%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET155+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 : n027.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 15:24:04 EDT 2023 % Result : Theorem 7.81s 1.86s % Output : Proof 10.31s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.14 % Problem : SET155+4 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.36 % Computer : n027.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Sat Aug 26 15:48:20 EDT 2023 % 0.14/0.36 % CPUTime : % 0.21/0.61 ________ _____ % 0.21/0.61 ___ __ \_________(_)________________________________ % 0.21/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.61 % 0.21/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.61 (2023-06-19) % 0.21/0.61 % 0.21/0.61 (c) Philipp Rümmer, 2009-2023 % 0.21/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.61 Amanda Stjerna. % 0.21/0.61 Free software under BSD-3-Clause. % 0.21/0.61 % 0.21/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.61 % 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.62 Running up to 7 provers in parallel. % 0.21/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.10/1.09 Prover 4: Preprocessing ... % 2.10/1.09 Prover 1: Preprocessing ... % 2.76/1.11 Prover 6: Preprocessing ... % 2.76/1.11 Prover 3: Preprocessing ... % 2.76/1.11 Prover 5: Preprocessing ... % 2.76/1.11 Prover 0: Preprocessing ... % 2.76/1.11 Prover 2: Preprocessing ... % 5.66/1.51 Prover 5: Proving ... % 5.66/1.51 Prover 1: Constructing countermodel ... % 5.66/1.52 Prover 2: Proving ... % 5.66/1.52 Prover 6: Proving ... % 5.66/1.53 Prover 0: Proving ... % 5.66/1.54 Prover 3: Constructing countermodel ... % 5.66/1.56 Prover 4: Constructing countermodel ... % 7.81/1.86 Prover 3: proved (1227ms) % 7.81/1.86 % 7.81/1.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.81/1.86 % 7.81/1.86 Prover 5: stopped % 7.81/1.86 Prover 0: stopped % 7.81/1.87 Prover 2: stopped % 8.33/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.33/1.88 Prover 6: stopped % 8.33/1.89 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.33/1.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.33/1.89 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.33/1.90 Prover 7: Preprocessing ... % 8.33/1.90 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.33/1.90 Prover 8: Preprocessing ... % 8.33/1.92 Prover 11: Preprocessing ... % 8.33/1.92 Prover 10: Preprocessing ... % 8.33/1.93 Prover 13: Preprocessing ... % 8.33/1.96 Prover 7: Warning: ignoring some quantifiers % 9.07/1.98 Prover 7: Constructing countermodel ... % 9.40/2.03 Prover 10: Warning: ignoring some quantifiers % 9.40/2.04 Prover 10: Constructing countermodel ... % 9.40/2.05 Prover 8: Warning: ignoring some quantifiers % 9.40/2.05 Prover 1: Found proof (size 109) % 9.40/2.05 Prover 1: proved (1421ms) % 9.40/2.05 Prover 4: stopped % 9.40/2.05 Prover 10: stopped % 9.40/2.06 Prover 7: stopped % 9.40/2.06 Prover 8: Constructing countermodel ... % 9.40/2.07 Prover 8: stopped % 9.40/2.08 Prover 13: Warning: ignoring some quantifiers % 9.40/2.09 Prover 13: Constructing countermodel ... % 9.40/2.09 Prover 11: Constructing countermodel ... % 9.40/2.09 Prover 13: stopped % 9.40/2.10 Prover 11: stopped % 9.40/2.10 % 9.40/2.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 9.40/2.10 % 9.94/2.11 % SZS output start Proof for theBenchmark % 9.94/2.12 Assumptions after simplification: % 9.94/2.12 --------------------------------- % 9.94/2.12 % 9.94/2.12 (difference) % 9.94/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 9.94/2.14 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 9.94/2.14 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v5 & % 9.94/2.14 member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] % 9.94/2.14 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0, % 9.94/2.14 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = % 9.94/2.14 0) & member(v0, v2) = 0 & member(v0, v1) = v4)) % 9.94/2.14 % 9.94/2.14 (equal_set) % 9.94/2.15 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) = % 9.94/2.15 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1, % 9.94/2.15 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0: % 9.94/2.15 $i] : ! [v1: $i] : ( ~ (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 9.94/2.15 (subset(v1, v0) = 0 & subset(v0, v1) = 0)) % 9.94/2.15 % 9.94/2.15 (intersection) % 9.94/2.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 9.94/2.15 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ % 9.94/2.15 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 & % 9.94/2.15 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 9.94/2.15 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~ % 9.94/2.15 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = % 9.94/2.15 0 & member(v0, v1) = 0)) % 9.94/2.15 % 9.94/2.15 (subset) % 9.94/2.15 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) % 9.94/2.15 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & % 9.94/2.15 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! % 9.94/2.15 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( % 9.94/2.15 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0)) % 9.94/2.15 % 9.94/2.15 (thI26) % 9.94/2.15 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 9.94/2.15 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) & % 9.94/2.15 difference(v2, v3) = v4 & difference(v2, v1) = v6 & difference(v2, v0) = v5 % 9.94/2.15 & union(v0, v1) = v3 & intersection(v5, v6) = v7 & equal_set(v4, v7) = v8 & % 9.94/2.15 subset(v1, v2) = 0 & subset(v0, v2) = 0 & $i(v7) & $i(v6) & $i(v5) & $i(v4) % 9.94/2.15 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 9.94/2.15 % 9.94/2.15 (union) % 9.94/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 9.94/2.16 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~ $i(v1) % 9.94/2.16 | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = 0) & % 9.94/2.16 member(v0, v2) = v6 & member(v0, v1) = v5)) & ! [v0: $i] : ! [v1: $i] : % 9.94/2.16 ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = 0) % 9.94/2.16 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 9.94/2.16 (member(v0, v2) = v5 & member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 9.94/2.16 % 9.94/2.16 (function-axioms) % 9.94/2.16 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.94/2.16 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: % 9.94/2.16 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.94/2.16 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : ! % 9.94/2.16 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~ % 9.94/2.16 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 9.94/2.16 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = % 9.94/2.16 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 9.94/2.16 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~ % 9.94/2.16 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 9.94/2.16 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, % 9.94/2.16 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 9.94/2.16 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 9.94/2.16 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1: % 9.94/2.16 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = % 9.94/2.16 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = % 9.94/2.16 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = % 9.94/2.16 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! % 9.94/2.16 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~ % 9.94/2.16 (power_set(v2) = v0)) % 9.94/2.16 % 9.94/2.16 Further assumptions not needed in the proof: % 9.94/2.16 -------------------------------------------- % 9.94/2.16 empty_set, power_set, product, singleton, sum, unordered_pair % 9.94/2.16 % 9.94/2.16 Those formulas are unsatisfiable: % 9.94/2.16 --------------------------------- % 9.94/2.16 % 9.94/2.16 Begin of proof % 9.94/2.16 | % 9.94/2.16 | ALPHA: (subset) implies: % 9.94/2.16 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 9.94/2.16 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 9.94/2.16 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 9.94/2.16 | % 9.94/2.16 | ALPHA: (equal_set) implies: % 9.94/2.16 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, % 9.94/2.16 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : % 9.94/2.16 | (subset(v1, v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = % 9.94/2.16 | 0)))) % 9.94/2.16 | % 9.94/2.16 | ALPHA: (intersection) implies: % 9.94/2.17 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 9.94/2.17 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | % 9.94/2.17 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0)) % 9.94/2.17 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 9.94/2.17 | (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | % 9.94/2.17 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 9.94/2.17 | (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = % 9.94/2.17 | 0)))) % 9.94/2.17 | % 9.94/2.17 | ALPHA: (union) implies: % 9.94/2.17 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (union(v1, % 9.94/2.17 | v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 9.94/2.17 | $i(v0) | ? [v4: any] : ? [v5: any] : (member(v0, v2) = v5 & % 9.94/2.17 | member(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 9.94/2.17 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 9.94/2.17 | (v4 = 0 | ~ (union(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ % 9.94/2.17 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ % 9.94/2.17 | (v6 = 0) & ~ (v5 = 0) & member(v0, v2) = v6 & member(v0, v1) = % 9.94/2.17 | v5)) % 9.94/2.17 | % 9.94/2.17 | ALPHA: (difference) implies: % 9.94/2.17 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 9.94/2.17 | (difference(v2, v1) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) | ~ % 9.94/2.17 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0, v2) = 0 % 9.94/2.17 | & member(v0, v1) = v4)) % 9.94/2.17 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 9.94/2.17 | (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ % 9.94/2.17 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 9.94/2.17 | (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) % 9.94/2.17 | % 9.94/2.17 | ALPHA: (function-axioms) implies: % 9.94/2.17 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 9.94/2.17 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 9.94/2.17 | = v0)) % 9.94/2.17 | % 9.94/2.17 | DELTA: instantiating (thI26) with fresh symbols all_15_0, all_15_1, all_15_2, % 9.94/2.17 | all_15_3, all_15_4, all_15_5, all_15_6, all_15_7, all_15_8 gives: % 9.94/2.17 | (10) ~ (all_15_0 = 0) & difference(all_15_6, all_15_5) = all_15_4 & % 9.94/2.17 | difference(all_15_6, all_15_7) = all_15_2 & difference(all_15_6, % 9.94/2.17 | all_15_8) = all_15_3 & union(all_15_8, all_15_7) = all_15_5 & % 9.94/2.17 | intersection(all_15_3, all_15_2) = all_15_1 & equal_set(all_15_4, % 9.94/2.17 | all_15_1) = all_15_0 & subset(all_15_7, all_15_6) = 0 & % 9.94/2.17 | subset(all_15_8, all_15_6) = 0 & $i(all_15_1) & $i(all_15_2) & % 9.94/2.17 | $i(all_15_3) & $i(all_15_4) & $i(all_15_5) & $i(all_15_6) & % 9.94/2.17 | $i(all_15_7) & $i(all_15_8) % 9.94/2.17 | % 9.94/2.17 | ALPHA: (10) implies: % 9.94/2.17 | (11) ~ (all_15_0 = 0) % 9.94/2.17 | (12) $i(all_15_8) % 9.94/2.17 | (13) $i(all_15_7) % 9.94/2.17 | (14) $i(all_15_6) % 9.94/2.17 | (15) $i(all_15_5) % 9.94/2.17 | (16) $i(all_15_4) % 9.94/2.17 | (17) $i(all_15_3) % 9.94/2.17 | (18) $i(all_15_2) % 9.94/2.17 | (19) $i(all_15_1) % 9.94/2.17 | (20) equal_set(all_15_4, all_15_1) = all_15_0 % 9.94/2.18 | (21) intersection(all_15_3, all_15_2) = all_15_1 % 9.94/2.18 | (22) union(all_15_8, all_15_7) = all_15_5 % 9.94/2.18 | (23) difference(all_15_6, all_15_8) = all_15_3 % 9.94/2.18 | (24) difference(all_15_6, all_15_7) = all_15_2 % 9.94/2.18 | (25) difference(all_15_6, all_15_5) = all_15_4 % 9.94/2.18 | % 9.94/2.18 | GROUND_INST: instantiating (2) with all_15_4, all_15_1, all_15_0, simplifying % 9.94/2.18 | with (16), (19), (20) gives: % 10.31/2.18 | (26) all_15_0 = 0 | ? [v0: any] : ? [v1: any] : (subset(all_15_1, % 10.31/2.18 | all_15_4) = v1 & subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) | % 10.31/2.18 | ~ (v0 = 0))) % 10.31/2.18 | % 10.31/2.18 | BETA: splitting (26) gives: % 10.31/2.18 | % 10.31/2.18 | Case 1: % 10.31/2.18 | | % 10.31/2.18 | | (27) all_15_0 = 0 % 10.31/2.18 | | % 10.31/2.18 | | REDUCE: (11), (27) imply: % 10.31/2.18 | | (28) $false % 10.31/2.18 | | % 10.31/2.18 | | CLOSE: (28) is inconsistent. % 10.31/2.18 | | % 10.31/2.18 | Case 2: % 10.31/2.18 | | % 10.31/2.18 | | (29) ? [v0: any] : ? [v1: any] : (subset(all_15_1, all_15_4) = v1 & % 10.31/2.18 | | subset(all_15_4, all_15_1) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 10.31/2.18 | | % 10.31/2.18 | | DELTA: instantiating (29) with fresh symbols all_27_0, all_27_1 gives: % 10.31/2.18 | | (30) subset(all_15_1, all_15_4) = all_27_0 & subset(all_15_4, all_15_1) = % 10.31/2.18 | | all_27_1 & ( ~ (all_27_0 = 0) | ~ (all_27_1 = 0)) % 10.31/2.18 | | % 10.31/2.18 | | ALPHA: (30) implies: % 10.31/2.18 | | (31) subset(all_15_4, all_15_1) = all_27_1 % 10.31/2.18 | | (32) subset(all_15_1, all_15_4) = all_27_0 % 10.31/2.18 | | (33) ~ (all_27_0 = 0) | ~ (all_27_1 = 0) % 10.31/2.18 | | % 10.31/2.18 | | GROUND_INST: instantiating (1) with all_15_4, all_15_1, all_27_1, % 10.31/2.18 | | simplifying with (16), (19), (31) gives: % 10.31/2.18 | | (34) all_27_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 10.31/2.18 | | member(v0, all_15_1) = v1 & member(v0, all_15_4) = 0 & $i(v0)) % 10.31/2.18 | | % 10.31/2.18 | | GROUND_INST: instantiating (1) with all_15_1, all_15_4, all_27_0, % 10.31/2.18 | | simplifying with (16), (19), (32) gives: % 10.31/2.18 | | (35) all_27_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 10.31/2.18 | | member(v0, all_15_1) = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 10.31/2.18 | | % 10.31/2.18 | | BETA: splitting (33) gives: % 10.31/2.18 | | % 10.31/2.18 | | Case 1: % 10.31/2.18 | | | % 10.31/2.18 | | | (36) ~ (all_27_0 = 0) % 10.31/2.18 | | | % 10.31/2.18 | | | BETA: splitting (35) gives: % 10.31/2.18 | | | % 10.31/2.18 | | | Case 1: % 10.31/2.18 | | | | % 10.31/2.18 | | | | (37) all_27_0 = 0 % 10.31/2.18 | | | | % 10.31/2.18 | | | | REDUCE: (36), (37) imply: % 10.31/2.18 | | | | (38) $false % 10.31/2.18 | | | | % 10.31/2.18 | | | | CLOSE: (38) is inconsistent. % 10.31/2.18 | | | | % 10.31/2.18 | | | Case 2: % 10.31/2.18 | | | | % 10.31/2.18 | | | | (39) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 10.31/2.18 | | | | = 0 & member(v0, all_15_4) = v1 & $i(v0)) % 10.31/2.18 | | | | % 10.31/2.18 | | | | DELTA: instantiating (39) with fresh symbols all_40_0, all_40_1 gives: % 10.31/2.18 | | | | (40) ~ (all_40_0 = 0) & member(all_40_1, all_15_1) = 0 & % 10.31/2.18 | | | | member(all_40_1, all_15_4) = all_40_0 & $i(all_40_1) % 10.31/2.18 | | | | % 10.31/2.18 | | | | ALPHA: (40) implies: % 10.31/2.19 | | | | (41) ~ (all_40_0 = 0) % 10.31/2.19 | | | | (42) $i(all_40_1) % 10.31/2.19 | | | | (43) member(all_40_1, all_15_4) = all_40_0 % 10.31/2.19 | | | | (44) member(all_40_1, all_15_1) = 0 % 10.31/2.19 | | | | % 10.31/2.19 | | | | GROUND_INST: instantiating (8) with all_40_1, all_15_5, all_15_6, % 10.31/2.19 | | | | all_15_4, all_40_0, simplifying with (14), (15), (25), % 10.31/2.19 | | | | (42), (43) gives: % 10.31/2.19 | | | | (45) all_40_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_40_1, % 10.31/2.19 | | | | all_15_5) = v1 & member(all_40_1, all_15_6) = v0 & ( ~ (v0 = % 10.31/2.19 | | | | 0) | v1 = 0)) % 10.31/2.19 | | | | % 10.31/2.19 | | | | GROUND_INST: instantiating (3) with all_40_1, all_15_3, all_15_2, % 10.31/2.19 | | | | all_15_1, simplifying with (17), (18), (21), (42), (44) % 10.31/2.19 | | | | gives: % 10.31/2.19 | | | | (46) member(all_40_1, all_15_2) = 0 & member(all_40_1, all_15_3) = 0 % 10.31/2.19 | | | | % 10.31/2.19 | | | | ALPHA: (46) implies: % 10.31/2.19 | | | | (47) member(all_40_1, all_15_3) = 0 % 10.31/2.19 | | | | (48) member(all_40_1, all_15_2) = 0 % 10.31/2.19 | | | | % 10.31/2.19 | | | | BETA: splitting (45) gives: % 10.31/2.19 | | | | % 10.31/2.19 | | | | Case 1: % 10.31/2.19 | | | | | % 10.31/2.19 | | | | | (49) all_40_0 = 0 % 10.31/2.19 | | | | | % 10.31/2.19 | | | | | REDUCE: (41), (49) imply: % 10.31/2.19 | | | | | (50) $false % 10.31/2.19 | | | | | % 10.31/2.19 | | | | | CLOSE: (50) is inconsistent. % 10.31/2.19 | | | | | % 10.31/2.19 | | | | Case 2: % 10.31/2.19 | | | | | % 10.31/2.19 | | | | | (51) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_5) = v1 % 10.31/2.19 | | | | | & member(all_40_1, all_15_6) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 10.31/2.19 | | | | | % 10.31/2.19 | | | | | DELTA: instantiating (51) with fresh symbols all_52_0, all_52_1 gives: % 10.31/2.19 | | | | | (52) member(all_40_1, all_15_5) = all_52_0 & member(all_40_1, % 10.31/2.19 | | | | | all_15_6) = all_52_1 & ( ~ (all_52_1 = 0) | all_52_0 = 0) % 10.31/2.19 | | | | | % 10.31/2.19 | | | | | ALPHA: (52) implies: % 10.31/2.19 | | | | | (53) member(all_40_1, all_15_6) = all_52_1 % 10.31/2.19 | | | | | (54) member(all_40_1, all_15_5) = all_52_0 % 10.31/2.19 | | | | | (55) ~ (all_52_1 = 0) | all_52_0 = 0 % 10.31/2.19 | | | | | % 10.31/2.19 | | | | | GROUND_INST: instantiating (7) with all_40_1, all_15_8, all_15_6, % 10.31/2.19 | | | | | all_15_3, simplifying with (12), (14), (23), (42), (47) % 10.31/2.19 | | | | | gives: % 10.31/2.19 | | | | | (56) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_6) = 0 & % 10.31/2.19 | | | | | member(all_40_1, all_15_8) = v0) % 10.31/2.19 | | | | | % 10.31/2.19 | | | | | GROUND_INST: instantiating (7) with all_40_1, all_15_7, all_15_6, % 10.31/2.19 | | | | | all_15_2, simplifying with (13), (14), (24), (42), (48) % 10.31/2.19 | | | | | gives: % 10.31/2.19 | | | | | (57) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_6) = 0 & % 10.31/2.19 | | | | | member(all_40_1, all_15_7) = v0) % 10.31/2.19 | | | | | % 10.31/2.19 | | | | | DELTA: instantiating (57) with fresh symbol all_59_0 gives: % 10.31/2.19 | | | | | (58) ~ (all_59_0 = 0) & member(all_40_1, all_15_6) = 0 & % 10.31/2.19 | | | | | member(all_40_1, all_15_7) = all_59_0 % 10.31/2.19 | | | | | % 10.31/2.19 | | | | | ALPHA: (58) implies: % 10.31/2.19 | | | | | (59) ~ (all_59_0 = 0) % 10.31/2.19 | | | | | (60) member(all_40_1, all_15_7) = all_59_0 % 10.31/2.19 | | | | | % 10.31/2.19 | | | | | DELTA: instantiating (56) with fresh symbol all_61_0 gives: % 10.31/2.19 | | | | | (61) ~ (all_61_0 = 0) & member(all_40_1, all_15_6) = 0 & % 10.31/2.19 | | | | | member(all_40_1, all_15_8) = all_61_0 % 10.31/2.19 | | | | | % 10.31/2.19 | | | | | ALPHA: (61) implies: % 10.31/2.19 | | | | | (62) ~ (all_61_0 = 0) % 10.31/2.20 | | | | | (63) member(all_40_1, all_15_8) = all_61_0 % 10.31/2.20 | | | | | (64) member(all_40_1, all_15_6) = 0 % 10.31/2.20 | | | | | % 10.31/2.20 | | | | | GROUND_INST: instantiating (9) with all_52_1, 0, all_15_6, all_40_1, % 10.31/2.20 | | | | | simplifying with (53), (64) gives: % 10.31/2.20 | | | | | (65) all_52_1 = 0 % 10.31/2.20 | | | | | % 10.31/2.20 | | | | | BETA: splitting (55) gives: % 10.31/2.20 | | | | | % 10.31/2.20 | | | | | Case 1: % 10.31/2.20 | | | | | | % 10.31/2.20 | | | | | | (66) ~ (all_52_1 = 0) % 10.31/2.20 | | | | | | % 10.31/2.20 | | | | | | REDUCE: (65), (66) imply: % 10.31/2.20 | | | | | | (67) $false % 10.31/2.20 | | | | | | % 10.31/2.20 | | | | | | CLOSE: (67) is inconsistent. % 10.31/2.20 | | | | | | % 10.31/2.20 | | | | | Case 2: % 10.31/2.20 | | | | | | % 10.31/2.20 | | | | | | (68) all_52_0 = 0 % 10.31/2.20 | | | | | | % 10.31/2.20 | | | | | | REDUCE: (54), (68) imply: % 10.31/2.20 | | | | | | (69) member(all_40_1, all_15_5) = 0 % 10.31/2.20 | | | | | | % 10.31/2.20 | | | | | | GROUND_INST: instantiating (5) with all_40_1, all_15_8, all_15_7, % 10.31/2.20 | | | | | | all_15_5, simplifying with (12), (13), (22), (42), (69) % 10.31/2.20 | | | | | | gives: % 10.31/2.20 | | | | | | (70) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_7) = % 10.31/2.20 | | | | | | v1 & member(all_40_1, all_15_8) = v0 & (v1 = 0 | v0 = 0)) % 10.31/2.20 | | | | | | % 10.31/2.20 | | | | | | DELTA: instantiating (70) with fresh symbols all_76_0, all_76_1 % 10.31/2.20 | | | | | | gives: % 10.31/2.20 | | | | | | (71) member(all_40_1, all_15_7) = all_76_0 & member(all_40_1, % 10.31/2.20 | | | | | | all_15_8) = all_76_1 & (all_76_0 = 0 | all_76_1 = 0) % 10.31/2.20 | | | | | | % 10.31/2.20 | | | | | | ALPHA: (71) implies: % 10.31/2.20 | | | | | | (72) member(all_40_1, all_15_8) = all_76_1 % 10.31/2.21 | | | | | | (73) member(all_40_1, all_15_7) = all_76_0 % 10.31/2.21 | | | | | | (74) all_76_0 = 0 | all_76_1 = 0 % 10.31/2.21 | | | | | | % 10.31/2.21 | | | | | | GROUND_INST: instantiating (9) with all_61_0, all_76_1, all_15_8, % 10.31/2.21 | | | | | | all_40_1, simplifying with (63), (72) gives: % 10.31/2.21 | | | | | | (75) all_76_1 = all_61_0 % 10.31/2.21 | | | | | | % 10.31/2.21 | | | | | | GROUND_INST: instantiating (9) with all_59_0, all_76_0, all_15_7, % 10.31/2.21 | | | | | | all_40_1, simplifying with (60), (73) gives: % 10.31/2.21 | | | | | | (76) all_76_0 = all_59_0 % 10.31/2.21 | | | | | | % 10.31/2.21 | | | | | | BETA: splitting (74) gives: % 10.31/2.21 | | | | | | % 10.31/2.21 | | | | | | Case 1: % 10.31/2.21 | | | | | | | % 10.31/2.21 | | | | | | | (77) all_76_0 = 0 % 10.31/2.21 | | | | | | | % 10.31/2.21 | | | | | | | COMBINE_EQS: (76), (77) imply: % 10.31/2.21 | | | | | | | (78) all_59_0 = 0 % 10.31/2.21 | | | | | | | % 10.31/2.21 | | | | | | | REDUCE: (59), (78) imply: % 10.31/2.21 | | | | | | | (79) $false % 10.31/2.21 | | | | | | | % 10.31/2.21 | | | | | | | CLOSE: (79) is inconsistent. % 10.31/2.21 | | | | | | | % 10.31/2.21 | | | | | | Case 2: % 10.31/2.21 | | | | | | | % 10.31/2.21 | | | | | | | (80) all_76_1 = 0 % 10.31/2.21 | | | | | | | % 10.31/2.21 | | | | | | | COMBINE_EQS: (75), (80) imply: % 10.31/2.21 | | | | | | | (81) all_61_0 = 0 % 10.31/2.21 | | | | | | | % 10.31/2.21 | | | | | | | SIMP: (81) implies: % 10.31/2.21 | | | | | | | (82) all_61_0 = 0 % 10.31/2.21 | | | | | | | % 10.31/2.21 | | | | | | | REDUCE: (62), (82) imply: % 10.31/2.21 | | | | | | | (83) $false % 10.31/2.21 | | | | | | | % 10.31/2.21 | | | | | | | CLOSE: (83) is inconsistent. % 10.31/2.21 | | | | | | | % 10.31/2.21 | | | | | | End of split % 10.31/2.21 | | | | | | % 10.31/2.21 | | | | | End of split % 10.31/2.21 | | | | | % 10.31/2.21 | | | | End of split % 10.31/2.21 | | | | % 10.31/2.21 | | | End of split % 10.31/2.21 | | | % 10.31/2.21 | | Case 2: % 10.31/2.21 | | | % 10.31/2.21 | | | (84) ~ (all_27_1 = 0) % 10.31/2.21 | | | % 10.31/2.21 | | | BETA: splitting (34) gives: % 10.31/2.21 | | | % 10.31/2.21 | | | Case 1: % 10.31/2.21 | | | | % 10.31/2.21 | | | | (85) all_27_1 = 0 % 10.31/2.22 | | | | % 10.31/2.22 | | | | REDUCE: (84), (85) imply: % 10.31/2.22 | | | | (86) $false % 10.31/2.22 | | | | % 10.31/2.22 | | | | CLOSE: (86) is inconsistent. % 10.31/2.22 | | | | % 10.31/2.22 | | | Case 2: % 10.31/2.22 | | | | % 10.31/2.22 | | | | (87) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1) % 10.31/2.22 | | | | = v1 & member(v0, all_15_4) = 0 & $i(v0)) % 10.31/2.22 | | | | % 10.31/2.22 | | | | DELTA: instantiating (87) with fresh symbols all_40_0, all_40_1 gives: % 10.31/2.22 | | | | (88) ~ (all_40_0 = 0) & member(all_40_1, all_15_1) = all_40_0 & % 10.31/2.22 | | | | member(all_40_1, all_15_4) = 0 & $i(all_40_1) % 10.31/2.22 | | | | % 10.31/2.22 | | | | ALPHA: (88) implies: % 10.31/2.22 | | | | (89) ~ (all_40_0 = 0) % 10.31/2.22 | | | | (90) $i(all_40_1) % 10.31/2.22 | | | | (91) member(all_40_1, all_15_4) = 0 % 10.31/2.22 | | | | (92) member(all_40_1, all_15_1) = all_40_0 % 10.31/2.22 | | | | % 10.31/2.22 | | | | GROUND_INST: instantiating (7) with all_40_1, all_15_5, all_15_6, % 10.31/2.22 | | | | all_15_4, simplifying with (14), (15), (25), (90), (91) % 10.31/2.22 | | | | gives: % 10.31/2.22 | | | | (93) ? [v0: int] : ( ~ (v0 = 0) & member(all_40_1, all_15_5) = v0 & % 10.31/2.22 | | | | member(all_40_1, all_15_6) = 0) % 10.31/2.22 | | | | % 10.31/2.22 | | | | GROUND_INST: instantiating (4) with all_40_1, all_15_3, all_15_2, % 10.31/2.22 | | | | all_15_1, all_40_0, simplifying with (17), (18), (21), % 10.31/2.22 | | | | (90), (92) gives: % 10.31/2.22 | | | | (94) all_40_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_40_1, % 10.31/2.22 | | | | all_15_2) = v1 & member(all_40_1, all_15_3) = v0 & ( ~ (v1 = % 10.31/2.22 | | | | 0) | ~ (v0 = 0))) % 10.31/2.22 | | | | % 10.31/2.22 | | | | DELTA: instantiating (93) with fresh symbol all_48_0 gives: % 10.31/2.22 | | | | (95) ~ (all_48_0 = 0) & member(all_40_1, all_15_5) = all_48_0 & % 10.31/2.22 | | | | member(all_40_1, all_15_6) = 0 % 10.31/2.22 | | | | % 10.31/2.22 | | | | ALPHA: (95) implies: % 10.31/2.22 | | | | (96) ~ (all_48_0 = 0) % 10.31/2.22 | | | | (97) member(all_40_1, all_15_6) = 0 % 10.31/2.22 | | | | (98) member(all_40_1, all_15_5) = all_48_0 % 10.31/2.22 | | | | % 10.31/2.22 | | | | BETA: splitting (94) gives: % 10.31/2.22 | | | | % 10.31/2.22 | | | | Case 1: % 10.31/2.22 | | | | | % 10.31/2.22 | | | | | (99) all_40_0 = 0 % 10.31/2.22 | | | | | % 10.31/2.22 | | | | | REDUCE: (89), (99) imply: % 10.31/2.22 | | | | | (100) $false % 10.31/2.22 | | | | | % 10.31/2.22 | | | | | CLOSE: (100) is inconsistent. % 10.31/2.22 | | | | | % 10.31/2.22 | | | | Case 2: % 10.31/2.22 | | | | | % 10.31/2.22 | | | | | (101) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_2) = % 10.31/2.22 | | | | | v1 & member(all_40_1, all_15_3) = v0 & ( ~ (v1 = 0) | ~ % 10.31/2.22 | | | | | (v0 = 0))) % 10.31/2.22 | | | | | % 10.31/2.22 | | | | | DELTA: instantiating (101) with fresh symbols all_54_0, all_54_1 % 10.31/2.22 | | | | | gives: % 10.31/2.22 | | | | | (102) member(all_40_1, all_15_2) = all_54_0 & member(all_40_1, % 10.31/2.22 | | | | | all_15_3) = all_54_1 & ( ~ (all_54_0 = 0) | ~ (all_54_1 = % 10.31/2.22 | | | | | 0)) % 10.31/2.22 | | | | | % 10.31/2.22 | | | | | ALPHA: (102) implies: % 10.31/2.22 | | | | | (103) member(all_40_1, all_15_3) = all_54_1 % 10.31/2.22 | | | | | (104) member(all_40_1, all_15_2) = all_54_0 % 10.31/2.22 | | | | | (105) ~ (all_54_0 = 0) | ~ (all_54_1 = 0) % 10.31/2.22 | | | | | % 10.31/2.22 | | | | | GROUND_INST: instantiating (6) with all_40_1, all_15_8, all_15_7, % 10.31/2.22 | | | | | all_15_5, all_48_0, simplifying with (12), (13), (22), % 10.31/2.22 | | | | | (90), (98) gives: % 10.31/2.22 | | | | | (106) all_48_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & % 10.31/2.22 | | | | | ~ (v0 = 0) & member(all_40_1, all_15_7) = v1 & % 10.31/2.22 | | | | | member(all_40_1, all_15_8) = v0) % 10.31/2.22 | | | | | % 10.31/2.22 | | | | | GROUND_INST: instantiating (8) with all_40_1, all_15_8, all_15_6, % 10.31/2.22 | | | | | all_15_3, all_54_1, simplifying with (12), (14), (23), % 10.31/2.22 | | | | | (90), (103) gives: % 10.31/2.23 | | | | | (107) all_54_1 = 0 | ? [v0: any] : ? [v1: any] : % 10.31/2.23 | | | | | (member(all_40_1, all_15_6) = v0 & member(all_40_1, all_15_8) % 10.31/2.23 | | | | | = v1 & ( ~ (v0 = 0) | v1 = 0)) % 10.31/2.23 | | | | | % 10.31/2.23 | | | | | GROUND_INST: instantiating (8) with all_40_1, all_15_7, all_15_6, % 10.31/2.23 | | | | | all_15_2, all_54_0, simplifying with (13), (14), (24), % 10.31/2.23 | | | | | (90), (104) gives: % 10.31/2.23 | | | | | (108) all_54_0 = 0 | ? [v0: any] : ? [v1: any] : % 10.31/2.23 | | | | | (member(all_40_1, all_15_6) = v0 & member(all_40_1, all_15_7) % 10.31/2.23 | | | | | = v1 & ( ~ (v0 = 0) | v1 = 0)) % 10.31/2.23 | | | | | % 10.31/2.23 | | | | | BETA: splitting (105) gives: % 10.31/2.23 | | | | | % 10.31/2.23 | | | | | Case 1: % 10.31/2.23 | | | | | | % 10.31/2.23 | | | | | | (109) ~ (all_54_0 = 0) % 10.31/2.23 | | | | | | % 10.31/2.23 | | | | | | BETA: splitting (108) gives: % 10.31/2.23 | | | | | | % 10.31/2.23 | | | | | | Case 1: % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | (110) all_54_0 = 0 % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | REDUCE: (109), (110) imply: % 10.31/2.23 | | | | | | | (111) $false % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | CLOSE: (111) is inconsistent. % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | Case 2: % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | (112) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_6) % 10.31/2.23 | | | | | | | = v0 & member(all_40_1, all_15_7) = v1 & ( ~ (v0 = 0) | % 10.31/2.23 | | | | | | | v1 = 0)) % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | DELTA: instantiating (112) with fresh symbols all_67_0, all_67_1 % 10.31/2.23 | | | | | | | gives: % 10.31/2.23 | | | | | | | (113) member(all_40_1, all_15_6) = all_67_1 & member(all_40_1, % 10.31/2.23 | | | | | | | all_15_7) = all_67_0 & ( ~ (all_67_1 = 0) | all_67_0 = % 10.31/2.23 | | | | | | | 0) % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | ALPHA: (113) implies: % 10.31/2.23 | | | | | | | (114) member(all_40_1, all_15_7) = all_67_0 % 10.31/2.23 | | | | | | | (115) member(all_40_1, all_15_6) = all_67_1 % 10.31/2.23 | | | | | | | (116) ~ (all_67_1 = 0) | all_67_0 = 0 % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | BETA: splitting (106) gives: % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | Case 1: % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | | (117) all_48_0 = 0 % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | | REDUCE: (96), (117) imply: % 10.31/2.23 | | | | | | | | (118) $false % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | | CLOSE: (118) is inconsistent. % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | Case 2: % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | | (119) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 10.31/2.23 | | | | | | | | 0) & member(all_40_1, all_15_7) = v1 & % 10.31/2.23 | | | | | | | | member(all_40_1, all_15_8) = v0) % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | | DELTA: instantiating (119) with fresh symbols all_73_0, all_73_1 % 10.31/2.23 | | | | | | | | gives: % 10.31/2.23 | | | | | | | | (120) ~ (all_73_0 = 0) & ~ (all_73_1 = 0) & % 10.31/2.23 | | | | | | | | member(all_40_1, all_15_7) = all_73_0 & % 10.31/2.23 | | | | | | | | member(all_40_1, all_15_8) = all_73_1 % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | | ALPHA: (120) implies: % 10.31/2.23 | | | | | | | | (121) ~ (all_73_0 = 0) % 10.31/2.23 | | | | | | | | (122) member(all_40_1, all_15_7) = all_73_0 % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | | GROUND_INST: instantiating (9) with all_67_0, all_73_0, % 10.31/2.23 | | | | | | | | all_15_7, all_40_1, simplifying with (114), (122) % 10.31/2.23 | | | | | | | | gives: % 10.31/2.23 | | | | | | | | (123) all_73_0 = all_67_0 % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_67_1, all_15_6, % 10.31/2.23 | | | | | | | | all_40_1, simplifying with (97), (115) gives: % 10.31/2.23 | | | | | | | | (124) all_67_1 = 0 % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | | REDUCE: (121), (123) imply: % 10.31/2.23 | | | | | | | | (125) ~ (all_67_0 = 0) % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | | BETA: splitting (116) gives: % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | | Case 1: % 10.31/2.23 | | | | | | | | | % 10.31/2.23 | | | | | | | | | (126) ~ (all_67_1 = 0) % 10.31/2.23 | | | | | | | | | % 10.31/2.23 | | | | | | | | | REDUCE: (124), (126) imply: % 10.31/2.23 | | | | | | | | | (127) $false % 10.31/2.23 | | | | | | | | | % 10.31/2.23 | | | | | | | | | CLOSE: (127) is inconsistent. % 10.31/2.23 | | | | | | | | | % 10.31/2.23 | | | | | | | | Case 2: % 10.31/2.23 | | | | | | | | | % 10.31/2.23 | | | | | | | | | (128) all_67_0 = 0 % 10.31/2.23 | | | | | | | | | % 10.31/2.23 | | | | | | | | | REDUCE: (125), (128) imply: % 10.31/2.23 | | | | | | | | | (129) $false % 10.31/2.23 | | | | | | | | | % 10.31/2.23 | | | | | | | | | CLOSE: (129) is inconsistent. % 10.31/2.23 | | | | | | | | | % 10.31/2.23 | | | | | | | | End of split % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | End of split % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | End of split % 10.31/2.23 | | | | | | % 10.31/2.23 | | | | | Case 2: % 10.31/2.23 | | | | | | % 10.31/2.23 | | | | | | (130) ~ (all_54_1 = 0) % 10.31/2.23 | | | | | | % 10.31/2.23 | | | | | | BETA: splitting (107) gives: % 10.31/2.23 | | | | | | % 10.31/2.23 | | | | | | Case 1: % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | (131) all_54_1 = 0 % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | REDUCE: (130), (131) imply: % 10.31/2.23 | | | | | | | (132) $false % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | CLOSE: (132) is inconsistent. % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | Case 2: % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | (133) ? [v0: any] : ? [v1: any] : (member(all_40_1, all_15_6) % 10.31/2.23 | | | | | | | = v0 & member(all_40_1, all_15_8) = v1 & ( ~ (v0 = 0) | % 10.31/2.23 | | | | | | | v1 = 0)) % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | DELTA: instantiating (133) with fresh symbols all_67_0, all_67_1 % 10.31/2.23 | | | | | | | gives: % 10.31/2.23 | | | | | | | (134) member(all_40_1, all_15_6) = all_67_1 & member(all_40_1, % 10.31/2.23 | | | | | | | all_15_8) = all_67_0 & ( ~ (all_67_1 = 0) | all_67_0 = % 10.31/2.23 | | | | | | | 0) % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | ALPHA: (134) implies: % 10.31/2.23 | | | | | | | (135) member(all_40_1, all_15_8) = all_67_0 % 10.31/2.23 | | | | | | | (136) member(all_40_1, all_15_6) = all_67_1 % 10.31/2.23 | | | | | | | (137) ~ (all_67_1 = 0) | all_67_0 = 0 % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | BETA: splitting (106) gives: % 10.31/2.23 | | | | | | | % 10.31/2.23 | | | | | | | Case 1: % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | | (138) all_48_0 = 0 % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | | REDUCE: (96), (138) imply: % 10.31/2.23 | | | | | | | | (139) $false % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | | CLOSE: (139) is inconsistent. % 10.31/2.23 | | | | | | | | % 10.31/2.23 | | | | | | | Case 2: % 10.31/2.23 | | | | | | | | % 10.31/2.24 | | | | | | | | (140) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 10.31/2.24 | | | | | | | | 0) & member(all_40_1, all_15_7) = v1 & % 10.31/2.24 | | | | | | | | member(all_40_1, all_15_8) = v0) % 10.31/2.24 | | | | | | | | % 10.31/2.24 | | | | | | | | DELTA: instantiating (140) with fresh symbols all_72_0, all_72_1 % 10.31/2.24 | | | | | | | | gives: % 10.31/2.24 | | | | | | | | (141) ~ (all_72_0 = 0) & ~ (all_72_1 = 0) & % 10.31/2.24 | | | | | | | | member(all_40_1, all_15_7) = all_72_0 & % 10.31/2.24 | | | | | | | | member(all_40_1, all_15_8) = all_72_1 % 10.31/2.24 | | | | | | | | % 10.31/2.24 | | | | | | | | ALPHA: (141) implies: % 10.31/2.24 | | | | | | | | (142) ~ (all_72_1 = 0) % 10.31/2.24 | | | | | | | | (143) member(all_40_1, all_15_8) = all_72_1 % 10.31/2.24 | | | | | | | | % 10.31/2.24 | | | | | | | | GROUND_INST: instantiating (9) with all_67_0, all_72_1, % 10.31/2.24 | | | | | | | | all_15_8, all_40_1, simplifying with (135), (143) % 10.31/2.24 | | | | | | | | gives: % 10.31/2.24 | | | | | | | | (144) all_72_1 = all_67_0 % 10.31/2.24 | | | | | | | | % 10.31/2.24 | | | | | | | | GROUND_INST: instantiating (9) with 0, all_67_1, all_15_6, % 10.31/2.24 | | | | | | | | all_40_1, simplifying with (97), (136) gives: % 10.31/2.24 | | | | | | | | (145) all_67_1 = 0 % 10.31/2.24 | | | | | | | | % 10.31/2.24 | | | | | | | | REDUCE: (142), (144) imply: % 10.31/2.24 | | | | | | | | (146) ~ (all_67_0 = 0) % 10.31/2.24 | | | | | | | | % 10.31/2.24 | | | | | | | | BETA: splitting (137) gives: % 10.31/2.24 | | | | | | | | % 10.31/2.24 | | | | | | | | Case 1: % 10.31/2.24 | | | | | | | | | % 10.31/2.24 | | | | | | | | | (147) ~ (all_67_1 = 0) % 10.31/2.24 | | | | | | | | | % 10.31/2.24 | | | | | | | | | REDUCE: (145), (147) imply: % 10.31/2.24 | | | | | | | | | (148) $false % 10.31/2.24 | | | | | | | | | % 10.31/2.24 | | | | | | | | | CLOSE: (148) is inconsistent. % 10.31/2.24 | | | | | | | | | % 10.31/2.24 | | | | | | | | Case 2: % 10.31/2.24 | | | | | | | | | % 10.31/2.24 | | | | | | | | | (149) all_67_0 = 0 % 10.31/2.24 | | | | | | | | | % 10.31/2.24 | | | | | | | | | REDUCE: (146), (149) imply: % 10.31/2.24 | | | | | | | | | (150) $false % 10.31/2.24 | | | | | | | | | % 10.31/2.24 | | | | | | | | | CLOSE: (150) is inconsistent. % 10.31/2.24 | | | | | | | | | % 10.31/2.24 | | | | | | | | End of split % 10.31/2.24 | | | | | | | | % 10.31/2.24 | | | | | | | End of split % 10.31/2.24 | | | | | | | % 10.31/2.24 | | | | | | End of split % 10.31/2.24 | | | | | | % 10.31/2.24 | | | | | End of split % 10.31/2.24 | | | | | % 10.31/2.24 | | | | End of split % 10.31/2.24 | | | | % 10.31/2.24 | | | End of split % 10.31/2.24 | | | % 10.31/2.24 | | End of split % 10.31/2.24 | | % 10.31/2.24 | End of split % 10.31/2.24 | % 10.31/2.24 End of proof % 10.31/2.24 % SZS output end Proof for theBenchmark % 10.31/2.24 % 10.31/2.24 1626ms %------------------------------------------------------------------------------