26/11.26 | (32) one_to_one(all_32_1, all_32_4, all_32_5) = 0 % 79.26/11.26 | % 79.26/11.26 | GROUND_INST: instantiating (12) with all_32_7, all_32_4, all_32_3, all_32_0, % 79.26/11.26 | simplifying with (18), (21), (22), (30) gives: % 79.26/11.26 | (33) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (surjective(all_32_7, % 79.26/11.26 | all_32_4, all_32_3) = v1 & injective(all_32_7, all_32_4, all_32_3) % 79.26/11.26 | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 79.26/11.26 | % 79.26/11.26 | GROUND_INST: instantiating (11) with all_32_2, all_32_5, all_32_3, simplifying % 79.26/11.26 | with (20), (22), (23), (31) gives: % 79.26/11.26 | (34) surjective(all_32_2, all_32_5, all_32_3) = 0 & injective(all_32_2, % 79.26/11.26 | all_32_5, all_32_3) = 0 % 79.26/11.26 | % 79.26/11.26 | ALPHA: (34) implies: % 79.26/11.26 | (35) surjective(all_32_2, all_32_5, all_32_3) = 0 % 79.26/11.26 | % 79.26/11.26 | GROUND_INST: instantiating (11) with all_32_1, all_32_4, all_32_5, simplifying % 79.26/11.26 | with (20), (21), (24), (32) gives: % 79.26/11.26 | (36) surjective(all_32_1, all_32_4, all_32_5) = 0 & injective(all_32_1, % 79.26/11.26 | all_32_4, all_32_5) = 0 % 79.26/11.26 | % 79.26/11.26 | ALPHA: (36) implies: % 79.26/11.26 | (37) injective(all_32_1, all_32_4, all_32_5) = 0 % 79.26/11.26 | (38) surjective(all_32_1, all_32_4, all_32_5) = 0 % 79.26/11.26 | % 79.26/11.26 | BETA: splitting (33) gives: % 79.26/11.26 | % 79.26/11.26 | Case 1: % 79.26/11.26 | | % 79.26/11.26 | | (39) all_32_0 = 0 % 79.26/11.26 | | % 79.26/11.26 | | REDUCE: (16), (39) imply: % 79.26/11.26 | | (40) $false % 79.26/11.27 | | % 79.26/11.27 | | CLOSE: (40) is inconsistent. % 79.26/11.27 | | % 79.26/11.27 | Case 2: % 79.26/11.27 | | % 79.26/11.27 | | (41) ? [v0: any] : ? [v1: any] : (surjective(all_32_7, all_32_4, % 79.26/11.27 | | all_32_3) = v1 & injective(all_32_7, all_32_4, all_32_3) = v0 & % 79.26/11.27 | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 79.26/11.27 | | % 79.26/11.27 | | DELTA: instantiating (41) with fresh symbols all_44_0, all_44_1 gives: % 79.26/11.27 | | (42) surjective(all_32_7, all_32_4, all_32_3) = all_44_0 & % 79.26/11.27 | | injective(all_32_7, all_32_4, all_32_3) = all_44_1 & ( ~ (all_44_0 = % 79.26/11.27 | | 0) | ~ (all_44_1 = 0)) % 79.26/11.27 | | % 79.26/11.27 | | ALPHA: (42) implies: % 79.26/11.27 | | (43) injective(all_32_7, all_32_4, all_32_3) = all_44_1 % 79.26/11.27 | | (44) surjective(all_32_7, all_32_4, all_32_3) = all_44_0 % 79.26/11.27 | | (45) ~ (all_44_0 = 0) | ~ (all_44_1 = 0) % 79.26/11.27 | | % 79.26/11.27 | | GROUND_INST: instantiating (7) with all_32_7, all_32_4, all_32_3, all_44_1, % 79.26/11.27 | | simplifying with (18), (21), (22), (43) gives: % 79.26/11.27 | | (46) all_44_1 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = % 79.26/11.27 | | v0) & apply(all_32_7, v1, v2) = 0 & apply(all_32_7, v0, v2) = 0 % 79.26/11.27 | | & member(v2, all_32_3) = 0 & member(v1, all_32_4) = 0 & member(v0, % 79.26/11.27 | | all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0)) % 79.26/11.27 | | % 79.26/11.27 | | GROUND_INST: instantiating (10) with all_32_7, all_32_4, all_32_3, all_44_0, % 79.26/11.27 | | simplifying with (18), (21), (22), (44) gives: % 79.26/11.27 | | (47) all_44_0 = 0 | ? [v0: $i] : (member(v0, all_32_3) = 0 & $i(v0) & ! % 79.26/11.27 | | [v1: $i] : ( ~ (apply(all_32_7, v1, v0) = 0) | ~ $i(v1) | ? [v2: % 79.26/11.27 | | int] : ( ~ (v2 = 0) & member(v1, all_32_4) = v2)) & ! [v1: % 79.26/11.27 | | $i] : ( ~ (member(v1, all_32_4) = 0) | ~ $i(v1) | ? [v2: int] % 79.26/11.27 | | : ( ~ (v2 = 0) & apply(all_32_7, v1, v0) = v2))) % 79.26/11.27 | | % 79.26/11.27 | | BETA: splitting (45) gives: % 79.26/11.27 | | % 79.26/11.27 | | Case 1: % 79.26/11.27 | | | % 79.26/11.27 | | | (48) ~ (all_44_0 = 0) % 79.26/11.27 | | | % 79.26/11.27 | | | BETA: splitting (47) gives: % 79.26/11.27 | | | % 79.26/11.27 | | | Case 1: % 79.26/11.27 | | | | % 79.26/11.27 | | | | (49) all_44_0 = 0 % 79.26/11.27 | | | | % 79.26/11.27 | | | | REDUCE: (48), (49) imply: % 79.26/11.27 | | | | (50) $false % 79.26/11.27 | | | | % 79.26/11.27 | | | | CLOSE: (50) is inconsistent. % 79.26/11.27 | | | | % 79.26/11.27 | | | Case 2: % 79.26/11.27 | | | | % 79.26/11.27 | | | | (51) ? [v0: $i] : (member(v0, all_32_3) = 0 & $i(v0) & ! [v1: $i] : % 79.26/11.27 | | | | ( ~ (apply(all_32_7, v1, v0) = 0) | ~ $i(v1) | ? [v2: int] : % 79.26/11.27 | | | | ( ~ (v2 = 0) & member(v1, all_32_4) = v2)) & ! [v1: $i] : ( % 79.26/11.27 | | | | ~ (member(v1, all_32_4) = 0) | ~ $i(v1) | ? [v2: int] : ( % 79.26/11.27 | | | | ~ (v2 = 0) & apply(all_32_7, v1, v0) = v2))) % 79.26/11.27 | | | | % 79.26/11.27 | | | | DELTA: instantiating (51) with fresh symbol all_57_0 gives: % 79.26/11.27 | | | | (52) member(all_57_0, all_32_3) = 0 & $i(all_57_0) & ! [v0: $i] : ( % 79.26/11.27 | | | | ~ (apply(all_32_7, v0, all_57_0) = 0) | ~ $i(v0) | ? [v1: % 79.26/11.27 | | | | int] : ( ~ (v1 = 0) & member(v0, all_32_4) = v1)) & ! [v0: % 79.26/11.27 | | | | $i] : ( ~ (member(v0, all_32_4) = 0) | ~ $i(v0) | ? [v1: % 79.26/11.27 | | | | int] : ( ~ (v1 = 0) & apply(all_32_7, v0, all_57_0) = v1)) % 79.26/11.27 | | | | % 79.26/11.27 | | | | ALPHA: (52) implies: % 79.26/11.27 | | | | (53) $i(all_57_0) % 79.26/11.27 | | | | (54) member(all_57_0, all_32_3) = 0 % 79.26/11.27 | | | | (55) ! [v0: $i] : ( ~ (apply(all_32_7, v0, all_57_0) = 0) | ~ % 79.26/11.27 | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_32_4) = % 79.26/11.27 | | | | v1)) % 79.26/11.27 | | | | % 79.26/11.27 | | | | GROUND_INST: instantiating (9) with all_32_2, all_32_5, all_32_3, % 79.26/11.27 | | | | all_57_0, simplifying with (20), (22), (23), (35), (53), % 79.26/11.27 | | | | (54) gives: % 79.26/11.27 | | | | (56) ? [v0: $i] : (apply(all_32_2, v0, all_57_0) = 0 & member(v0, % 79.26/11.27 | | | | all_32_5) = 0 & $i(v0)) % 79.26/11.27 | | | | % 79.26/11.27 | | | | DELTA: instantiating (56) with fresh symbol all_65_0 gives: % 79.26/11.27 | | | | (57) apply(all_32_2, all_65_0, all_57_0) = 0 & member(all_65_0, % 79.26/11.27 | | | | all_32_5) = 0 & $i(all_65_0) % 79.26/11.27 | | | | % 79.26/11.27 | | | | ALPHA: (57) implies: % 79.26/11.27 | | | | (58) $i(all_65_0) % 79.26/11.27 | | | | (59) member(all_65_0, all_32_5) = 0 % 79.26/11.27 | | | | (60) apply(all_32_2, all_65_0, all_57_0) = 0 % 79.26/11.27 | | | | % 79.26/11.27 | | | | GROUND_INST: instantiating (4) with all_32_7, all_32_8, all_32_5, % 79.26/11.27 | | | | all_32_4, all_32_3, all_65_0, all_57_0, all_32_2, % 79.26/11.27 | | | | simplifying with (17), (18), (20), (21), (22), (28), (53), % 79.26/11.27 | | | | (58), (60) gives: % 79.26/11.28 | | | | (61) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: int] : ? % 79.26/11.28 | | | | [v4: int] : ? [v5: int] : ($i(v2) & ((v5 = 0 & v4 = 0 & v3 = 0 % 79.26/11.28 | | | | & apply(all_32_7, v2, all_57_0) = 0 & apply(all_32_8, % 79.26/11.28 | | | | all_65_0, v2) = 0 & member(v2, all_32_4) = 0) | % 79.26/11.28 | | | | (member(all_65_0, all_32_5) = v0 & member(all_57_0, % 79.26/11.28 | | | | all_32_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))) % 79.26/11.28 | | | | % 79.26/11.28 | | | | DELTA: instantiating (61) with fresh symbols all_82_0, all_82_1, % 79.26/11.28 | | | | all_82_2, all_82_3, all_82_4, all_82_5 gives: % 79.26/11.28 | | | | (62) $i(all_82_3) & ((all_82_0 = 0 & all_82_1 = 0 & all_82_2 = 0 & % 79.26/11.28 | | | | apply(all_32_7, all_82_3, all_57_0) = 0 & apply(all_32_8, % 79.26/11.28 | | | | all_65_0, all_82_3) = 0 & member(all_82_3, all_32_4) = 0) % 79.26/11.28 | | | | | (member(all_65_0, all_32_5) = all_82_5 & member(all_57_0, % 79.26/11.28 | | | | all_32_3) = all_82_4 & ( ~ (all_82_4 = 0) | ~ (all_82_5 = % 79.26/11.28 | | | | 0)))) % 79.26/11.28 | | | | % 79.26/11.28 | | | | ALPHA: (62) implies: % 79.26/11.28 | | | | (63) $i(all_82_3) % 79.26/11.28 | | | | (64) (all_82_0 = 0 & all_82_1 = 0 & all_82_2 = 0 & apply(all_32_7, % 79.26/11.28 | | | | all_82_3, all_57_0) = 0 & apply(all_32_8, all_65_0, % 79.26/11.28 | | | | all_82_3) = 0 & member(all_82_3, all_32_4) = 0) | % 79.26/11.28 | | | | (member(all_65_0, all_32_5) = all_82_5 & member(all_57_0, % 79.26/11.28 | | | | all_32_3) = all_82_4 & ( ~ (all_82_4 = 0) | ~ (all_82_5 = % 79.26/11.28 | | | | 0))) % 79.26/11.28 | | | | % 79.26/11.28 | | | | BETA: splitting (64) gives: % 79.26/11.28 | | | | % 79.26/11.28 | | | | Case 1: % 79.26/11.28 | | | | | % 79.26/11.28 | | | | | (65) all_82_0 = 0 & all_82_1 = 0 & all_82_2 = 0 & apply(all_32_7, % 79.26/11.28 | | | | | all_82_3, all_57_0) = 0 & apply(all_32_8, all_65_0, % 79.26/11.28 | | | | | all_82_3) = 0 & member(all_82_3, all_32_4) = 0 % 79.26/11.28 | | | | | % 79.26/11.28 | | | | | ALPHA: (65) implies: % 79.26/11.28 | | | | | (66) member(all_82_3, all_32_4) = 0 % 79.26/11.28 | | | | | (67) apply(all_32_7, all_82_3, all_57_0) = 0 % 79.26/11.28 | | | | | % 79.26/11.28 | | | | | GROUND_INST: instantiating (55) with all_82_3, simplifying with (63), % 79.26/11.28 | | | | | (67) gives: % 79.26/11.28 | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & member(all_82_3, all_32_4) = v0) % 79.26/11.28 | | | | | % 79.26/11.28 | | | | | DELTA: instantiating (68) with fresh symbol all_93_0 gives: % 79.26/11.28 | | | | | (69) ~ (all_93_0 = 0) & member(all_82_3, all_32_4) = all_93_0 % 79.26/11.28 | | | | | % 79.26/11.28 | | | | | ALPHA: (69) implies: % 79.26/11.28 | | | | | (70) ~ (all_93_0 = 0) % 79.26/11.28 | | | | | (71) member(all_82_3, all_32_4) = all_93_0 % 79.26/11.28 | | | | | % 79.26/11.28 | | | | | GROUND_INST: instantiating (13) with 0, all_93_0, all_32_4, all_82_3, % 79.26/11.28 | | | | | simplifying with (66), (71) gives: % 79.26/11.28 | | | | | (72) all_93_0 = 0 % 79.26/11.28 | | | | | % 79.26/11.28 | | | | | REDUCE: (70), (72) imply: % 79.26/11.28 | | | | | (73) $false % 79.26/11.28 | | | | | % 79.26/11.28 | | | | | CLOSE: (73) is inconsistent. % 79.26/11.28 | | | | | % 79.26/11.28 | | | | Case 2: % 79.26/11.28 | | | | | % 79.26/11.28 | | | | | (74) member(all_65_0, all_32_5) = all_82_5 & member(all_57_0, % 79.26/11.28 | | | | | all_32_3) = all_82_4 & ( ~ (all_82_4 = 0) | ~ (all_82_5 = % 79.26/11.28 | | | | | 0)) % 79.26/11.28 | | | | | % 79.26/11.28 | | | | | ALPHA: (74) implies: % 79.26/11.28 | | | | | (75) member(all_57_0, all_32_3) = all_82_4 % 79.26/11.28 | | | | | (76) member(all_65_0, all_32_5) = all_82_5 % 79.26/11.28 | | | | | (77) ~ (all_82_4 = 0) | ~ (all_82_5 = 0) % 79.26/11.28 | | | | | % 79.26/11.28 | | | | | GROUND_INST: instantiating (13) with 0, all_82_4, all_32_3, all_57_0, % 79.26/11.28 | | | | | simplifying with (54), (75) gives: % 79.26/11.28 | | | | | (78) all_82_4 = 0 % 79.26/11.28 | | | | | % 79.26/11.28 | | | | | GROUND_INST: instantiating (13) with 0, all_82_5, all_32_5, all_65_0, % 79.26/11.28 | | | | | simplifying with (59), (76) gives: % 79.26/11.28 | | | | | (79) all_82_5 = 0 % 79.26/11.28 | | | | | % 79.26/11.28 | | | | | BETA: splitting (77) gives: % 79.26/11.28 | | | | | % 79.26/11.28 | | | | | Case 1: % 79.26/11.28 | | | | | | % 79.26/11.28 | | | | | | (80) ~ (all_82_4 = 0) % 79.26/11.28 | | | | | | % 79.26/11.28 | | | | | | REDUCE: (78), (80) imply: % 79.26/11.28 | | | | | | (81) $false % 79.26/11.28 | | | | | | % 79.26/11.28 | | | | | | CLOSE: (81) is inconsistent. % 79.26/11.28 | | | | | | % 79.26/11.28 | | | | | Case 2: % 79.26/11.28 | | | | | | % 79.26/11.28 | | | | | | (82) ~ (all_82_5 = 0) % 79.26/11.28 | | | | | | % 79.26/11.28 | | | | | | REDUCE: (79), (82) imply: % 79.26/11.28 | | | | | | (83) $false % 79.26/11.28 | | | | | | % 79.26/11.28 | | | | | | CLOSE: (83) is inconsistent. % 79.26/11.28 | | | | | | % 79.26/11.28 | | | | | End of split % 79.26/11.28 | | | | | % 79.26/11.28 | | | | End of split % 79.26/11.28 | | | | % 79.26/11.28 | | | End of split % 79.26/11.28 | | | % 79.26/11.28 | | Case 2: % 79.26/11.28 | | | % 79.26/11.28 | | | (84) all_44_0 = 0 % 79.26/11.28 | | | (85) ~ (all_44_1 = 0) % 79.26/11.28 | | | % 79.26/11.28 | | | REDUCE: (44), (84) imply: % 79.26/11.28 | | | (86) surjective(all_32_7, all_32_4, all_32_3) = 0 % 79.26/11.28 | | | % 79.26/11.28 | | | BETA: splitting (46) gives: % 79.26/11.28 | | | % 79.26/11.28 | | | Case 1: % 79.26/11.28 | | | | % 79.26/11.28 | | | | (87) all_44_1 = 0 % 79.26/11.28 | | | | % 79.26/11.28 | | | | REDUCE: (85), (87) imply: % 79.26/11.28 | | | | (88) $false % 79.26/11.28 | | | | % 79.26/11.28 | | | | CLOSE: (88) is inconsistent. % 79.26/11.28 | | | | % 79.26/11.28 | | | Case 2: % 79.26/11.28 | | | | % 79.26/11.28 | | | | (89) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) & % 79.26/11.28 | | | | apply(all_32_7, v1, v2) = 0 & apply(all_32_7, v0, v2) = 0 & % 79.26/11.28 | | | | member(v2, all_32_3) = 0 & member(v1, all_32_4) = 0 & % 79.26/11.28 | | | | member(v0, all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0)) % 79.26/11.28 | | | | % 79.26/11.28 | | | | DELTA: instantiating (89) with fresh symbols all_57_0, all_57_1, % 79.26/11.28 | | | | all_57_2 gives: % 79.26/11.28 | | | | (90) ~ (all_57_1 = all_57_2) & apply(all_32_7, all_57_1, all_57_0) = % 79.26/11.28 | | | | 0 & apply(all_32_7, all_57_2, all_57_0) = 0 & member(all_57_0, % 79.26/11.28 | | | | all_32_3) = 0 & member(all_57_1, all_32_4) = 0 & % 79.26/11.28 | | | | member(all_57_2, all_32_4) = 0 & $i(all_57_0) & $i(all_57_1) & % 79.26/11.28 | | | | $i(all_57_2) % 79.26/11.28 | | | | % 79.26/11.28 | | | | ALPHA: (90) implies: % 79.26/11.28 | | | | (91) ~ (all_57_1 = all_57_2) % 79.26/11.28 | | | | (92) $i(all_57_2) % 79.26/11.28 | | | | (93) $i(all_57_1) % 79.26/11.28 | | | | (94) $i(all_57_0) % 79.26/11.28 | | | | (95) member(all_57_2, all_32_4) = 0 % 79.26/11.28 | | | | (96) member(all_57_1, all_32_4) = 0 % 79.26/11.28 | | | | (97) member(all_57_0, all_32_3) = 0 % 79.26/11.28 | | | | (98) apply(all_32_7, all_57_2, all_57_0) = 0 % 79.26/11.28 | | | | (99) apply(all_32_7, all_57_1, all_57_0) = 0 % 79.26/11.28 | | | | % 79.26/11.28 | | | | GROUND_INST: instantiating (1) with all_32_6, all_32_3, all_32_5, % 79.26/11.28 | | | | all_57_0, simplifying with (19), (20), (22), (27), (94), % 79.26/11.28 | | | | (97) gives: % 79.26/11.28 | | | | (100) ? [v0: $i] : (apply(all_32_6, all_57_0, v0) = 0 & member(v0, % 79.26/11.28 | | | | all_32_5) = 0 & $i(v0)) % 79.26/11.28 | | | | % 79.26/11.28 | | | | GROUND_INST: instantiating (9) with all_32_2, all_32_5, all_32_3, % 79.26/11.28 | | | | all_57_0, simplifying with (20), (22), (23), (35), (94), % 79.26/11.28 | | | | (97) gives: % 79.26/11.28 | | | | (101) ? [v0: $i] : (apply(all_32_2, v0, all_57_0) = 0 & member(v0, % 79.26/11.28 | | | | all_32_5) = 0 & $i(v0)) % 79.26/11.28 | | | | % 79.26/11.28 | | | | GROUND_INST: instantiating (9) with all_32_7, all_32_4, all_32_3, % 79.26/11.28 | | | | all_57_0, simplifying with (18), (21), (22), (86), (94), % 79.26/11.28 | | | | (97) gives: % 79.26/11.28 | | | | (102) ? [v0: $i] : (apply(all_32_7, v0, all_57_0) = 0 & member(v0, % 79.26/11.28 | | | | all_32_4) = 0 & $i(v0)) % 79.26/11.28 | | | | % 79.26/11.28 | | | | DELTA: instantiating (102) with fresh symbol all_64_0 gives: % 79.26/11.29 | | | | (103) apply(all_32_7, all_64_0, all_57_0) = 0 & member(all_64_0, % 79.26/11.29 | | | | all_32_4) = 0 & $i(all_64_0) % 79.26/11.29 | | | | % 79.26/11.29 | | | | ALPHA: (103) implies: % 79.26/11.29 | | | | (104) $i(all_64_0) % 79.26/11.29 | | | | (105) member(all_64_0, all_32_4) = 0 % 79.26/11.29 | | | | (106) apply(all_32_7, all_64_0, all_57_0) = 0 % 79.26/11.29 | | | | % 79.26/11.29 | | | | DELTA: instantiating (101) with fresh symbol all_66_0 gives: % 79.26/11.29 | | | | (107) apply(all_32_2, all_66_0, all_57_0) = 0 & member(all_66_0, % 79.26/11.29 | | | | all_32_5) = 0 & $i(all_66_0) % 79.26/11.29 | | | | % 79.26/11.29 | | | | ALPHA: (107) implies: % 79.26/11.29 | | | | (108) $i(all_66_0) % 79.26/11.29 | | | | (109) member(all_66_0, all_32_5) = 0 % 79.26/11.29 | | | | % 79.26/11.29 | | | | DELTA: instantiating (100) with fresh symbol all_68_0 gives: % 79.26/11.29 | | | | (110) apply(all_32_6, all_57_0, all_68_0) = 0 & member(all_68_0, % 79.26/11.29 | | | | all_32_5) = 0 & $i(all_68_0) % 79.26/11.29 | | | | % 79.26/11.29 | | | | ALPHA: (110) implies: % 79.26/11.29 | | | | (111) $i(all_68_0) % 79.26/11.29 | | | | (112) member(all_68_0, all_32_5) = 0 % 79.26/11.29 | | | | (113) apply(all_32_6, all_57_0, all_68_0) = 0 % 79.26/11.29 | | | | % 79.26/11.29 | | | | GROUND_INST: instantiating (1) with all_32_7, all_32_4, all_32_3, % 79.26/11.29 | | | | all_64_0, simplifying with (18), (21), (22), (26), (104), % 79.26/11.29 | | | | (105) gives: % 79.26/11.29 | | | | (114) ? [v0: $i] : (apply(all_32_7, all_64_0, v0) = 0 & member(v0, % 79.26/11.29 | | | | all_32_3) = 0 & $i(v0)) % 79.26/11.29 | | | | % 79.26/11.29 | | | | GROUND_INST: instantiating (9) with all_32_1, all_32_4, all_32_5, % 79.26/11.29 | | | | all_66_0, simplifying with (20), (21), (24), (38), (108), % 79.26/11.29 | | | | (109) gives: % 79.26/11.29 | | | | (115) ? [v0: $i] : (apply(all_32_1, v0, all_66_0) = 0 & member(v0, % 79.26/11.29 | | | | all_32_4) = 0 & $i(v0)) % 79.26/11.29 | | | | % 79.26/11.29 | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5, all_32_4, % 79.26/11.29 | | | | all_68_0, all_57_1, all_57_2, simplifying with (17), (20), % 79.26/11.29 | | | | (21), (25), (92), (93), (95), (96), (111), (112) gives: % 79.26/11.29 | | | | (116) all_57_1 = all_57_2 | ? [v0: any] : ? [v1: any] : % 79.26/11.29 | | | | (apply(all_32_8, all_68_0, all_57_1) = v0 & apply(all_32_8, % 79.26/11.29 | | | | all_68_0, all_57_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 79.26/11.29 | | | | % 79.26/11.29 | | | | GROUND_INST: instantiating (1) with all_32_8, all_32_5, all_32_4, % 79.26/11.29 | | | | all_68_0, simplifying with (17), (20), (21), (25), (111), % 79.26/11.29 | | | | (112) gives: % 79.26/11.29 | | | | (117) ? [v0: $i] : (apply(all_32_8, all_68_0, v0) = 0 & member(v0, % 79.26/11.29 | | | | all_32_4) = 0 & $i(v0)) % 79.26/11.29 | | | | % 79.26/11.29 | | | | GROUND_INST: instantiating (8) with all_32_1, all_32_4, all_32_5, % 79.26/11.29 | | | | all_57_2, all_57_1, all_68_0, simplifying with (20), (21), % 79.26/11.29 | | | | (24), (37), (92), (93), (95), (96), (111), (112) gives: % 79.26/11.29 | | | | (118) all_57_1 = all_57_2 | ? [v0: any] : ? [v1: any] : % 79.26/11.29 | | | | (apply(all_32_1, all_57_1, all_68_0) = v1 & apply(all_32_1, % 79.26/11.29 | | | | all_57_2, all_68_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 79.26/11.29 | | | | % 79.26/11.29 | | | | GROUND_INST: instantiating (8) with all_32_1, all_32_4, all_32_5, % 79.26/11.29 | | | | all_57_1, all_57_2, all_68_0, simplifying with (20), (21), % 79.26/11.29 | | | | (24), (37), (92), (93), (95), (96), (111), (112) gives: % 79.26/11.29 | | | | (119) all_57_1 = all_57_2 | ? [v0: any] : ? [v1: any] : % 79.26/11.29 | | | | (apply(all_32_1, all_57_1, all_68_0) = v0 & apply(all_32_1, % 79.26/11.29 | | | | all_57_2, all_68_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 79.26/11.29 | | | | % 79.26/11.29 | | | | DELTA: instantiating (117) with fresh symbol all_83_0 gives: % 79.26/11.29 | | | | (120) apply(all_32_8, all_68_0, all_83_0) = 0 & member(all_83_0, % 79.26/11.29 | | | | all_32_4) = 0 & $i(all_83_0) % 79.26/11.29 | | | | % 79.26/11.29 | | | | ALPHA: (120) implies: % 79.26/11.29 | | | | (121) $i(all_83_0) % 79.26/11.29 | | | | (122) member(all_83_0, all_32_4) = 0 % 79.26/11.29 | | | | % 79.26/11.29 | | | | DELTA: instantiating (115) with fresh symbol all_91_0 gives: % 79.26/11.29 | | | | (123) apply(all_32_1, all_91_0, all_66_0) = 0 & member(all_91_0, % 79.26/11.29 | | | | all_32_4) = 0 & $i(all_91_0) % 79.26/11.29 | | | | % 79.26/11.29 | | | | ALPHA: (123) implies: % 79.26/11.29 | | | | (124) $i(all_91_0) % 79.26/11.29 | | | | (125) member(all_91_0, all_32_4) = 0 % 79.26/11.29 | | | | (126) apply(all_32_1, all_91_0, all_66_0) = 0 % 79.26/11.29 | | | | % 79.26/11.29 | | | | DELTA: instantiating (114) with fresh symbol all_97_0 gives: % 79.26/11.29 | | | | (127) apply(all_32_7, all_64_0, all_97_0) = 0 & member(all_97_0, % 79.26/11.29 | | | | all_32_3) = 0 & $i(all_97_0) % 79.26/11.29 | | | | % 79.26/11.29 | | | | ALPHA: (127) implies: % 79.26/11.29 | | | | (128) $i(all_97_0) % 79.26/11.29 | | | | (129) member(all_97_0, all_32_3) = 0 % 79.26/11.29 | | | | (130) apply(all_32_7, all_64_0, all_97_0) = 0 % 79.26/11.29 | | | | % 79.26/11.29 | | | | BETA: splitting (118) gives: % 79.26/11.29 | | | | % 79.26/11.29 | | | | Case 1: % 79.26/11.29 | | | | | % 79.26/11.29 | | | | | (131) all_57_1 = all_57_2 % 79.26/11.29 | | | | | % 79.26/11.29 | | | | | REDUCE: (91), (131) imply: % 79.26/11.29 | | | | | (132) $false % 79.26/11.29 | | | | | % 79.26/11.29 | | | | | CLOSE: (132) is inconsistent. % 79.26/11.29 | | | | | % 79.26/11.29 | | | | Case 2: % 79.26/11.29 | | | | | % 79.26/11.29 | | | | | (133) ? [v0: any] : ? [v1: any] : (apply(all_32_1, all_57_1, % 79.26/11.29 | | | | | all_68_0) = v1 & apply(all_32_1, all_57_2, all_68_0) = v0 % 79.26/11.29 | | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) % 79.26/11.29 | | | | | % 79.26/11.29 | | | | | DELTA: instantiating (133) with fresh symbols all_123_0, all_123_1 % 79.26/11.29 | | | | | gives: % 79.26/11.29 | | | | | (134) apply(all_32_1, all_57_1, all_68_0) = all_123_0 & % 79.26/11.29 | | | | | apply(all_32_1, all_57_2, all_68_0) = all_123_1 & ( ~ % 79.26/11.29 | | | | | (all_123_0 = 0) | ~ (all_123_1 = 0)) % 79.26/11.29 | | | | | % 79.26/11.29 | | | | | ALPHA: (134) implies: % 79.26/11.29 | | | | | (135) apply(all_32_1, all_57_2, all_68_0) = all_123_1 % 79.26/11.29 | | | | | (136) apply(all_32_1, all_57_1, all_68_0) = all_123_0 % 79.26/11.29 | | | | | (137) ~ (all_123_0 = 0) | ~ (all_123_1 = 0) % 79.26/11.29 | | | | | % 79.26/11.29 | | | | | BETA: splitting (119) gives: % 79.26/11.29 | | | | | % 79.26/11.29 | | | | | Case 1: % 79.26/11.29 | | | | | | % 79.26/11.29 | | | | | | (138) all_57_1 = all_57_2 % 79.26/11.29 | | | | | | % 79.26/11.29 | | | | | | REDUCE: (91), (138) imply: % 79.26/11.29 | | | | | | (139) $false % 79.26/11.29 | | | | | | % 79.26/11.29 | | | | | | CLOSE: (139) is inconsistent. % 79.26/11.29 | | | | | | % 79.26/11.29 | | | | | Case 2: % 79.26/11.29 | | | | | | % 79.26/11.29 | | | | | | (140) ? [v0: any] : ? [v1: any] : (apply(all_32_1, all_57_1, % 79.26/11.29 | | | | | | all_68_0) = v0 & apply(all_32_1, all_57_2, all_68_0) = % 79.26/11.29 | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 79.26/11.29 | | | | | | % 79.26/11.29 | | | | | | DELTA: instantiating (140) with fresh symbols all_128_0, all_128_1 % 79.26/11.29 | | | | | | gives: % 79.26/11.29 | | | | | | (141) apply(all_32_1, all_57_1, all_68_0) = all_128_1 & % 79.26/11.29 | | | | | | apply(all_32_1, all_57_2, all_68_0) = all_128_0 & ( ~ % 79.26/11.29 | | | | | | (all_128_0 = 0) | ~ (all_128_1 = 0)) % 79.26/11.29 | | | | | | % 79.26/11.29 | | | | | | ALPHA: (141) implies: % 79.26/11.29 | | | | | | (142) apply(all_32_1, all_57_2, all_68_0) = all_128_0 % 79.26/11.29 | | | | | | (143) apply(all_32_1, all_57_1, all_68_0) = all_128_1 % 79.26/11.29 | | | | | | % 79.26/11.29 | | | | | | BETA: splitting (116) gives: % 79.26/11.29 | | | | | | % 79.26/11.29 | | | | | | Case 1: % 79.26/11.29 | | | | | | | % 79.26/11.29 | | | | | | | (144) all_57_1 = all_57_2 % 79.26/11.29 | | | | | | | % 79.26/11.29 | | | | | | | REDUCE: (91), (144) imply: % 79.26/11.29 | | | | | | | (145) $false % 79.26/11.29 | | | | | | | % 79.26/11.29 | | | | | | | CLOSE: (145) is inconsistent. % 79.26/11.29 | | | | | | | % 79.26/11.29 | | | | | | Case 2: % 79.26/11.29 | | | | | | | % 79.26/11.30 | | | | | | | % 79.26/11.30 | | | | | | | GROUND_INST: instantiating (14) with all_123_1, all_128_0, % 79.26/11.30 | | | | | | | all_68_0, all_57_2, all_32_1, simplifying with (135), % 79.26/11.30 | | | | | | | (142) gives: % 79.26/11.30 | | | | | | | (146) all_128_0 = all_123_1 % 79.26/11.30 | | | | | | | % 79.26/11.30 | | | | | | | GROUND_INST: instantiating (14) with all_123_0, all_128_1, % 79.26/11.30 | | | | | | | all_68_0, all_57_1, all_32_1, simplifying with (136), % 79.26/11.30 | | | | | | | (143) gives: % 79.26/11.30 | | | | | | | (147) all_128_1 = all_123_0 % 79.26/11.30 | | | | | | | % 79.26/11.30 | | | | | | | GROUND_INST: instantiating (2) with all_32_7, all_32_4, all_32_3, % 79.26/11.30 | | | | | | | all_83_0, all_97_0, all_57_0, simplifying with (18), % 79.26/11.30 | | | | | | | (21), (22), (26), (94), (97), (121), (122), (128), % 79.26/11.30 | | | | | | | (129) gives: % 79.26/11.30 | | | | | | | (148) all_97_0 = all_57_0 | ? [v0: any] : ? [v1: any] : % 79.26/11.30 | | | | | | | (apply(all_32_7, all_83_0, all_97_0) = v0 & % 79.26/11.30 | | | | | | | apply(all_32_7, all_83_0, all_57_0) = v1 & ( ~ (v1 = 0) % 79.26/11.30 | | | | | | | | ~ (v0 = 0))) % 79.26/11.30 | | | | | | | % 79.48/11.30 | | | | | | | GROUND_INST: instantiating (3) with all_32_7, all_32_4, all_32_3, % 79.48/11.30 | | | | | | | all_64_0, all_97_0, all_57_0, simplifying with (18), % 79.48/11.30 | | | | | | | (21), (22), (26), (94), (104), (106), (128), (130) % 79.48/11.30 | | | | | | | gives: % 79.48/11.30 | | | | | | | (149) all_97_0 = all_57_0 | ? [v0: any] : ? [v1: any] : ? % 79.48/11.30 | | | | | | | [v2: any] : (member(all_97_0, all_32_3) = v1 & % 79.48/11.30 | | | | | | | member(all_64_0, all_32_4) = v0 & member(all_57_0, % 79.48/11.30 | | | | | | | all_32_3) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 % 79.48/11.30 | | | | | | | = 0))) % 79.48/11.30 | | | | | | | % 79.48/11.30 | | | | | | | GROUND_INST: instantiating (6) with all_32_6, all_32_7, all_32_4, % 79.48/11.30 | | | | | | | all_32_3, all_32_5, all_57_2, all_68_0, all_32_1, % 79.48/11.30 | | | | | | | all_123_1, all_57_0, simplifying with (18), (19), % 79.48/11.30 | | | | | | | (20), (21), (22), (29), (92), (94), (111), (113), % 79.48/11.30 | | | | | | | (135) gives: % 79.48/11.30 | | | | | | | (150) all_123_1 = 0 | ? [v0: any] : ? [v1: any] : % 79.48/11.30 | | | | | | | ((apply(all_32_7, all_57_2, all_57_0) = v1 & % 79.48/11.30 | | | | | | | member(all_57_0, all_32_3) = v0 & ( ~ (v1 = 0) | ~ % 79.48/11.30 | | | | | | | (v0 = 0))) | (member(all_68_0, all_32_5) = v1 & % 79.48/11.30 | | | | | | | member(all_57_2, all_32_4) = v0 & ( ~ (v1 = 0) | ~ % 79.48/11.30 | | | | | | | (v0 = 0)))) % 79.48/11.30 | | | | | | | % 79.48/11.30 | | | | | | | GROUND_INST: instantiating (5) with all_32_6, all_32_7, all_32_4, % 79.48/11.30 | | | | | | | all_32_3, all_32_5, all_57_2, all_68_0, all_32_1, % 79.48/11.30 | | | | | | | all_123_1, all_57_0, simplifying with (18), (19), % 79.48/11.30 | | | | | | | (20), (21), (22), (29), (92), (94), (97), (111), % 79.48/11.30 | | | | | | | (135) gives: % 79.48/11.30 | | | | | | | (151) all_123_1 = 0 | ? [v0: any] : ? [v1: any] : % 79.48/11.30 | | | | | | | ((apply(all_32_6, all_57_0, all_68_0) = v1 & % 79.48/11.30 | | | | | | | apply(all_32_7, all_57_2, all_57_0) = v0 & ( ~ (v1 = % 79.48/11.30 | | | | | | | 0) | ~ (v0 = 0))) | (member(all_68_0, all_32_5) % 79.48/11.30 | | | | | | | = v1 & member(all_57_2, all_32_4) = v0 & ( ~ (v1 = 0) % 79.48/11.30 | | | | | | | | ~ (v0 = 0)))) % 79.48/11.30 | | | | | | | % 79.48/11.30 | | | | | | | GROUND_INST: instantiating (6) with all_32_6, all_32_7, all_32_4, % 79.48/11.30 | | | | | | | all_32_3, all_32_5, all_57_1, all_68_0, all_32_1, % 79.48/11.30 | | | | | | | all_123_0, all_57_0, simplifying with (18), (19), % 79.48/11.30 | | | | | | | (20), (21), (22), (29), (93), (94), (111), (113), % 79.48/11.30 | | | | | | | (136) gives: % 79.48/11.31 | | | | | | | (152) all_123_0 = 0 | ? [v0: any] : ? [v1: any] : % 79.48/11.31 | | | | | | | ((apply(all_32_7, all_57_1, all_57_0) = v1 & % 79.48/11.31 | | | | | | | member(all_57_0, all_32_3) = v0 & ( ~ (v1 = 0) | ~ % 79.48/11.31 | | | | | | | (v0 = 0))) | (member(all_68_0, all_32_5) = v1 & % 79.48/11.31 | | | | | | | member(all_57_1, all_32_4) = v0 & ( ~ (v1 = 0) | ~ % 79.48/11.31 | | | | | | | (v0 = 0)))) % 79.48/11.31 | | | | | | | % 79.48/11.31 | | | | | | | GROUND_INST: instantiating (5) with all_32_6, all_32_7, all_32_4, % 79.48/11.31 | | | | | | | all_32_3, all_32_5, all_57_1, all_68_0, all_32_1, % 79.48/11.31 | | | | | | | all_123_0, all_97_0, simplifying with (18), (19), % 79.48/11.31 | | | | | | | (20), (21), (22), (29), (93), (111), (128), (129), % 79.48/11.31 | | | | | | | (136) gives: % 79.48/11.31 | | | | | | | (153) all_123_0 = 0 | ? [v0: any] : ? [v1: any] : % 79.48/11.31 | | | | | | | ((apply(all_32_6, all_97_0, all_68_0) = v1 & % 79.48/11.31 | | | | | | | apply(all_32_7, all_57_1, all_97_0) = v0 & ( ~ (v1 = % 79.48/11.31 | | | | | | | 0) | ~ (v0 = 0))) | (member(all_68_0, all_32_5) % 79.48/11.31 | | | | | | | = v1 & member(all_57_1, all_32_4) = v0 & ( ~ (v1 = 0) % 79.48/11.31 | | | | | | | | ~ (v0 = 0)))) % 79.48/11.31 | | | | | | | % 79.48/11.31 | | | | | | | GROUND_INST: instantiating (4) with all_32_6, all_32_7, all_32_4, % 79.48/11.31 | | | | | | | all_32_3, all_32_5, all_91_0, all_66_0, all_32_1, % 79.48/11.31 | | | | | | | simplifying with (18), (19), (20), (21), (22), (29), % 79.48/11.31 | | | | | | | (108), (124), (126) gives: % 79.48/11.31 | | | | | | | (154) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: int] % 79.48/11.31 | | | | | | | : ? [v4: int] : ? [v5: int] : ($i(v2) & ((v5 = 0 & v4 = % 79.48/11.31 | | | | | | | 0 & v3 = 0 & apply(all_32_6, v2, all_66_0) = 0 & % 79.48/11.31 | | | | | | | apply(all_32_7, all_91_0, v2) = 0 & member(v2, % 79.48/11.31 | | | | | | | all_32_3) = 0) | (member(all_91_0, all_32_4) = v0 % 79.48/11.31 | | | | | | | & member(all_66_0, all_32_5) = v1 & ( ~ (v1 = 0) | % 79.48/11.31 | | | | | | | ~ (v0 = 0))))) % 79.48/11.31 | | | | | | | % 79.48/11.31 | | | | | | | DELTA: instantiating (154) with fresh symbols all_196_0, % 79.48/11.31 | | | | | | | all_196_1, all_196_2, all_196_3, all_196_4, all_196_5 % 79.48/11.31 | | | | | | | gives: % 79.48/11.31 | | | | | | | (155) $i(all_196_3) & ((all_196_0 = 0 & all_196_1 = 0 & % 79.48/11.31 | | | | | | | all_196_2 = 0 & apply(all_32_6, all_196_3, all_66_0) % 79.48/11.31 | | | | | | | = 0 & apply(all_32_7, all_91_0, all_196_3) = 0 & % 79.48/11.31 | | | | | | | member(all_196_3, all_32_3) = 0) | (member(all_91_0, % 79.48/11.31 | | | | | | | all_32_4) = all_196_5 & member(all_66_0, all_32_5) % 79.48/11.31 | | | | | | | = all_196_4 & ( ~ (all_196_4 = 0) | ~ (all_196_5 = % 79.48/11.31 | | | | | | | 0)))) % 79.48/11.31 | | | | | | | % 79.48/11.31 | | | | | | | ALPHA: (155) implies: % 79.48/11.31 | | | | | | | (156) (all_196_0 = 0 & all_196_1 = 0 & all_196_2 = 0 & % 79.48/11.31 | | | | | | | apply(all_32_6, all_196_3, all_66_0) = 0 & % 79.48/11.31 | | | | | | | apply(all_32_7, all_91_0, all_196_3) = 0 & % 79.48/11.31 | | | | | | | member(all_196_3, all_32_3) = 0) | (member(all_91_0, % 79.48/11.31 | | | | | | | all_32_4) = all_196_5 & member(all_66_0, all_32_5) = % 79.48/11.31 | | | | | | | all_196_4 & ( ~ (all_196_4 = 0) | ~ (all_196_5 = 0))) % 79.48/11.31 | | | | | | | % 79.48/11.31 | | | | | | | BETA: splitting (149) gives: % 79.48/11.31 | | | | | | | % 79.48/11.31 | | | | | | | Case 1: % 79.48/11.31 | | | | | | | | % 79.48/11.31 | | | | | | | | (157) all_97_0 = all_57_0 % 79.48/11.31 | | | | | | | | % 79.48/11.31 | | | | | | | | REF_CLOSE: (13), (14), (95), (96), (97), (98), (99), (109), % 79.48/11.31 | | | | | | | | (112), (113), (125), (137), (150), (151), (152), % 79.48/11.31 | | | | | | | | (153), (156), (157) are inconsistent by sub-proof #1. % 79.48/11.31 | | | | | | | | % 79.48/11.31 | | | | | | | Case 2: % 79.48/11.31 | | | | | | | | % 79.48/11.31 | | | | | | | | (158) ? [v0: any] : ? [v1: any] : ? [v2: any] : % 79.48/11.31 | | | | | | | | (member(all_97_0, all_32_3) = v1 & member(all_64_0, % 79.48/11.31 | | | | | | | | all_32_4) = v0 & member(all_57_0, all_32_3) = v2 & % 79.48/11.31 | | | | | | | | ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0))) % 79.48/11.31 | | | | | | | | % 79.48/11.31 | | | | | | | | DELTA: instantiating (158) with fresh symbols all_239_0, % 79.48/11.31 | | | | | | | | all_239_1, all_239_2 gives: % 79.48/11.31 | | | | | | | | (159) member(all_97_0, all_32_3) = all_239_1 & % 79.48/11.31 | | | | | | | | member(all_64_0, all_32_4) = all_239_2 & % 79.48/11.31 | | | | | | | | member(all_57_0, all_32_3) = all_239_0 & ( ~ (all_239_0 % 79.48/11.31 | | | | | | | | = 0) | ~ (all_239_1 = 0) | ~ (all_239_2 = 0)) % 79.48/11.31 | | | | | | | | % 79.48/11.31 | | | | | | | | ALPHA: (159) implies: % 79.48/11.31 | | | | | | | | (160) member(all_57_0, all_32_3) = all_239_0 % 79.48/11.31 | | | | | | | | (161) member(all_64_0, all_32_4) = all_239_2 % 79.48/11.31 | | | | | | | | (162) member(all_97_0, all_32_3) = all_239_1 % 79.48/11.31 | | | | | | | | (163) ~ (all_239_0 = 0) | ~ (all_239_1 = 0) | ~ (all_239_2 % 79.48/11.31 | | | | | | | | = 0) % 79.48/11.31 | | | | | | | | % 79.48/11.31 | | | | | | | | BETA: splitting (148) gives: % 79.48/11.31 | | | | | | | | % 79.48/11.31 | | | | | | | | Case 1: % 79.48/11.31 | | | | | | | | | % 79.48/11.31 | | | | | | | | | (164) all_97_0 = all_57_0 % 79.48/11.31 | | | | | | | | | % 79.48/11.31 | | | | | | | | | REF_CLOSE: (13), (14), (95), (96), (97), (98), (99), (109), % 79.48/11.31 | | | | | | | | | (112), (113), (125), (137), (150), (151), (152), % 79.48/11.31 | | | | | | | | | (153), (156), (164) are inconsistent by sub-proof % 79.48/11.31 | | | | | | | | | #1. % 79.48/11.31 | | | | | | | | | % 79.48/11.31 | | | | | | | | Case 2: % 79.48/11.31 | | | | | | | | | % 79.48/11.31 | | | | | | | | | % 79.48/11.31 | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_239_0, all_32_3, % 79.48/11.31 | | | | | | | | | all_57_0, simplifying with (97), (160) gives: % 79.48/11.31 | | | | | | | | | (165) all_239_0 = 0 % 79.48/11.31 | | | | | | | | | % 79.48/11.31 | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_239_2, all_32_4, % 79.48/11.31 | | | | | | | | | all_64_0, simplifying with (105), (161) gives: % 79.48/11.31 | | | | | | | | | (166) all_239_2 = 0 % 79.48/11.31 | | | | | | | | | % 79.48/11.31 | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_239_1, all_32_3, % 79.48/11.31 | | | | | | | | | all_97_0, simplifying with (129), (162) gives: % 79.48/11.31 | | | | | | | | | (167) all_239_1 = 0 % 79.48/11.31 | | | | | | | | | % 79.48/11.31 | | | | | | | | | BETA: splitting (163) gives: % 79.48/11.31 | | | | | | | | | % 79.48/11.31 | | | | | | | | | Case 1: % 79.48/11.31 | | | | | | | | | | % 79.48/11.31 | | | | | | | | | | (168) ~ (all_239_0 = 0) % 79.48/11.31 | | | | | | | | | | % 79.48/11.31 | | | | | | | | | | REDUCE: (165), (168) imply: % 79.48/11.31 | | | | | | | | | | (169) $false % 79.48/11.31 | | | | | | | | | | % 79.48/11.31 | | | | | | | | | | CLOSE: (169) is inconsistent. % 79.48/11.31 | | | | | | | | | | % 79.48/11.31 | | | | | | | | | Case 2: % 79.48/11.31 | | | | | | | | | | % 79.48/11.31 | | | | | | | | | | (170) ~ (all_239_1 = 0) | ~ (all_239_2 = 0) % 79.48/11.31 | | | | | | | | | | % 79.48/11.31 | | | | | | | | | | BETA: splitting (170) gives: % 79.48/11.31 | | | | | | | | | | % 79.48/11.31 | | | | | | | | | | Case 1: % 79.48/11.31 | | | | | | | | | | | % 79.48/11.31 | | | | | | | | | | | (171) ~ (all_239_1 = 0) % 79.48/11.31 | | | | | | | | | | | % 79.48/11.31 | | | | | | | | | | | REDUCE: (167), (171) imply: % 79.48/11.31 | | | | | | | | | | | (172) $false % 79.48/11.31 | | | | | | | | | | | % 79.48/11.31 | | | | | | | | | | | CLOSE: (172) is inconsistent. % 79.48/11.31 | | | | | | | | | | | % 79.48/11.31 | | | | | | | | | | Case 2: % 79.48/11.31 | | | | | | | | | | | % 79.48/11.31 | | | | | | | | | | | (173) ~ (all_239_2 = 0) % 79.48/11.31 | | | | | | | | | | | % 79.48/11.31 | | | | | | | | | | | REDUCE: (166), (173) imply: % 79.48/11.31 | | | | | | | | | | | (174) $false % 79.48/11.31 | | | | | | | | | | | % 79.48/11.31 | | | | | | | | | | | CLOSE: (174) is inconsistent. % 79.48/11.31 | | | | | | | | | | | % 79.48/11.31 | | | | | | | | | | End of split % 79.48/11.31 | | | | | | | | | | % 79.48/11.31 | | | | | | | | | End of split % 79.48/11.31 | | | | | | | | | % 79.48/11.31 | | | | | | | | End of split % 79.48/11.31 | | | | | | | | % 79.48/11.31 | | | | | | | End of split % 79.48/11.31 | | | | | | | % 79.48/11.31 | | | | | | End of split % 79.48/11.31 | | | | | | % 79.48/11.31 | | | | | End of split % 79.48/11.31 | | | | | % 79.48/11.31 | | | | End of split % 79.48/11.31 | | | | % 79.48/11.31 | | | End of split % 79.48/11.31 | | | % 79.48/11.31 | | End of split % 79.48/11.31 | | % 79.48/11.31 | End of split % 79.48/11.31 | % 79.48/11.31 End of proof % 79.48/11.31 % 79.48/11.31 Sub-proof #1 shows that the following formulas are inconsistent: % 79.48/11.31 ---------------------------------------------------------------- % 79.48/11.31 (1) member(all_68_0, all_32_5) = 0 % 79.48/11.31 (2) member(all_91_0, all_32_4) = 0 % 79.48/11.31 (3) member(all_57_1, all_32_4) = 0 % 79.48/11.31 (4) all_123_1 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_6, all_57_0, % 79.48/11.31 all_68_0) = v1 & apply(all_32_7, all_57_2, all_57_0) = v0 & ( ~ (v1 % 79.48/11.31 = 0) | ~ (v0 = 0))) | (member(all_68_0, all_32_5) = v1 & % 79.48/11.31 member(all_57_2, all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 79.48/11.31 (5) all_123_0 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_7, all_57_1, % 79.48/11.31 all_57_0) = v1 & member(all_57_0, all_32_3) = v0 & ( ~ (v1 = 0) | % 79.48/11.31 ~ (v0 = 0))) | (member(all_68_0, all_32_5) = v1 & member(all_57_1, % 79.48/11.31 all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 79.48/11.31 (6) member(all_57_2, all_32_4) = 0 % 79.48/11.31 (7) member(all_66_0, all_32_5) = 0 % 79.48/11.31 (8) all_123_1 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_7, all_57_2, % 79.48/11.31 all_57_0) = v1 & member(all_57_0, all_32_3) = v0 & ( ~ (v1 = 0) | % 79.48/11.31 ~ (v0 = 0))) | (member(all_68_0, all_32_5) = v1 & member(all_57_2, % 79.48/11.31 all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 79.48/11.32 (9) (all_196_0 = 0 & all_196_1 = 0 & all_196_2 = 0 & apply(all_32_6, % 79.48/11.32 all_196_3, all_66_0) = 0 & apply(all_32_7, all_91_0, all_196_3) = 0 & % 79.48/11.32 member(all_196_3, all_32_3) = 0) | (member(all_91_0, all_32_4) = % 79.48/11.32 all_196_5 & member(all_66_0, all_32_5) = all_196_4 & ( ~ (all_196_4 = % 79.48/11.32 0) | ~ (all_196_5 = 0))) % 79.48/11.32 (10) all_97_0 = all_57_0 % 79.48/11.32 (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 79.48/11.32 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ % 79.48/11.32 (apply(v4, v3, v2) = v0)) % 79.48/11.32 (12) all_123_0 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_6, % 79.48/11.32 all_97_0, all_68_0) = v1 & apply(all_32_7, all_57_1, all_97_0) = % 79.48/11.32 v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_68_0, all_32_5) = v1 % 79.48/11.32 & member(all_57_1, all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 79.48/11.32 (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 79.48/11.32 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = % 79.48/11.32 v0)) % 79.48/11.32 (14) ~ (all_123_0 = 0) | ~ (all_123_1 = 0) % 79.48/11.32 (15) apply(all_32_6, all_57_0, all_68_0) = 0 % 79.48/11.32 (16) apply(all_32_7, all_57_2, all_57_0) = 0 % 79.48/11.32 (17) apply(all_32_7, all_57_1, all_57_0) = 0 % 79.48/11.32 (18) member(all_57_0, all_32_3) = 0 % 79.48/11.32 % 79.48/11.32 Begin of proof % 79.48/11.32 | % 79.48/11.32 | BETA: splitting (12) gives: % 79.48/11.32 | % 79.48/11.32 | Case 1: % 79.48/11.32 | | % 79.48/11.32 | | (19) all_123_0 = 0 % 79.48/11.32 | | % 79.48/11.32 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (11), (13), (14), (16), (18), % 79.48/11.32 | | (19) are inconsistent by sub-proof #3. % 79.48/11.32 | | % 79.48/11.32 | Case 2: % 79.48/11.32 | | % 79.48/11.32 | | (20) ? [v0: any] : ? [v1: any] : ((apply(all_32_6, all_97_0, all_68_0) % 79.48/11.32 | | = v1 & apply(all_32_7, all_57_1, all_97_0) = v0 & ( ~ (v1 = 0) | % 79.48/11.32 | | ~ (v0 = 0))) | (member(all_68_0, all_32_5) = v1 & % 79.48/11.32 | | member(all_57_1, all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 79.48/11.32 | | % 79.48/11.32 | | DELTA: instantiating (20) with fresh symbols all_264_0, all_264_1 gives: % 79.48/11.32 | | (21) (apply(all_32_6, all_97_0, all_68_0) = all_264_0 & apply(all_32_7, % 79.48/11.32 | | all_57_1, all_97_0) = all_264_1 & ( ~ (all_264_0 = 0) | ~ % 79.48/11.32 | | (all_264_1 = 0))) | (member(all_68_0, all_32_5) = all_264_0 & % 79.48/11.32 | | member(all_57_1, all_32_4) = all_264_1 & ( ~ (all_264_0 = 0) | ~ % 79.48/11.32 | | (all_264_1 = 0))) % 79.48/11.32 | | % 79.48/11.32 | | BETA: splitting (21) gives: % 79.48/11.32 | | % 79.48/11.32 | | Case 1: % 79.48/11.32 | | | % 79.48/11.32 | | | (22) apply(all_32_6, all_97_0, all_68_0) = all_264_0 & apply(all_32_7, % 79.48/11.32 | | | all_57_1, all_97_0) = all_264_1 & ( ~ (all_264_0 = 0) | ~ % 79.48/11.32 | | | (all_264_1 = 0)) % 79.48/11.32 | | | % 79.48/11.32 | | | ALPHA: (22) implies: % 79.48/11.32 | | | (23) apply(all_32_7, all_57_1, all_97_0) = all_264_1 % 79.48/11.32 | | | (24) apply(all_32_6, all_97_0, all_68_0) = all_264_0 % 79.48/11.32 | | | (25) ~ (all_264_0 = 0) | ~ (all_264_1 = 0) % 79.48/11.32 | | | % 79.48/11.32 | | | REDUCE: (10), (24) imply: % 79.48/11.32 | | | (26) apply(all_32_6, all_57_0, all_68_0) = all_264_0 % 79.48/11.32 | | | % 79.48/11.32 | | | REDUCE: (10), (23) imply: % 79.48/11.32 | | | (27) apply(all_32_7, all_57_1, all_57_0) = all_264_1 % 79.48/11.32 | | | % 79.48/11.32 | | | BETA: splitting (5) gives: % 79.48/11.32 | | | % 79.48/11.32 | | | Case 1: % 79.48/11.32 | | | | % 79.48/11.32 | | | | (28) all_123_0 = 0 % 79.48/11.32 | | | | % 79.48/11.32 | | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (11), (13), (14), (16), % 79.48/11.32 | | | | (18), (28) are inconsistent by sub-proof #3. % 79.48/11.32 | | | | % 79.48/11.32 | | | Case 2: % 79.48/11.32 | | | | % 79.48/11.32 | | | | % 79.48/11.32 | | | | GROUND_INST: instantiating (11) with 0, all_264_1, all_57_0, all_57_1, % 79.48/11.32 | | | | all_32_7, simplifying with (17), (27) gives: % 79.48/11.32 | | | | (29) all_264_1 = 0 % 79.48/11.32 | | | | % 79.48/11.32 | | | | GROUND_INST: instantiating (11) with 0, all_264_0, all_68_0, all_57_0, % 79.48/11.32 | | | | all_32_6, simplifying with (15), (26) gives: % 79.48/11.32 | | | | (30) all_264_0 = 0 % 79.48/11.32 | | | | % 79.48/11.32 | | | | REF_CLOSE: (25), (29), (30) are inconsistent by sub-proof #2. % 79.48/11.32 | | | | % 79.48/11.32 | | | End of split % 79.48/11.32 | | | % 79.48/11.32 | | Case 2: % 79.48/11.32 | | | % 79.48/11.32 | | | (31) member(all_68_0, all_32_5) = all_264_0 & member(all_57_1, % 79.48/11.32 | | | all_32_4) = all_264_1 & ( ~ (all_264_0 = 0) | ~ (all_264_1 = % 79.48/11.32 | | | 0)) % 79.48/11.32 | | | % 79.48/11.32 | | | ALPHA: (31) implies: % 79.48/11.32 | | | (32) member(all_57_1, all_32_4) = all_264_1 % 79.48/11.32 | | | (33) member(all_68_0, all_32_5) = all_264_0 % 79.48/11.32 | | | (34) ~ (all_264_0 = 0) | ~ (all_264_1 = 0) % 79.48/11.32 | | | % 79.48/11.32 | | | GROUND_INST: instantiating (13) with 0, all_264_1, all_32_4, all_57_1, % 79.48/11.32 | | | simplifying with (3), (32) gives: % 79.48/11.32 | | | (35) all_264_1 = 0 % 79.48/11.32 | | | % 79.48/11.32 | | | GROUND_INST: instantiating (13) with 0, all_264_0, all_32_5, all_68_0, % 79.48/11.32 | | | simplifying with (1), (33) gives: % 79.48/11.32 | | | (36) all_264_0 = 0 % 79.48/11.32 | | | % 79.48/11.32 | | | REF_CLOSE: (34), (35), (36) are inconsistent by sub-proof #2. % 79.48/11.32 | | | % 79.48/11.32 | | End of split % 79.48/11.32 | | % 79.48/11.32 | End of split % 79.48/11.32 | % 79.48/11.32 End of proof % 79.48/11.32 % 79.48/11.32 Sub-proof #2 shows that the following formulas are inconsistent: % 79.48/11.32 ---------------------------------------------------------------- % 79.48/11.32 (1) ~ (all_264_0 = 0) | ~ (all_264_1 = 0) % 79.48/11.32 (2) all_264_0 = 0 % 79.48/11.32 (3) all_264_1 = 0 % 79.48/11.32 % 79.48/11.32 Begin of proof % 79.48/11.32 | % 79.48/11.32 | BETA: splitting (1) gives: % 79.48/11.32 | % 79.48/11.32 | Case 1: % 79.48/11.32 | | % 79.48/11.32 | | (4) ~ (all_264_0 = 0) % 79.48/11.32 | | % 79.48/11.32 | | REDUCE: (2), (4) imply: % 79.48/11.32 | | (5) $false % 79.48/11.32 | | % 79.48/11.32 | | CLOSE: (5) is inconsistent. % 79.48/11.32 | | % 79.48/11.32 | Case 2: % 79.48/11.32 | | % 79.48/11.32 | | (6) ~ (all_264_1 = 0) % 79.48/11.32 | | % 79.48/11.32 | | REDUCE: (3), (6) imply: % 79.48/11.32 | | (7) $false % 79.48/11.32 | | % 79.48/11.32 | | CLOSE: (7) is inconsistent. % 79.48/11.32 | | % 79.48/11.32 | End of split % 79.48/11.32 | % 79.48/11.32 End of proof % 79.48/11.32 % 79.48/11.32 Sub-proof #3 shows that the following formulas are inconsistent: % 79.48/11.32 ---------------------------------------------------------------- % 79.48/11.32 (1) member(all_68_0, all_32_5) = 0 % 79.48/11.32 (2) member(all_91_0, all_32_4) = 0 % 79.48/11.32 (3) all_123_1 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_6, all_57_0, % 79.48/11.32 all_68_0) = v1 & apply(all_32_7, all_57_2, all_57_0) = v0 & ( ~ (v1 % 79.48/11.32 = 0) | ~ (v0 = 0))) | (member(all_68_0, all_32_5) = v1 & % 79.48/11.32 member(all_57_2, all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 79.48/11.32 (4) member(all_57_2, all_32_4) = 0 % 79.48/11.32 (5) member(all_66_0, all_32_5) = 0 % 79.48/11.32 (6) all_123_1 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_7, all_57_2, % 79.48/11.32 all_57_0) = v1 & member(all_57_0, all_32_3) = v0 & ( ~ (v1 = 0) | % 79.48/11.32 ~ (v0 = 0))) | (member(all_68_0, all_32_5) = v1 & member(all_57_2, % 79.48/11.32 all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 79.48/11.32 (7) (all_196_0 = 0 & all_196_1 = 0 & all_196_2 = 0 & apply(all_32_6, % 79.48/11.32 all_196_3, all_66_0) = 0 & apply(all_32_7, all_91_0, all_196_3) = 0 & % 79.48/11.32 member(all_196_3, all_32_3) = 0) | (member(all_91_0, all_32_4) = % 79.48/11.32 all_196_5 & member(all_66_0, all_32_5) = all_196_4 & ( ~ (all_196_4 = % 79.48/11.32 0) | ~ (all_196_5 = 0))) % 79.48/11.32 (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 79.48/11.32 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~ % 79.48/11.32 (apply(v4, v3, v2) = v0)) % 79.48/11.32 (9) all_123_0 = 0 % 79.48/11.32 (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 79.48/11.32 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = % 79.48/11.32 v0)) % 79.48/11.32 (11) ~ (all_123_0 = 0) | ~ (all_123_1 = 0) % 79.48/11.32 (12) apply(all_32_7, all_57_2, all_57_0) = 0 % 79.48/11.32 (13) member(all_57_0, all_32_3) = 0 % 79.48/11.32 % 79.48/11.32 Begin of proof % 79.48/11.32 | % 79.48/11.32 | BETA: splitting (3) gives: % 79.48/11.32 | % 79.48/11.32 | Case 1: % 79.48/11.32 | | % 79.48/11.32 | | (14) all_123_1 = 0 % 79.48/11.32 | | % 79.48/11.32 | | BETA: splitting (11) gives: % 79.48/11.32 | | % 79.48/11.32 | | Case 1: % 79.48/11.32 | | | % 79.48/11.32 | | | (15) ~ (all_123_0 = 0) % 79.48/11.32 | | | % 79.48/11.32 | | | REDUCE: (9), (15) imply: % 79.48/11.32 | | | (16) $false % 79.48/11.32 | | | % 79.48/11.32 | | | CLOSE: (16) is inconsistent. % 79.48/11.32 | | | % 79.48/11.32 | | Case 2: % 79.48/11.32 | | | % 79.48/11.32 | | | (17) ~ (all_123_1 = 0) % 79.48/11.33 | | | % 79.48/11.33 | | | REDUCE: (14), (17) imply: % 79.48/11.33 | | | (18) $false % 79.48/11.33 | | | % 79.48/11.33 | | | CLOSE: (18) is inconsistent. % 79.48/11.33 | | | % 79.48/11.33 | | End of split % 79.48/11.33 | | % 79.48/11.33 | Case 2: % 79.48/11.33 | | % 79.48/11.33 | | (19) ~ (all_123_1 = 0) % 79.48/11.33 | | (20) ? [v0: any] : ? [v1: any] : ((apply(all_32_6, all_57_0, all_68_0) % 79.48/11.33 | | = v1 & apply(all_32_7, all_57_2, all_57_0) = v0 & ( ~ (v1 = 0) | % 79.48/11.33 | | ~ (v0 = 0))) | (member(all_68_0, all_32_5) = v1 & % 79.48/11.33 | | member(all_57_2, all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))) % 79.48/11.33 | | % 79.48/11.33 | | DELTA: instantiating (20) with fresh symbols all_268_0, all_268_1 gives: % 79.48/11.33 | | (21) (apply(all_32_6, all_57_0, all_68_0) = all_268_0 & apply(all_32_7, % 79.48/11.33 | | all_57_2, all_57_0) = all_268_1 & ( ~ (all_268_0 = 0) | ~ % 79.48/11.33 | | (all_268_1 = 0))) | (member(all_68_0, all_32_5) = all_268_0 & % 79.48/11.33 | | member(all_57_2, all_32_4) = all_268_1 & ( ~ (all_268_0 = 0) | ~ % 79.48/11.33 | | (all_268_1 = 0))) % 79.48/11.33 | | % 79.48/11.33 | | BETA: splitting (21) gives: % 79.48/11.33 | | % 79.48/11.33 | | Case 1: % 79.48/11.33 | | | % 79.48/11.33 | | | (22) apply(all_32_6, all_57_0, all_68_0) = all_268_0 & apply(all_32_7, % 79.48/11.33 | | | all_57_2, all_57_0) = all_268_1 & ( ~ (all_268_0 = 0) | ~ % 79.48/11.33 | | | (all_268_1 = 0)) % 79.48/11.33 | | | % 79.48/11.33 | | | ALPHA: (22) implies: % 79.48/11.33 | | | (23) apply(all_32_7, all_57_2, all_57_0) = all_268_1 % 79.48/11.33 | | | % 79.48/11.33 | | | BETA: splitting (6) gives: % 79.48/11.33 | | | % 79.48/11.33 | | | Case 1: % 79.48/11.33 | | | | % 79.48/11.33 | | | | (24) all_123_1 = 0 % 79.48/11.33 | | | | % 79.48/11.33 | | | | REDUCE: (19), (24) imply: % 79.48/11.33 | | | | (25) $false % 79.48/11.33 | | | | % 79.48/11.33 | | | | CLOSE: (25) is inconsistent. % 79.48/11.33 | | | | % 79.48/11.33 | | | Case 2: % 79.48/11.33 | | | | % 79.48/11.33 | | | | (26) ? [v0: any] : ? [v1: any] : ((apply(all_32_7, all_57_2, % 79.48/11.33 | | | | all_57_0) = v1 & member(all_57_0, all_32_3) = v0 & ( ~ (v1 % 79.48/11.33 | | | | = 0) | ~ (v0 = 0))) | (member(all_68_0, all_32_5) = v1 % 79.48/11.33 | | | | & member(all_57_2, all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = % 79.48/11.33 | | | | 0)))) % 79.48/11.33 | | | | % 79.48/11.33 | | | | DELTA: instantiating (26) with fresh symbols all_277_0, all_277_1 gives: % 79.48/11.33 | | | | (27) (apply(all_32_7, all_57_2, all_57_0) = all_277_0 & % 79.48/11.33 | | | | member(all_57_0, all_32_3) = all_277_1 & ( ~ (all_277_0 = 0) | % 79.48/11.33 | | | | ~ (all_277_1 = 0))) | (member(all_68_0, all_32_5) = % 79.48/11.33 | | | | all_277_0 & member(all_57_2, all_32_4) = all_277_1 & ( ~ % 79.48/11.33 | | | | (all_277_0 = 0) | ~ (all_277_1 = 0))) % 79.48/11.33 | | | | % 79.48/11.33 | | | | BETA: splitting (27) gives: % 79.48/11.33 | | | | % 79.48/11.33 | | | | Case 1: % 79.48/11.33 | | | | | % 79.48/11.33 | | | | | (28) apply(all_32_7, all_57_2, all_57_0) = all_277_0 & % 79.48/11.33 | | | | | member(all_57_0, all_32_3) = all_277_1 & ( ~ (all_277_0 = 0) | % 79.48/11.33 | | | | | ~ (all_277_1 = 0)) % 79.48/11.33 | | | | | % 79.48/11.33 | | | | | ALPHA: (28) implies: % 79.48/11.33 | | | | | (29) member(all_57_0, all_32_3) = all_277_1 % 79.48/11.33 | | | | | (30) apply(all_32_7, all_57_2, all_57_0) = all_277_0 % 79.48/11.33 | | | | | (31) ~ (all_277_0 = 0) | ~ (all_277_1 = 0) % 79.48/11.33 | | | | | % 79.48/11.33 | | | | | BETA: splitting (7) gives: % 79.48/11.33 | | | | | % 79.48/11.33 | | | | | Case 1: % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | GROUND_INST: instantiating (10) with 0, all_277_1, all_32_3, % 79.48/11.33 | | | | | | all_57_0, simplifying with (13), (29) gives: % 79.48/11.33 | | | | | | (32) all_277_1 = 0 % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | GROUND_INST: instantiating (8) with 0, all_277_0, all_57_0, % 79.48/11.33 | | | | | | all_57_2, all_32_7, simplifying with (12), (30) gives: % 79.48/11.33 | | | | | | (33) all_277_0 = 0 % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | GROUND_INST: instantiating (8) with all_268_1, all_277_0, all_57_0, % 79.48/11.33 | | | | | | all_57_2, all_32_7, simplifying with (23), (30) gives: % 79.48/11.33 | | | | | | (34) all_277_0 = all_268_1 % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | COMBINE_EQS: (33), (34) imply: % 79.48/11.33 | | | | | | (35) all_268_1 = 0 % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | BETA: splitting (31) gives: % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | Case 1: % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | | (36) ~ (all_277_0 = 0) % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | | REDUCE: (33), (36) imply: % 79.48/11.33 | | | | | | | (37) $false % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | | CLOSE: (37) is inconsistent. % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | Case 2: % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | | (38) ~ (all_277_1 = 0) % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | | REDUCE: (32), (38) imply: % 79.48/11.33 | | | | | | | (39) $false % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | | CLOSE: (39) is inconsistent. % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | End of split % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | Case 2: % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | (40) member(all_91_0, all_32_4) = all_196_5 & member(all_66_0, % 79.48/11.33 | | | | | | all_32_5) = all_196_4 & ( ~ (all_196_4 = 0) | ~ % 79.48/11.33 | | | | | | (all_196_5 = 0)) % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | ALPHA: (40) implies: % 79.48/11.33 | | | | | | (41) member(all_66_0, all_32_5) = all_196_4 % 79.48/11.33 | | | | | | (42) member(all_91_0, all_32_4) = all_196_5 % 79.48/11.33 | | | | | | (43) ~ (all_196_4 = 0) | ~ (all_196_5 = 0) % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | GROUND_INST: instantiating (10) with 0, all_196_4, all_32_5, % 79.48/11.33 | | | | | | all_66_0, simplifying with (5), (41) gives: % 79.48/11.33 | | | | | | (44) all_196_4 = 0 % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | GROUND_INST: instantiating (10) with 0, all_196_5, all_32_4, % 79.48/11.33 | | | | | | all_91_0, simplifying with (2), (42) gives: % 79.48/11.33 | | | | | | (45) all_196_5 = 0 % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | BETA: splitting (43) gives: % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | Case 1: % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | | (46) ~ (all_196_4 = 0) % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | | REDUCE: (44), (46) imply: % 79.48/11.33 | | | | | | | (47) $false % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | | CLOSE: (47) is inconsistent. % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | Case 2: % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | | (48) ~ (all_196_5 = 0) % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | | REDUCE: (45), (48) imply: % 79.48/11.33 | | | | | | | (49) $false % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | | CLOSE: (49) is inconsistent. % 79.48/11.33 | | | | | | | % 79.48/11.33 | | | | | | End of split % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | End of split % 79.48/11.33 | | | | | % 79.48/11.33 | | | | Case 2: % 79.48/11.33 | | | | | % 79.48/11.33 | | | | | (50) member(all_68_0, all_32_5) = all_277_0 & member(all_57_2, % 79.48/11.33 | | | | | all_32_4) = all_277_1 & ( ~ (all_277_0 = 0) | ~ (all_277_1 % 79.48/11.33 | | | | | = 0)) % 79.48/11.33 | | | | | % 79.48/11.33 | | | | | ALPHA: (50) implies: % 79.48/11.33 | | | | | (51) member(all_57_2, all_32_4) = all_277_1 % 79.48/11.33 | | | | | (52) member(all_68_0, all_32_5) = all_277_0 % 79.48/11.33 | | | | | (53) ~ (all_277_0 = 0) | ~ (all_277_1 = 0) % 79.48/11.33 | | | | | % 79.48/11.33 | | | | | GROUND_INST: instantiating (10) with 0, all_277_1, all_32_4, all_57_2, % 79.48/11.33 | | | | | simplifying with (4), (51) gives: % 79.48/11.33 | | | | | (54) all_277_1 = 0 % 79.48/11.33 | | | | | % 79.48/11.33 | | | | | GROUND_INST: instantiating (10) with 0, all_277_0, all_32_5, all_68_0, % 79.48/11.33 | | | | | simplifying with (1), (52) gives: % 79.48/11.33 | | | | | (55) all_277_0 = 0 % 79.48/11.33 | | | | | % 79.48/11.33 | | | | | BETA: splitting (53) gives: % 79.48/11.33 | | | | | % 79.48/11.33 | | | | | Case 1: % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | (56) ~ (all_277_0 = 0) % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | REDUCE: (55), (56) imply: % 79.48/11.33 | | | | | | (57) $false % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | CLOSE: (57) is inconsistent. % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | Case 2: % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | (58) ~ (all_277_1 = 0) % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | REDUCE: (54), (58) imply: % 79.48/11.33 | | | | | | (59) $false % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | | CLOSE: (59) is inconsistent. % 79.48/11.33 | | | | | | % 79.48/11.33 | | | | | End of split % 79.48/11.33 | | | | | % 79.48/11.33 | | | | End of split % 79.48/11.33 | | | | % 79.48/11.33 | | | End of split % 79.48/11.33 | | | % 79.48/11.33 | | Case 2: % 79.48/11.33 | | | % 79.48/11.33 | | | (60) member(all_68_0, all_32_5) = all_268_0 & member(all_57_2, % 79.48/11.33 | | | all_32_4) = all_268_1 & ( ~ (all_268_0 = 0) | ~ (all_268_1 = % 79.48/11.33 | | | 0)) % 79.48/11.33 | | | % 79.48/11.33 | | | ALPHA: (60) implies: % 79.48/11.33 | | | (61) member(all_57_2, all_32_4) = all_268_1 % 79.48/11.33 | | | (62) member(all_68_0, all_32_5) = all_268_0 % 79.48/11.33 | | | (63) ~ (all_268_0 = 0) | ~ (all_268_1 = 0) % 79.48/11.33 | | | % 79.48/11.33 | | | GROUND_INST: instantiating (10) with 0, all_268_1, all_32_4, all_57_2, % 79.48/11.33 | | | simplifying with (4), (61) gives: % 79.48/11.33 | | | (64) all_268_1 = 0 % 79.48/11.33 | | | % 79.48/11.33 | | | GROUND_INST: instantiating (10) with 0, all_268_0, all_32_5, all_68_0, % 79.48/11.33 | | | simplifying with (1), (62) gives: % 79.48/11.33 | | | (65) all_268_0 = 0 % 79.48/11.33 | | | % 79.48/11.33 | | | BETA: splitting (63) gives: % 79.48/11.33 | | | % 79.48/11.33 | | | Case 1: % 79.48/11.33 | | | | % 79.48/11.33 | | | | (66) ~ (all_268_0 = 0) % 79.48/11.33 | | | | % 79.48/11.33 | | | | REDUCE: (65), (66) imply: % 79.48/11.33 | | | | (67) $false % 79.48/11.33 | | | | % 79.48/11.33 | | | | CLOSE: (67) is inconsistent. % 79.48/11.33 | | | | % 79.48/11.33 | | | Case 2: % 79.48/11.33 | | | | % 79.48/11.33 | | | | (68) ~ (all_268_1 = 0) % 79.48/11.33 | | | | % 79.48/11.33 | | | | REDUCE: (64), (68) imply: % 79.48/11.33 | | | | (69) $false % 79.48/11.33 | | | | % 79.48/11.33 | | | | CLOSE: (69) is inconsistent. % 79.48/11.33 | | | | % 79.48/11.33 | | | End of split % 79.48/11.33 | | | % 79.48/11.33 | | End of split % 79.48/11.33 | | % 79.48/11.33 | End of split % 79.48/11.33 | % 79.48/11.33 End of proof % 79.48/11.33 % SZS output end Proof for theBenchmark % 79.48/11.33 % 79.48/11.33 10722ms %------------------------------------------------------------------------------