%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET014+4 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n032.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 15:23:06 EDT 2023 % Result : Theorem 9.07s 1.89s % Output : Proof 11.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SET014+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.31 % Computer : n032.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 300 % 0.11/0.31 % DateTime : Sat Aug 26 16:32:44 EDT 2023 % 0.11/0.31 % CPUTime : % 0.17/0.53 ________ _____ % 0.17/0.53 ___ __ \_________(_)________________________________ % 0.17/0.53 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.53 % 0.17/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.53 (2023-06-19) % 0.17/0.53 % 0.17/0.53 (c) Philipp Rümmer, 2009-2023 % 0.17/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.53 Amanda Stjerna. % 0.17/0.53 Free software under BSD-3-Clause. % 0.17/0.53 % 0.17/0.53 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.53 % 0.17/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.17/0.54 Running up to 7 provers in parallel. % 0.17/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.77/0.94 Prover 1: Preprocessing ... % 1.77/0.94 Prover 4: Preprocessing ... % 2.43/0.98 Prover 2: Preprocessing ... % 2.43/0.98 Prover 0: Preprocessing ... % 2.43/0.98 Prover 3: Preprocessing ... % 2.43/0.98 Prover 6: Preprocessing ... % 2.43/0.98 Prover 5: Preprocessing ... % 4.92/1.33 Prover 6: Proving ... % 4.92/1.33 Prover 5: Proving ... % 4.92/1.33 Prover 3: Constructing countermodel ... % 4.92/1.35 Prover 1: Constructing countermodel ... % 4.92/1.37 Prover 4: Constructing countermodel ... % 4.92/1.38 Prover 2: Proving ... % 4.92/1.40 Prover 0: Proving ... % 6.78/1.60 Prover 3: gave up % 6.78/1.61 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 6.78/1.62 Prover 1: gave up % 7.24/1.63 Prover 7: Preprocessing ... % 7.24/1.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.54/1.66 Prover 8: Preprocessing ... % 7.54/1.69 Prover 7: Warning: ignoring some quantifiers % 7.54/1.70 Prover 7: Constructing countermodel ... % 8.15/1.74 Prover 7: gave up % 8.15/1.74 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 8.15/1.77 Prover 8: Warning: ignoring some quantifiers % 8.15/1.77 Prover 8: Constructing countermodel ... % 8.46/1.78 Prover 9: Preprocessing ... % 9.07/1.88 Prover 8: gave up % 9.07/1.89 Prover 0: proved (1334ms) % 9.07/1.89 % 9.07/1.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.07/1.89 % 9.07/1.90 Prover 5: stopped % 9.07/1.90 Prover 6: stopped % 9.07/1.90 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 9.07/1.90 Prover 2: stopped % 9.07/1.90 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 9.07/1.90 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 9.07/1.90 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.07/1.91 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 9.07/1.92 Prover 13: Preprocessing ... % 9.07/1.92 Prover 10: Preprocessing ... % 9.51/1.92 Prover 16: Preprocessing ... % 9.51/1.92 Prover 19: Preprocessing ... % 9.51/1.93 Prover 11: Preprocessing ... % 9.51/1.96 Prover 9: Constructing countermodel ... % 9.51/1.97 Prover 9: stopped % 9.51/1.97 Prover 10: Warning: ignoring some quantifiers % 9.51/1.97 Prover 10: Constructing countermodel ... % 9.51/1.99 Prover 16: Warning: ignoring some quantifiers % 9.51/2.00 Prover 10: gave up % 9.51/2.01 Prover 16: Constructing countermodel ... % 9.51/2.01 Prover 13: Warning: ignoring some quantifiers % 9.51/2.03 Prover 13: Constructing countermodel ... % 9.51/2.04 Prover 11: Constructing countermodel ... % 9.51/2.05 Prover 19: Warning: ignoring some quantifiers % 9.51/2.06 Prover 19: Constructing countermodel ... % 9.85/2.12 Prover 4: Found proof (size 152) % 9.85/2.12 Prover 4: proved (1568ms) % 9.85/2.12 Prover 16: stopped % 9.85/2.13 Prover 19: stopped % 9.85/2.13 Prover 13: stopped % 9.85/2.13 Prover 11: stopped % 9.85/2.13 % 9.85/2.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.85/2.13 % 9.85/2.15 % SZS output start Proof for theBenchmark % 9.85/2.15 Assumptions after simplification: % 9.85/2.15 --------------------------------- % 9.85/2.15 % 9.85/2.15 (equal_set) % 11.17/2.18 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 11.17/2.18 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 11.17/2.18 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 11.17/2.18 $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) | ~ $i(v1) | % 11.17/2.18 ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 & % 11.17/2.18 subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] : % 11.17/2.18 ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 11.17/2.18 | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) = % 11.17/2.18 v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 11.17/2.18 (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | (subset(v1, v0) = 0 & % 11.17/2.18 subset(v0, v1) = 0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v1, v0) = % 11.17/2.18 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0, % 11.17/2.18 v1) = v3 & subset(v0, v1) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i] % 11.17/2.18 : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: % 11.17/2.18 any] : ? [v3: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) = v2 & ( ~ % 11.17/2.18 (v2 = 0) | v3 = 0))) % 11.17/2.18 % 11.17/2.18 (subset) % 11.17/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 11.17/2.19 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 11.17/2.19 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] : % 11.17/2.19 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | % 11.17/2.19 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 & % 11.17/2.19 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 11.17/2.19 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | % 11.17/2.19 ~ $i(v0) | member(v2, v1) = 0) % 11.17/2.19 % 11.17/2.19 (thI45) % 11.17/2.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] : ? % 11.17/2.19 [v5: $i] : ? [v6: any] : (union(v1, v2) = v5 & subset(v5, v0) = v6 & % 11.17/2.19 subset(v2, v0) = v4 & subset(v1, v0) = v3 & $i(v5) & $i(v2) & $i(v1) & % 11.17/2.19 $i(v0) & ((v6 = 0 & ( ~ (v4 = 0) | ~ (v3 = 0))) | (v4 = 0 & v3 = 0 & ~ (v6 % 11.17/2.19 = 0)))) % 11.17/2.19 % 11.17/2.19 (union) % 11.17/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 11.17/2.19 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 11.17/2.19 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 11.17/2.19 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 11.17/2.19 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) % 11.17/2.19 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 11.17/2.19 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 11.17/2.19 % 11.17/2.19 (function-axioms) % 11.17/2.20 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.17/2.20 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 11.17/2.20 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.17/2.20 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 11.17/2.20 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 11.17/2.20 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 11.17/2.20 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 11.17/2.20 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 11.17/2.20 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 11.17/2.20 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 11.17/2.20 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 11.17/2.20 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 11.17/2.20 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.17/2.20 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 11.17/2.20 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 11.17/2.20 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 11.17/2.20 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 11.17/2.20 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 11.17/2.20 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 11.17/2.20 (power_set(v2) = v0)) % 11.17/2.20 % 11.17/2.20 Further assumptions not needed in the proof: % 11.17/2.20 -------------------------------------------- % 11.17/2.20 difference, empty_set, intersection, power_set, product, singleton, sum, % 11.17/2.20 unordered_pair % 11.17/2.20 % 11.17/2.20 Those formulas are unsatisfiable: % 11.17/2.20 --------------------------------- % 11.17/2.20 % 11.17/2.20 Begin of proof % 11.17/2.20 | % 11.37/2.20 | ALPHA: (subset) implies: % 11.37/2.20 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 11.37/2.20 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 11.37/2.20 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 11.37/2.20 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 11.37/2.20 | (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ % 11.37/2.20 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = % 11.37/2.20 | v4)) % 11.37/2.20 | % 11.37/2.20 | ALPHA: (equal_set) implies: % 11.37/2.21 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | % 11.37/2.21 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0, % 11.37/2.21 | v1) = v3 & subset(v1, v0) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = % 11.37/2.21 | 0)))) % 11.37/2.21 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) | % 11.37/2.21 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0, % 11.37/2.21 | v1) = v3 & subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = % 11.37/2.21 | 0)))) % 11.37/2.21 | % 11.37/2.21 | ALPHA: (union) implies: % 11.37/2.21 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, % 11.37/2.21 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 11.37/2.21 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 & % 11.37/2.21 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 11.37/2.21 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 11.37/2.21 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ % 11.37/2.21 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 11.37/2.21 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = % 11.37/2.21 | v5)) % 11.37/2.21 | % 11.37/2.21 | ALPHA: (function-axioms) implies: % 11.37/2.21 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 11.37/2.21 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 11.37/2.21 | = v0)) % 11.37/2.21 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 11.37/2.21 | ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) % 11.37/2.21 | = v0)) % 11.37/2.21 | % 11.37/2.21 | DELTA: instantiating (thI45) with fresh symbols all_15_0, all_15_1, all_15_2, % 11.37/2.21 | all_15_3, all_15_4, all_15_5, all_15_6 gives: % 11.37/2.21 | (9) union(all_15_5, all_15_4) = all_15_1 & subset(all_15_1, all_15_6) = % 11.37/2.21 | all_15_0 & subset(all_15_4, all_15_6) = all_15_2 & subset(all_15_5, % 11.37/2.21 | all_15_6) = all_15_3 & $i(all_15_1) & $i(all_15_4) & $i(all_15_5) & % 11.37/2.21 | $i(all_15_6) & ((all_15_0 = 0 & ( ~ (all_15_2 = 0) | ~ (all_15_3 = % 11.37/2.21 | 0))) | (all_15_2 = 0 & all_15_3 = 0 & ~ (all_15_0 = 0))) % 11.37/2.21 | % 11.37/2.21 | ALPHA: (9) implies: % 11.37/2.21 | (10) $i(all_15_6) % 11.37/2.21 | (11) $i(all_15_5) % 11.37/2.21 | (12) $i(all_15_4) % 11.37/2.21 | (13) $i(all_15_1) % 11.37/2.21 | (14) subset(all_15_5, all_15_6) = all_15_3 % 11.37/2.21 | (15) subset(all_15_4, all_15_6) = all_15_2 % 11.37/2.21 | (16) subset(all_15_1, all_15_6) = all_15_0 % 11.37/2.21 | (17) union(all_15_5, all_15_4) = all_15_1 % 11.37/2.21 | (18) (all_15_0 = 0 & ( ~ (all_15_2 = 0) | ~ (all_15_3 = 0))) | (all_15_2 = % 11.37/2.21 | 0 & all_15_3 = 0 & ~ (all_15_0 = 0)) % 11.37/2.21 | % 11.37/2.21 | GROUND_INST: instantiating (1) with all_15_5, all_15_6, all_15_3, simplifying % 11.37/2.21 | with (10), (11), (14) gives: % 11.37/2.21 | (19) all_15_3 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 11.37/2.21 | all_15_5) = 0 & member(v0, all_15_6) = v1 & $i(v0)) % 11.37/2.21 | % 11.37/2.21 | GROUND_INST: instantiating (4) with all_15_6, all_15_5, all_15_3, simplifying % 11.37/2.21 | with (10), (11), (14) gives: % 11.37/2.22 | (20) ? [v0: any] : ? [v1: any] : (equal_set(all_15_6, all_15_5) = v0 & % 11.37/2.22 | subset(all_15_6, all_15_5) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_3 % 11.37/2.22 | = 0))) % 11.37/2.22 | % 11.37/2.22 | GROUND_INST: instantiating (3) with all_15_5, all_15_6, all_15_3, simplifying % 11.37/2.22 | with (10), (11), (14) gives: % 11.37/2.22 | (21) ? [v0: any] : ? [v1: any] : (equal_set(all_15_5, all_15_6) = v0 & % 11.37/2.22 | subset(all_15_6, all_15_5) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_3 % 11.37/2.22 | = 0))) % 11.37/2.22 | % 11.37/2.22 | GROUND_INST: instantiating (1) with all_15_4, all_15_6, all_15_2, simplifying % 11.37/2.22 | with (10), (12), (15) gives: % 11.37/2.22 | (22) all_15_2 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 11.37/2.22 | all_15_4) = 0 & member(v0, all_15_6) = v1 & $i(v0)) % 11.37/2.22 | % 11.37/2.22 | GROUND_INST: instantiating (4) with all_15_6, all_15_4, all_15_2, simplifying % 11.37/2.22 | with (10), (12), (15) gives: % 11.37/2.22 | (23) ? [v0: any] : ? [v1: any] : (equal_set(all_15_6, all_15_4) = v0 & % 11.37/2.22 | subset(all_15_6, all_15_4) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_2 % 11.37/2.22 | = 0))) % 11.37/2.22 | % 11.37/2.22 | GROUND_INST: instantiating (3) with all_15_4, all_15_6, all_15_2, simplifying % 11.37/2.22 | with (10), (12), (15) gives: % 11.37/2.22 | (24) ? [v0: any] : ? [v1: any] : (equal_set(all_15_4, all_15_6) = v0 & % 11.37/2.22 | subset(all_15_6, all_15_4) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_2 % 11.37/2.22 | = 0))) % 11.37/2.22 | % 11.37/2.22 | GROUND_INST: instantiating (1) with all_15_1, all_15_6, all_15_0, simplifying % 11.37/2.22 | with (10), (13), (16) gives: % 11.37/2.22 | (25) all_15_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 11.37/2.22 | all_15_1) = 0 & member(v0, all_15_6) = v1 & $i(v0)) % 11.37/2.22 | % 11.37/2.22 | GROUND_INST: instantiating (4) with all_15_6, all_15_1, all_15_0, simplifying % 11.37/2.22 | with (10), (13), (16) gives: % 11.37/2.22 | (26) ? [v0: any] : ? [v1: any] : (equal_set(all_15_6, all_15_1) = v0 & % 11.37/2.22 | subset(all_15_6, all_15_1) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_0 % 11.37/2.22 | = 0))) % 11.37/2.22 | % 11.37/2.22 | GROUND_INST: instantiating (3) with all_15_1, all_15_6, all_15_0, simplifying % 11.37/2.22 | with (10), (13), (16) gives: % 11.37/2.22 | (27) ? [v0: any] : ? [v1: any] : (equal_set(all_15_1, all_15_6) = v0 & % 11.37/2.22 | subset(all_15_6, all_15_1) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_0 % 11.37/2.22 | = 0))) % 11.37/2.22 | % 11.37/2.22 | DELTA: instantiating (27) with fresh symbols all_22_0, all_22_1 gives: % 11.37/2.22 | (28) equal_set(all_15_1, all_15_6) = all_22_1 & subset(all_15_6, all_15_1) % 11.37/2.22 | = all_22_0 & ( ~ (all_22_1 = 0) | (all_22_0 = 0 & all_15_0 = 0)) % 11.37/2.22 | % 11.37/2.22 | ALPHA: (28) implies: % 11.37/2.22 | (29) subset(all_15_6, all_15_1) = all_22_0 % 11.37/2.22 | % 11.37/2.22 | DELTA: instantiating (23) with fresh symbols all_24_0, all_24_1 gives: % 11.37/2.22 | (30) equal_set(all_15_6, all_15_4) = all_24_1 & subset(all_15_6, all_15_4) % 11.37/2.22 | = all_24_0 & ( ~ (all_24_1 = 0) | (all_24_0 = 0 & all_15_2 = 0)) % 11.37/2.22 | % 11.37/2.22 | ALPHA: (30) implies: % 11.37/2.22 | (31) subset(all_15_6, all_15_4) = all_24_0 % 11.37/2.22 | % 11.37/2.22 | DELTA: instantiating (21) with fresh symbols all_26_0, all_26_1 gives: % 11.37/2.22 | (32) equal_set(all_15_5, all_15_6) = all_26_1 & subset(all_15_6, all_15_5) % 11.37/2.22 | = all_26_0 & ( ~ (all_26_1 = 0) | (all_26_0 = 0 & all_15_3 = 0)) % 11.37/2.22 | % 11.37/2.22 | ALPHA: (32) implies: % 11.37/2.22 | (33) subset(all_15_6, all_15_5) = all_26_0 % 11.37/2.22 | % 11.37/2.22 | DELTA: instantiating (20) with fresh symbols all_28_0, all_28_1 gives: % 11.37/2.22 | (34) equal_set(all_15_6, all_15_5) = all_28_1 & subset(all_15_6, all_15_5) % 11.37/2.22 | = all_28_0 & ( ~ (all_28_1 = 0) | (all_28_0 = 0 & all_15_3 = 0)) % 11.37/2.22 | % 11.37/2.22 | ALPHA: (34) implies: % 11.37/2.22 | (35) subset(all_15_6, all_15_5) = all_28_0 % 11.37/2.22 | % 11.37/2.22 | DELTA: instantiating (26) with fresh symbols all_30_0, all_30_1 gives: % 11.37/2.22 | (36) equal_set(all_15_6, all_15_1) = all_30_1 & subset(all_15_6, all_15_1) % 11.37/2.22 | = all_30_0 & ( ~ (all_30_1 = 0) | (all_30_0 = 0 & all_15_0 = 0)) % 11.37/2.22 | % 11.37/2.22 | ALPHA: (36) implies: % 11.37/2.22 | (37) subset(all_15_6, all_15_1) = all_30_0 % 11.37/2.22 | % 11.37/2.22 | DELTA: instantiating (24) with fresh symbols all_32_0, all_32_1 gives: % 11.37/2.22 | (38) equal_set(all_15_4, all_15_6) = all_32_1 & subset(all_15_6, all_15_4) % 11.37/2.22 | = all_32_0 & ( ~ (all_32_1 = 0) | (all_32_0 = 0 & all_15_2 = 0)) % 11.37/2.23 | % 11.37/2.23 | ALPHA: (38) implies: % 11.37/2.23 | (39) subset(all_15_6, all_15_4) = all_32_0 % 11.37/2.23 | (40) ~ (all_32_1 = 0) | (all_32_0 = 0 & all_15_2 = 0) % 11.37/2.23 | % 11.37/2.23 | GROUND_INST: instantiating (8) with all_26_0, all_28_0, all_15_5, all_15_6, % 11.37/2.23 | simplifying with (33), (35) gives: % 11.37/2.23 | (41) all_28_0 = all_26_0 % 11.37/2.23 | % 11.37/2.23 | GROUND_INST: instantiating (8) with all_24_0, all_32_0, all_15_4, all_15_6, % 11.37/2.23 | simplifying with (31), (39) gives: % 11.37/2.23 | (42) all_32_0 = all_24_0 % 11.37/2.23 | % 11.37/2.23 | GROUND_INST: instantiating (8) with all_22_0, all_30_0, all_15_1, all_15_6, % 11.37/2.23 | simplifying with (29), (37) gives: % 11.37/2.23 | (43) all_30_0 = all_22_0 % 11.37/2.23 | % 11.37/2.23 | GROUND_INST: instantiating (4) with all_15_5, all_15_6, all_26_0, simplifying % 11.37/2.23 | with (10), (11), (33) gives: % 11.37/2.23 | (44) ? [v0: any] : ? [v1: any] : (equal_set(all_15_5, all_15_6) = v0 & % 11.37/2.23 | subset(all_15_5, all_15_6) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_26_0 % 11.37/2.23 | = 0))) % 11.37/2.23 | % 11.37/2.23 | GROUND_INST: instantiating (3) with all_15_6, all_15_5, all_26_0, simplifying % 11.37/2.23 | with (10), (11), (33) gives: % 11.37/2.23 | (45) ? [v0: any] : ? [v1: any] : (equal_set(all_15_6, all_15_5) = v0 & % 11.37/2.23 | subset(all_15_5, all_15_6) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_26_0 % 11.37/2.23 | = 0))) % 11.37/2.23 | % 11.37/2.23 | GROUND_INST: instantiating (4) with all_15_4, all_15_6, all_24_0, simplifying % 11.37/2.23 | with (10), (12), (31) gives: % 11.37/2.23 | (46) ? [v0: any] : ? [v1: any] : (equal_set(all_15_4, all_15_6) = v0 & % 11.37/2.23 | subset(all_15_4, all_15_6) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_24_0 % 11.37/2.23 | = 0))) % 11.37/2.23 | % 11.37/2.23 | GROUND_INST: instantiating (3) with all_15_6, all_15_4, all_24_0, simplifying % 11.37/2.23 | with (10), (12), (31) gives: % 11.37/2.23 | (47) ? [v0: any] : ? [v1: any] : (equal_set(all_15_6, all_15_4) = v0 & % 11.37/2.23 | subset(all_15_4, all_15_6) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_24_0 % 11.37/2.23 | = 0))) % 11.37/2.23 | % 11.37/2.23 | GROUND_INST: instantiating (4) with all_15_1, all_15_6, all_22_0, simplifying % 11.37/2.23 | with (10), (13), (29) gives: % 11.37/2.23 | (48) ? [v0: any] : ? [v1: any] : (equal_set(all_15_1, all_15_6) = v0 & % 11.37/2.23 | subset(all_15_1, all_15_6) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_22_0 % 11.37/2.23 | = 0))) % 11.37/2.23 | % 11.37/2.23 | GROUND_INST: instantiating (3) with all_15_6, all_15_1, all_22_0, simplifying % 11.37/2.23 | with (10), (13), (29) gives: % 11.37/2.23 | (49) ? [v0: any] : ? [v1: any] : (equal_set(all_15_6, all_15_1) = v0 & % 11.37/2.23 | subset(all_15_1, all_15_6) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_22_0 % 11.37/2.23 | = 0))) % 11.37/2.23 | % 11.37/2.23 | DELTA: instantiating (49) with fresh symbols all_43_0, all_43_1 gives: % 11.37/2.23 | (50) equal_set(all_15_6, all_15_1) = all_43_1 & subset(all_15_1, all_15_6) % 11.37/2.23 | = all_43_0 & ( ~ (all_43_1 = 0) | (all_43_0 = 0 & all_22_0 = 0)) % 11.37/2.23 | % 11.37/2.23 | ALPHA: (50) implies: % 11.37/2.23 | (51) subset(all_15_1, all_15_6) = all_43_0 % 11.37/2.23 | % 11.37/2.23 | DELTA: instantiating (47) with fresh symbols all_45_0, all_45_1 gives: % 11.37/2.23 | (52) equal_set(all_15_6, all_15_4) = all_45_1 & subset(all_15_4, all_15_6) % 11.37/2.23 | = all_45_0 & ( ~ (all_45_1 = 0) | (all_45_0 = 0 & all_24_0 = 0)) % 11.37/2.23 | % 11.37/2.23 | ALPHA: (52) implies: % 11.37/2.23 | (53) subset(all_15_4, all_15_6) = all_45_0 % 11.37/2.23 | % 11.37/2.23 | DELTA: instantiating (46) with fresh symbols all_47_0, all_47_1 gives: % 11.37/2.23 | (54) equal_set(all_15_4, all_15_6) = all_47_1 & subset(all_15_4, all_15_6) % 11.37/2.23 | = all_47_0 & ( ~ (all_47_1 = 0) | (all_47_0 = 0 & all_24_0 = 0)) % 11.37/2.23 | % 11.37/2.23 | ALPHA: (54) implies: % 11.37/2.23 | (55) subset(all_15_4, all_15_6) = all_47_0 % 11.37/2.23 | % 11.37/2.23 | DELTA: instantiating (45) with fresh symbols all_49_0, all_49_1 gives: % 11.37/2.23 | (56) equal_set(all_15_6, all_15_5) = all_49_1 & subset(all_15_5, all_15_6) % 11.37/2.23 | = all_49_0 & ( ~ (all_49_1 = 0) | (all_49_0 = 0 & all_26_0 = 0)) % 11.37/2.23 | % 11.37/2.23 | ALPHA: (56) implies: % 11.37/2.23 | (57) subset(all_15_5, all_15_6) = all_49_0 % 11.37/2.23 | % 11.37/2.23 | DELTA: instantiating (44) with fresh symbols all_51_0, all_51_1 gives: % 11.37/2.23 | (58) equal_set(all_15_5, all_15_6) = all_51_1 & subset(all_15_5, all_15_6) % 11.37/2.23 | = all_51_0 & ( ~ (all_51_1 = 0) | (all_51_0 = 0 & all_26_0 = 0)) % 11.37/2.23 | % 11.37/2.23 | ALPHA: (58) implies: % 11.37/2.24 | (59) subset(all_15_5, all_15_6) = all_51_0 % 11.37/2.24 | % 11.37/2.24 | DELTA: instantiating (48) with fresh symbols all_53_0, all_53_1 gives: % 11.37/2.24 | (60) equal_set(all_15_1, all_15_6) = all_53_1 & subset(all_15_1, all_15_6) % 11.37/2.24 | = all_53_0 & ( ~ (all_53_1 = 0) | (all_53_0 = 0 & all_22_0 = 0)) % 11.37/2.24 | % 11.37/2.24 | ALPHA: (60) implies: % 11.37/2.24 | (61) subset(all_15_1, all_15_6) = all_53_0 % 11.37/2.24 | % 11.37/2.24 | GROUND_INST: instantiating (8) with all_15_3, all_51_0, all_15_6, all_15_5, % 11.37/2.24 | simplifying with (14), (59) gives: % 11.37/2.24 | (62) all_51_0 = all_15_3 % 11.37/2.24 | % 11.37/2.24 | GROUND_INST: instantiating (8) with all_49_0, all_51_0, all_15_6, all_15_5, % 11.37/2.24 | simplifying with (57), (59) gives: % 11.37/2.24 | (63) all_51_0 = all_49_0 % 11.37/2.24 | % 11.37/2.24 | GROUND_INST: instantiating (8) with all_15_2, all_47_0, all_15_6, all_15_4, % 11.37/2.24 | simplifying with (15), (55) gives: % 11.37/2.24 | (64) all_47_0 = all_15_2 % 11.37/2.24 | % 11.37/2.24 | GROUND_INST: instantiating (8) with all_45_0, all_47_0, all_15_6, all_15_4, % 11.37/2.24 | simplifying with (53), (55) gives: % 11.37/2.24 | (65) all_47_0 = all_45_0 % 11.37/2.24 | % 11.37/2.24 | GROUND_INST: instantiating (8) with all_15_0, all_53_0, all_15_6, all_15_1, % 11.37/2.24 | simplifying with (16), (61) gives: % 11.55/2.24 | (66) all_53_0 = all_15_0 % 11.55/2.24 | % 11.55/2.24 | GROUND_INST: instantiating (8) with all_43_0, all_53_0, all_15_6, all_15_1, % 11.55/2.24 | simplifying with (51), (61) gives: % 11.55/2.24 | (67) all_53_0 = all_43_0 % 11.55/2.24 | % 11.55/2.24 | COMBINE_EQS: (66), (67) imply: % 11.55/2.24 | (68) all_43_0 = all_15_0 % 11.55/2.24 | % 11.55/2.24 | SIMP: (68) implies: % 11.55/2.24 | (69) all_43_0 = all_15_0 % 11.55/2.24 | % 11.55/2.24 | COMBINE_EQS: (62), (63) imply: % 11.55/2.24 | (70) all_49_0 = all_15_3 % 11.55/2.24 | % 11.55/2.24 | COMBINE_EQS: (64), (65) imply: % 11.55/2.24 | (71) all_45_0 = all_15_2 % 11.55/2.24 | % 11.55/2.24 | BETA: splitting (18) gives: % 11.55/2.24 | % 11.55/2.24 | Case 1: % 11.55/2.24 | | % 11.55/2.24 | | (72) all_15_0 = 0 & ( ~ (all_15_2 = 0) | ~ (all_15_3 = 0)) % 11.55/2.24 | | % 11.55/2.24 | | ALPHA: (72) implies: % 11.55/2.24 | | (73) all_15_0 = 0 % 11.55/2.24 | | (74) ~ (all_15_2 = 0) | ~ (all_15_3 = 0) % 11.55/2.24 | | % 11.55/2.24 | | REDUCE: (16), (73) imply: % 11.55/2.24 | | (75) subset(all_15_1, all_15_6) = 0 % 11.55/2.24 | | % 11.55/2.24 | | BETA: splitting (22) gives: % 11.55/2.24 | | % 11.55/2.24 | | Case 1: % 11.55/2.24 | | | % 11.55/2.24 | | | (76) all_15_2 = 0 % 11.55/2.24 | | | % 11.55/2.24 | | | BETA: splitting (74) gives: % 11.55/2.24 | | | % 11.55/2.24 | | | Case 1: % 11.55/2.24 | | | | % 11.55/2.24 | | | | (77) ~ (all_15_2 = 0) % 11.55/2.24 | | | | % 11.55/2.24 | | | | REDUCE: (76), (77) imply: % 11.55/2.24 | | | | (78) $false % 11.55/2.24 | | | | % 11.55/2.24 | | | | CLOSE: (78) is inconsistent. % 11.55/2.24 | | | | % 11.55/2.24 | | | Case 2: % 11.55/2.24 | | | | % 11.55/2.24 | | | | (79) ~ (all_15_3 = 0) % 11.55/2.24 | | | | % 11.55/2.24 | | | | BETA: splitting (19) gives: % 11.55/2.24 | | | | % 11.55/2.24 | | | | Case 1: % 11.55/2.24 | | | | | % 11.55/2.24 | | | | | (80) all_15_3 = 0 % 11.55/2.24 | | | | | % 11.55/2.24 | | | | | REDUCE: (79), (80) imply: % 11.55/2.24 | | | | | (81) $false % 11.55/2.24 | | | | | % 11.55/2.24 | | | | | CLOSE: (81) is inconsistent. % 11.55/2.24 | | | | | % 11.55/2.24 | | | | Case 2: % 11.55/2.24 | | | | | % 11.55/2.24 | | | | | (82) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, % 11.55/2.24 | | | | | all_15_5) = 0 & member(v0, all_15_6) = v1 & $i(v0)) % 11.55/2.24 | | | | | % 11.55/2.24 | | | | | DELTA: instantiating (82) with fresh symbols all_108_0, all_108_1 % 11.55/2.24 | | | | | gives: % 11.55/2.24 | | | | | (83) ~ (all_108_0 = 0) & member(all_108_1, all_15_5) = 0 & % 11.55/2.24 | | | | | member(all_108_1, all_15_6) = all_108_0 & $i(all_108_1) % 11.55/2.24 | | | | | % 11.55/2.24 | | | | | ALPHA: (83) implies: % 11.55/2.24 | | | | | (84) ~ (all_108_0 = 0) % 11.55/2.24 | | | | | (85) $i(all_108_1) % 11.55/2.24 | | | | | (86) member(all_108_1, all_15_6) = all_108_0 % 11.55/2.24 | | | | | (87) member(all_108_1, all_15_5) = 0 % 11.55/2.24 | | | | | % 11.55/2.24 | | | | | GROUND_INST: instantiating (2) with all_15_1, all_15_6, all_108_1, % 11.55/2.24 | | | | | all_108_0, simplifying with (10), (13), (75), (85), (86) % 11.55/2.25 | | | | | gives: % 11.55/2.25 | | | | | (88) all_108_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 11.55/2.25 | | | | | member(all_108_1, all_15_1) = v0) % 11.55/2.25 | | | | | % 11.55/2.25 | | | | | BETA: splitting (88) gives: % 11.55/2.25 | | | | | % 11.55/2.25 | | | | | Case 1: % 11.55/2.25 | | | | | | % 11.55/2.25 | | | | | | (89) all_108_0 = 0 % 11.55/2.25 | | | | | | % 11.55/2.25 | | | | | | REDUCE: (84), (89) imply: % 11.55/2.25 | | | | | | (90) $false % 11.55/2.25 | | | | | | % 11.55/2.25 | | | | | | CLOSE: (90) is inconsistent. % 11.55/2.25 | | | | | | % 11.55/2.25 | | | | | Case 2: % 11.55/2.25 | | | | | | % 11.55/2.25 | | | | | | (91) ? [v0: int] : ( ~ (v0 = 0) & member(all_108_1, all_15_1) = % 11.55/2.25 | | | | | | v0) % 11.55/2.25 | | | | | | % 11.55/2.25 | | | | | | DELTA: instantiating (91) with fresh symbol all_134_0 gives: % 11.55/2.25 | | | | | | (92) ~ (all_134_0 = 0) & member(all_108_1, all_15_1) = all_134_0 % 11.55/2.25 | | | | | | % 11.55/2.25 | | | | | | ALPHA: (92) implies: % 11.55/2.25 | | | | | | (93) ~ (all_134_0 = 0) % 11.55/2.25 | | | | | | (94) member(all_108_1, all_15_1) = all_134_0 % 11.55/2.25 | | | | | | % 11.55/2.25 | | | | | | GROUND_INST: instantiating (6) with all_108_1, all_15_5, all_15_4, % 11.55/2.25 | | | | | | all_15_1, all_134_0, simplifying with (11), (12), (17), % 11.55/2.25 | | | | | | (85), (94) gives: % 11.55/2.25 | | | | | | (95) all_134_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 11.55/2.25 | | | | | | ~ (v0 = 0) & member(all_108_1, all_15_4) = v1 & % 11.55/2.25 | | | | | | member(all_108_1, all_15_5) = v0) % 11.55/2.25 | | | | | | % 11.55/2.25 | | | | | | BETA: splitting (95) gives: % 11.55/2.25 | | | | | | % 11.55/2.25 | | | | | | Case 1: % 11.55/2.25 | | | | | | | % 11.55/2.25 | | | | | | | (96) all_134_0 = 0 % 11.55/2.25 | | | | | | | % 11.55/2.25 | | | | | | | REDUCE: (93), (96) imply: % 11.55/2.25 | | | | | | | (97) $false % 11.55/2.25 | | | | | | | % 11.55/2.25 | | | | | | | CLOSE: (97) is inconsistent. % 11.55/2.25 | | | | | | | % 11.55/2.25 | | | | | | Case 2: % 11.55/2.25 | | | | | | | % 11.55/2.25 | | | | | | | (98) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 11.55/2.25 | | | | | | | member(all_108_1, all_15_4) = v1 & member(all_108_1, % 11.55/2.25 | | | | | | | all_15_5) = v0) % 11.55/2.25 | | | | | | | % 11.55/2.25 | | | | | | | DELTA: instantiating (98) with fresh symbols all_155_0, all_155_1 % 11.55/2.25 | | | | | | | gives: % 11.55/2.25 | | | | | | | (99) ~ (all_155_0 = 0) & ~ (all_155_1 = 0) & % 11.55/2.25 | | | | | | | member(all_108_1, all_15_4) = all_155_0 & % 11.55/2.25 | | | | | | | member(all_108_1, all_15_5) = all_155_1 % 11.55/2.25 | | | | | | | % 11.55/2.25 | | | | | | | ALPHA: (99) implies: % 11.55/2.25 | | | | | | | (100) ~ (all_155_1 = 0) % 11.55/2.25 | | | | | | | (101) member(all_108_1, all_15_5) = all_155_1 % 11.55/2.25 | | | | | | | % 11.55/2.25 | | | | | | | GROUND_INST: instantiating (7) with 0, all_155_1, all_15_5, % 11.55/2.25 | | | | | | | all_108_1, simplifying with (87), (101) gives: % 11.55/2.25 | | | | | | | (102) all_155_1 = 0 % 11.55/2.25 | | | | | | | % 11.55/2.25 | | | | | | | REDUCE: (100), (102) imply: % 11.55/2.25 | | | | | | | (103) $false % 11.55/2.25 | | | | | | | % 11.55/2.25 | | | | | | | CLOSE: (103) is inconsistent. % 11.55/2.25 | | | | | | | % 11.55/2.25 | | | | | | End of split % 11.55/2.25 | | | | | | % 11.55/2.25 | | | | | End of split % 11.55/2.25 | | | | | % 11.55/2.25 | | | | End of split % 11.55/2.25 | | | | % 11.55/2.25 | | | End of split % 11.55/2.25 | | | % 11.55/2.25 | | Case 2: % 11.55/2.25 | | | % 11.55/2.25 | | | (104) ~ (all_15_2 = 0) % 11.55/2.25 | | | (105) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_4) % 11.55/2.25 | | | = 0 & member(v0, all_15_6) = v1 & $i(v0)) % 11.55/2.25 | | | % 11.55/2.25 | | | DELTA: instantiating (105) with fresh symbols all_88_0, all_88_1 gives: % 11.55/2.25 | | | (106) ~ (all_88_0 = 0) & member(all_88_1, all_15_4) = 0 & % 11.55/2.25 | | | member(all_88_1, all_15_6) = all_88_0 & $i(all_88_1) % 11.55/2.25 | | | % 11.55/2.25 | | | ALPHA: (106) implies: % 11.55/2.25 | | | (107) ~ (all_88_0 = 0) % 11.55/2.25 | | | (108) $i(all_88_1) % 11.55/2.25 | | | (109) member(all_88_1, all_15_6) = all_88_0 % 11.55/2.25 | | | (110) member(all_88_1, all_15_4) = 0 % 11.55/2.25 | | | % 11.55/2.25 | | | BETA: splitting (40) gives: % 11.55/2.25 | | | % 11.55/2.25 | | | Case 1: % 11.55/2.25 | | | | % 11.55/2.25 | | | | % 11.55/2.25 | | | | GROUND_INST: instantiating (2) with all_15_1, all_15_6, all_88_1, % 11.55/2.25 | | | | all_88_0, simplifying with (10), (13), (75), (108), (109) % 11.55/2.25 | | | | gives: % 11.55/2.25 | | | | (111) all_88_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_88_1, % 11.55/2.25 | | | | all_15_1) = v0) % 11.55/2.25 | | | | % 11.55/2.25 | | | | BETA: splitting (111) gives: % 11.55/2.25 | | | | % 11.55/2.25 | | | | Case 1: % 11.55/2.25 | | | | | % 11.55/2.25 | | | | | (112) all_88_0 = 0 % 11.55/2.25 | | | | | % 11.55/2.25 | | | | | REDUCE: (107), (112) imply: % 11.55/2.25 | | | | | (113) $false % 11.55/2.25 | | | | | % 11.55/2.25 | | | | | CLOSE: (113) is inconsistent. % 11.55/2.25 | | | | | % 11.55/2.25 | | | | Case 2: % 11.55/2.25 | | | | | % 11.55/2.25 | | | | | (114) ? [v0: int] : ( ~ (v0 = 0) & member(all_88_1, all_15_1) = % 11.55/2.25 | | | | | v0) % 11.55/2.25 | | | | | % 11.55/2.25 | | | | | DELTA: instantiating (114) with fresh symbol all_118_0 gives: % 11.55/2.25 | | | | | (115) ~ (all_118_0 = 0) & member(all_88_1, all_15_1) = all_118_0 % 11.55/2.25 | | | | | % 11.55/2.25 | | | | | ALPHA: (115) implies: % 11.55/2.26 | | | | | (116) ~ (all_118_0 = 0) % 11.55/2.26 | | | | | (117) member(all_88_1, all_15_1) = all_118_0 % 11.55/2.26 | | | | | % 11.55/2.26 | | | | | GROUND_INST: instantiating (6) with all_88_1, all_15_5, all_15_4, % 11.55/2.26 | | | | | all_15_1, all_118_0, simplifying with (11), (12), (17), % 11.55/2.26 | | | | | (108), (117) gives: % 11.55/2.26 | | | | | (118) all_118_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 11.55/2.26 | | | | | ~ (v0 = 0) & member(all_88_1, all_15_4) = v1 & % 11.55/2.26 | | | | | member(all_88_1, all_15_5) = v0) % 11.55/2.26 | | | | | % 11.55/2.26 | | | | | BETA: splitting (118) gives: % 11.55/2.26 | | | | | % 11.55/2.26 | | | | | Case 1: % 11.55/2.26 | | | | | | % 11.55/2.26 | | | | | | (119) all_118_0 = 0 % 11.55/2.26 | | | | | | % 11.55/2.26 | | | | | | REDUCE: (116), (119) imply: % 11.55/2.26 | | | | | | (120) $false % 11.55/2.26 | | | | | | % 11.55/2.26 | | | | | | CLOSE: (120) is inconsistent. % 11.55/2.26 | | | | | | % 11.55/2.26 | | | | | Case 2: % 11.55/2.26 | | | | | | % 11.55/2.26 | | | | | | (121) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 11.55/2.26 | | | | | | member(all_88_1, all_15_4) = v1 & member(all_88_1, % 11.55/2.26 | | | | | | all_15_5) = v0) % 11.55/2.26 | | | | | | % 11.55/2.26 | | | | | | DELTA: instantiating (121) with fresh symbols all_135_0, all_135_1 % 11.55/2.26 | | | | | | gives: % 11.55/2.26 | | | | | | (122) ~ (all_135_0 = 0) & ~ (all_135_1 = 0) & member(all_88_1, % 11.55/2.26 | | | | | | all_15_4) = all_135_0 & member(all_88_1, all_15_5) = % 11.55/2.26 | | | | | | all_135_1 % 11.55/2.26 | | | | | | % 11.55/2.26 | | | | | | ALPHA: (122) implies: % 11.55/2.26 | | | | | | (123) ~ (all_135_0 = 0) % 11.55/2.26 | | | | | | (124) member(all_88_1, all_15_4) = all_135_0 % 11.55/2.26 | | | | | | % 11.55/2.26 | | | | | | GROUND_INST: instantiating (7) with 0, all_135_0, all_15_4, % 11.55/2.26 | | | | | | all_88_1, simplifying with (110), (124) gives: % 11.55/2.26 | | | | | | (125) all_135_0 = 0 % 11.55/2.26 | | | | | | % 11.55/2.26 | | | | | | REDUCE: (123), (125) imply: % 11.55/2.26 | | | | | | (126) $false % 11.55/2.26 | | | | | | % 11.55/2.26 | | | | | | CLOSE: (126) is inconsistent. % 11.55/2.26 | | | | | | % 11.55/2.26 | | | | | End of split % 11.55/2.26 | | | | | % 11.55/2.26 | | | | End of split % 11.55/2.26 | | | | % 11.55/2.26 | | | Case 2: % 11.55/2.26 | | | | % 11.55/2.26 | | | | (127) all_32_0 = 0 & all_15_2 = 0 % 11.55/2.26 | | | | % 11.55/2.26 | | | | ALPHA: (127) implies: % 11.55/2.26 | | | | (128) all_15_2 = 0 % 11.55/2.26 | | | | % 11.55/2.26 | | | | REDUCE: (104), (128) imply: % 11.55/2.26 | | | | (129) $false % 11.55/2.26 | | | | % 11.55/2.26 | | | | CLOSE: (129) is inconsistent. % 11.55/2.26 | | | | % 11.55/2.26 | | | End of split % 11.55/2.26 | | | % 11.55/2.26 | | End of split % 11.55/2.26 | | % 11.55/2.26 | Case 2: % 11.55/2.26 | | % 11.55/2.26 | | (130) all_15_2 = 0 & all_15_3 = 0 & ~ (all_15_0 = 0) % 11.55/2.26 | | % 11.55/2.26 | | ALPHA: (130) implies: % 11.55/2.26 | | (131) all_15_3 = 0 % 11.55/2.26 | | (132) all_15_2 = 0 % 11.55/2.26 | | (133) ~ (all_15_0 = 0) % 11.55/2.26 | | % 11.55/2.26 | | REDUCE: (15), (132) imply: % 11.55/2.26 | | (134) subset(all_15_4, all_15_6) = 0 % 11.55/2.26 | | % 11.55/2.26 | | REDUCE: (14), (131) imply: % 11.55/2.26 | | (135) subset(all_15_5, all_15_6) = 0 % 11.55/2.26 | | % 11.55/2.26 | | BETA: splitting (25) gives: % 11.55/2.26 | | % 11.55/2.26 | | Case 1: % 11.55/2.26 | | | % 11.55/2.26 | | | (136) all_15_0 = 0 % 11.55/2.26 | | | % 11.55/2.26 | | | REDUCE: (133), (136) imply: % 11.55/2.26 | | | (137) $false % 11.55/2.26 | | | % 11.55/2.26 | | | CLOSE: (137) is inconsistent. % 11.55/2.26 | | | % 11.55/2.26 | | Case 2: % 11.55/2.26 | | | % 11.55/2.26 | | | (138) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 11.55/2.26 | | | = 0 & member(v0, all_15_6) = v1 & $i(v0)) % 11.55/2.26 | | | % 11.55/2.26 | | | DELTA: instantiating (138) with fresh symbols all_73_0, all_73_1 gives: % 11.55/2.26 | | | (139) ~ (all_73_0 = 0) & member(all_73_1, all_15_1) = 0 & % 11.55/2.26 | | | member(all_73_1, all_15_6) = all_73_0 & $i(all_73_1) % 11.55/2.26 | | | % 11.55/2.26 | | | ALPHA: (139) implies: % 11.55/2.26 | | | (140) ~ (all_73_0 = 0) % 11.55/2.26 | | | (141) $i(all_73_1) % 11.55/2.26 | | | (142) member(all_73_1, all_15_6) = all_73_0 % 11.55/2.26 | | | (143) member(all_73_1, all_15_1) = 0 % 11.55/2.26 | | | % 11.55/2.26 | | | GROUND_INST: instantiating (5) with all_73_1, all_15_5, all_15_4, % 11.55/2.26 | | | all_15_1, simplifying with (11), (12), (17), (141), (143) % 11.55/2.26 | | | gives: % 11.55/2.26 | | | (144) ? [v0: any] : ? [v1: any] : (member(all_73_1, all_15_4) = v1 & % 11.55/2.26 | | | member(all_73_1, all_15_5) = v0 & (v1 = 0 | v0 = 0)) % 11.55/2.26 | | | % 11.55/2.26 | | | GROUND_INST: instantiating (2) with all_15_5, all_15_6, all_73_1, % 11.55/2.26 | | | all_73_0, simplifying with (10), (11), (135), (141), (142) % 11.55/2.26 | | | gives: % 11.55/2.26 | | | (145) all_73_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_73_1, % 11.55/2.26 | | | all_15_5) = v0) % 11.55/2.26 | | | % 11.55/2.26 | | | GROUND_INST: instantiating (2) with all_15_4, all_15_6, all_73_1, % 11.55/2.26 | | | all_73_0, simplifying with (10), (12), (134), (141), (142) % 11.55/2.26 | | | gives: % 11.55/2.26 | | | (146) all_73_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_73_1, % 11.55/2.26 | | | all_15_4) = v0) % 11.55/2.26 | | | % 11.55/2.26 | | | DELTA: instantiating (144) with fresh symbols all_101_0, all_101_1 gives: % 11.55/2.26 | | | (147) member(all_73_1, all_15_4) = all_101_0 & member(all_73_1, % 11.55/2.26 | | | all_15_5) = all_101_1 & (all_101_0 = 0 | all_101_1 = 0) % 11.55/2.26 | | | % 11.55/2.26 | | | ALPHA: (147) implies: % 11.55/2.27 | | | (148) member(all_73_1, all_15_5) = all_101_1 % 11.55/2.27 | | | (149) member(all_73_1, all_15_4) = all_101_0 % 11.55/2.27 | | | (150) all_101_0 = 0 | all_101_1 = 0 % 11.55/2.27 | | | % 11.55/2.27 | | | BETA: splitting (146) gives: % 11.55/2.27 | | | % 11.55/2.27 | | | Case 1: % 11.55/2.27 | | | | % 11.55/2.27 | | | | (151) all_73_0 = 0 % 11.55/2.27 | | | | % 11.55/2.27 | | | | REDUCE: (140), (151) imply: % 11.55/2.27 | | | | (152) $false % 11.55/2.27 | | | | % 11.55/2.27 | | | | CLOSE: (152) is inconsistent. % 11.55/2.27 | | | | % 11.55/2.27 | | | Case 2: % 11.55/2.27 | | | | % 11.55/2.27 | | | | (153) ? [v0: int] : ( ~ (v0 = 0) & member(all_73_1, all_15_4) = v0) % 11.55/2.27 | | | | % 11.55/2.27 | | | | DELTA: instantiating (153) with fresh symbol all_107_0 gives: % 11.55/2.27 | | | | (154) ~ (all_107_0 = 0) & member(all_73_1, all_15_4) = all_107_0 % 11.55/2.27 | | | | % 11.55/2.27 | | | | ALPHA: (154) implies: % 11.55/2.27 | | | | (155) ~ (all_107_0 = 0) % 11.55/2.27 | | | | (156) member(all_73_1, all_15_4) = all_107_0 % 11.55/2.27 | | | | % 11.55/2.27 | | | | BETA: splitting (145) gives: % 11.55/2.27 | | | | % 11.55/2.27 | | | | Case 1: % 11.55/2.27 | | | | | % 11.55/2.27 | | | | | (157) all_73_0 = 0 % 11.55/2.27 | | | | | % 11.55/2.27 | | | | | REDUCE: (140), (157) imply: % 11.55/2.27 | | | | | (158) $false % 11.55/2.27 | | | | | % 11.55/2.27 | | | | | CLOSE: (158) is inconsistent. % 11.55/2.27 | | | | | % 11.55/2.27 | | | | Case 2: % 11.55/2.27 | | | | | % 11.55/2.27 | | | | | (159) ? [v0: int] : ( ~ (v0 = 0) & member(all_73_1, all_15_5) = % 11.55/2.27 | | | | | v0) % 11.55/2.27 | | | | | % 11.55/2.27 | | | | | DELTA: instantiating (159) with fresh symbol all_113_0 gives: % 11.55/2.27 | | | | | (160) ~ (all_113_0 = 0) & member(all_73_1, all_15_5) = all_113_0 % 11.55/2.27 | | | | | % 11.55/2.27 | | | | | ALPHA: (160) implies: % 11.55/2.27 | | | | | (161) ~ (all_113_0 = 0) % 11.55/2.27 | | | | | (162) member(all_73_1, all_15_5) = all_113_0 % 11.55/2.27 | | | | | % 11.55/2.27 | | | | | GROUND_INST: instantiating (7) with all_101_1, all_113_0, all_15_5, % 11.55/2.27 | | | | | all_73_1, simplifying with (148), (162) gives: % 11.55/2.27 | | | | | (163) all_113_0 = all_101_1 % 11.55/2.27 | | | | | % 11.55/2.27 | | | | | GROUND_INST: instantiating (7) with all_101_0, all_107_0, all_15_4, % 11.55/2.27 | | | | | all_73_1, simplifying with (149), (156) gives: % 11.55/2.27 | | | | | (164) all_107_0 = all_101_0 % 11.55/2.27 | | | | | % 11.55/2.27 | | | | | REDUCE: (161), (163) imply: % 11.55/2.27 | | | | | (165) ~ (all_101_1 = 0) % 11.55/2.27 | | | | | % 11.55/2.27 | | | | | REDUCE: (155), (164) imply: % 11.55/2.27 | | | | | (166) ~ (all_101_0 = 0) % 11.55/2.27 | | | | | % 11.55/2.27 | | | | | BETA: splitting (150) gives: % 11.55/2.27 | | | | | % 11.55/2.27 | | | | | Case 1: % 11.55/2.27 | | | | | | % 11.55/2.27 | | | | | | (167) all_101_0 = 0 % 11.55/2.27 | | | | | | % 11.55/2.27 | | | | | | REDUCE: (166), (167) imply: % 11.55/2.27 | | | | | | (168) $false % 11.55/2.27 | | | | | | % 11.55/2.27 | | | | | | CLOSE: (168) is inconsistent. % 11.55/2.27 | | | | | | % 11.55/2.27 | | | | | Case 2: % 11.55/2.27 | | | | | | % 11.55/2.27 | | | | | | (169) all_101_1 = 0 % 11.55/2.27 | | | | | | % 11.55/2.27 | | | | | | REDUCE: (165), (169) imply: % 11.55/2.27 | | | | | | (170) $false % 11.55/2.27 | | | | | | % 11.55/2.27 | | | | | | CLOSE: (170) is inconsistent. % 11.55/2.27 | | | | | | % 11.55/2.27 | | | | | End of split % 11.55/2.27 | | | | | % 11.55/2.27 | | | | End of split % 11.55/2.27 | | | | % 11.55/2.27 | | | End of split % 11.55/2.27 | | | % 11.55/2.27 | | End of split % 11.55/2.27 | | % 11.55/2.27 | End of split % 11.55/2.27 | % 11.55/2.27 End of proof % 11.55/2.27 % SZS output end Proof for theBenchmark % 11.55/2.27 % 11.55/2.27 1737ms %------------------------------------------------------------------------------