%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU132+2 : TPTP v8.1.2. Released v3.3.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n012.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 17:42:40 EDT 2023 % Result : Theorem 10.97s 2.30s % Output : Proof 14.27s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU132+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n012.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Wed Aug 23 12:32:12 EDT 2023 % 0.13/0.35 % CPUTime : % 0.21/0.60 ________ _____ % 0.21/0.60 ___ __ \_________(_)________________________________ % 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.60 % 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.60 (2023-06-19) % 0.21/0.60 % 0.21/0.60 (c) Philipp Rümmer, 2009-2023 % 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.60 Amanda Stjerna. % 0.21/0.60 Free software under BSD-3-Clause. % 0.21/0.60 % 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.60 % 0.21/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.21/0.61 Running up to 7 provers in parallel. % 0.21/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.79/1.10 Prover 1: Preprocessing ... % 2.79/1.10 Prover 4: Preprocessing ... % 2.79/1.13 Prover 3: Preprocessing ... % 2.79/1.13 Prover 5: Preprocessing ... % 2.79/1.13 Prover 2: Preprocessing ... % 2.79/1.13 Prover 0: Preprocessing ... % 2.79/1.15 Prover 6: Preprocessing ... % 6.69/1.64 Prover 1: Warning: ignoring some quantifiers % 6.69/1.65 Prover 5: Proving ... % 6.97/1.67 Prover 6: Proving ... % 6.97/1.70 Prover 1: Constructing countermodel ... % 6.97/1.70 Prover 3: Warning: ignoring some quantifiers % 6.97/1.72 Prover 3: Constructing countermodel ... % 7.46/1.75 Prover 2: Proving ... % 7.66/1.81 Prover 4: Warning: ignoring some quantifiers % 8.38/1.87 Prover 4: Constructing countermodel ... % 8.38/1.88 Prover 0: Proving ... % 9.93/2.27 Prover 3: gave up % 10.97/2.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.97/2.30 Prover 0: proved (1680ms) % 10.97/2.30 % 10.97/2.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.97/2.30 % 10.97/2.30 Prover 5: stopped % 10.97/2.30 Prover 6: stopped % 11.72/2.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.72/2.32 Prover 2: stopped % 11.72/2.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.72/2.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.72/2.32 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.72/2.33 Prover 7: Preprocessing ... % 11.72/2.36 Prover 8: Preprocessing ... % 11.72/2.37 Prover 10: Preprocessing ... % 11.72/2.38 Prover 11: Preprocessing ... % 12.27/2.40 Prover 13: Preprocessing ... % 12.27/2.47 Prover 7: Warning: ignoring some quantifiers % 12.27/2.47 Prover 10: Warning: ignoring some quantifiers % 12.89/2.48 Prover 7: Constructing countermodel ... % 12.89/2.48 Prover 10: Constructing countermodel ... % 13.08/2.50 Prover 8: Warning: ignoring some quantifiers % 13.27/2.52 Prover 8: Constructing countermodel ... % 13.27/2.54 Prover 1: gave up % 13.27/2.54 Prover 13: Warning: ignoring some quantifiers % 13.27/2.54 Prover 4: Found proof (size 87) % 13.27/2.54 Prover 4: proved (1921ms) % 13.27/2.54 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 13.27/2.54 Prover 8: stopped % 13.27/2.54 Prover 7: stopped % 13.27/2.55 Prover 10: stopped % 13.27/2.56 Prover 13: Constructing countermodel ... % 13.27/2.57 Prover 13: stopped % 13.27/2.57 Prover 16: Preprocessing ... % 13.27/2.59 Prover 11: Warning: ignoring some quantifiers % 13.27/2.60 Prover 16: stopped % 13.27/2.61 Prover 11: Constructing countermodel ... % 13.27/2.62 Prover 11: stopped % 13.27/2.62 % 13.27/2.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.27/2.62 % 13.90/2.63 % SZS output start Proof for theBenchmark % 13.90/2.63 Assumptions after simplification: % 13.90/2.63 --------------------------------- % 13.90/2.63 % 13.90/2.63 (commutativity_k2_xboole_0) % 13.90/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 13.90/2.66 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 13.90/2.66 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 13.90/2.66 | (set_union2(v1, v0) = v2 & $i(v2))) % 13.90/2.66 % 13.90/2.66 (commutativity_k3_xboole_0) % 13.90/2.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, v0) = v2) % 13.90/2.66 | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = v2 & $i(v2))) & ! % 13.90/2.66 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | % 13.90/2.66 ~ $i(v1) | ~ $i(v0) | (set_intersection2(v1, v0) = v2 & $i(v2))) % 13.90/2.66 % 13.90/2.66 (d2_xboole_0) % 13.90/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 13.90/2.67 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~ % 13.90/2.67 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) % 13.90/2.67 & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0: $i] : ! % 13.90/2.67 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 13.90/2.67 (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 13.90/2.67 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & % 13.90/2.67 in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : % 13.90/2.67 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (set_union2(v0, v1) = % 13.90/2.67 v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 13.90/2.67 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 % 13.90/2.67 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 13.90/2.67 $i] : ! [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | % 13.90/2.67 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 13.90/2.67 (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = % 13.90/2.67 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 13.90/2.67 [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | % 13.90/2.67 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, % 13.90/2.67 v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & % 13.90/2.67 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) % 13.90/2.67 = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 13.90/2.67 $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v1) = v5 & in(v3, v0) = v4 & % 13.90/2.67 (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 13.90/2.67 $i] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 13.90/2.67 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, % 13.90/2.67 v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( % 13.90/2.67 ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) % 13.90/2.67 % 13.90/2.67 (d3_tarski) % 13.90/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.90/2.68 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 13.90/2.68 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 13.90/2.68 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 13.90/2.68 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 13.90/2.68 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 13.90/2.68 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 13.90/2.68 $i(v0) | in(v2, v1) = 0) % 13.90/2.68 % 13.90/2.68 (d3_xboole_0) % 13.90/2.68 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 13.90/2.68 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | % 13.90/2.68 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1) % 13.90/2.68 = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 13.90/2.68 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 13.90/2.68 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 13.90/2.68 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = % 13.90/2.68 v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : % 13.90/2.68 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 13.90/2.68 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ % 13.90/2.68 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = % 13.90/2.68 v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : % 13.90/2.68 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 13.90/2.68 | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 13.90/2.68 (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 13.90/2.68 : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | % 13.90/2.68 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 13.90/2.68 (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] % 13.90/2.68 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = % 13.90/2.68 v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 13.90/2.68 | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 % 13.90/2.68 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 13.90/2.68 $i] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 13.90/2.68 | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 13.90/2.68 (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0) % 13.90/2.68 | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) % 13.90/2.68 % 13.90/2.69 (d4_xboole_0) % 13.90/2.69 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 13.90/2.69 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~ % 13.90/2.69 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1) = % 13.90/2.69 v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: % 13.90/2.69 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 13.90/2.69 (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) % 13.90/2.69 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v6 & % 13.90/2.69 in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : % 13.90/2.69 ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (set_difference(v0, v1) = v2) | % 13.90/2.69 ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 13.90/2.69 [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) % 13.90/2.69 | (v6 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 13.90/2.69 ! [v3: $i] : ! [v4: any] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) % 13.90/2.69 = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? % 13.90/2.69 [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ % 13.90/2.69 (v6 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 13.90/2.69 ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 13.90/2.69 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = % 13.90/2.69 v4 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 13.90/2.69 $i] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | % 13.90/2.69 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v2) % 13.90/2.69 = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : % 13.90/2.69 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ~ % 13.90/2.69 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : % 13.90/2.69 ? [v7: any] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) % 13.90/2.69 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = % 13.90/2.69 0))))) % 13.90/2.69 % 13.90/2.69 (l32_xboole_1) % 14.27/2.69 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~ % 14.27/2.69 (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ % 14.27/2.69 (v3 = 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 14.27/2.69 int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 14.27/2.69 $i] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3 & $i(v3))) & ! % 14.27/2.70 [v0: $i] : ! [v1: $i] : ( ~ (set_difference(v0, v1) = empty_set) | ~ $i(v1) % 14.27/2.70 | ~ $i(v0) | subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 14.27/2.70 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | set_difference(v0, v1) = % 14.27/2.70 empty_set) % 14.27/2.70 % 14.27/2.70 (rc1_xboole_0) % 14.27/2.70 ? [v0: $i] : (empty(v0) = 0 & $i(v0)) % 14.27/2.70 % 14.27/2.70 (t12_xboole_1) % 14.27/2.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (set_union2(v0, v1) = % 14.27/2.70 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & subset(v0, v1) % 14.27/2.70 = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) % 14.27/2.70 | ~ $i(v0) | set_union2(v0, v1) = v1) % 14.27/2.70 % 14.27/2.70 (t28_xboole_1) % 14.27/2.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (set_intersection2(v0, % 14.27/2.70 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 14.27/2.70 subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = % 14.27/2.70 0) | ~ $i(v1) | ~ $i(v0) | set_intersection2(v0, v1) = v0) % 14.27/2.70 % 14.27/2.70 (t33_xboole_1) % 14.27/2.70 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 14.27/2.70 int] : ( ~ (v5 = 0) & set_difference(v1, v2) = v4 & set_difference(v0, v2) = % 14.27/2.70 v3 & subset(v3, v4) = v5 & subset(v0, v1) = 0 & $i(v4) & $i(v3) & $i(v2) & % 14.27/2.70 $i(v1) & $i(v0)) % 14.27/2.70 % 14.27/2.70 (t6_boole) % 14.27/2.70 $i(empty_set) & ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ % 14.27/2.70 $i(v0)) % 14.27/2.70 % 14.27/2.70 (function-axioms) % 14.27/2.70 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 14.27/2.70 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 14.27/2.70 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.27/2.70 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 14.27/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.27/2.70 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 14.27/2.70 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.27/2.70 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 14.27/2.70 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 14.27/2.70 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: % 14.27/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 14.27/2.70 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 14.27/2.70 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 14.27/2.70 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) % 14.27/2.70 % 14.27/2.70 Further assumptions not needed in the proof: % 14.27/2.70 -------------------------------------------- % 14.27/2.70 antisymmetry_r2_hidden, d10_xboole_0, d1_xboole_0, d7_xboole_0, dt_k1_xboole_0, % 14.27/2.70 dt_k2_xboole_0, dt_k3_xboole_0, dt_k4_xboole_0, fc1_xboole_0, fc2_xboole_0, % 14.27/2.70 fc3_xboole_0, idempotence_k2_xboole_0, idempotence_k3_xboole_0, rc2_xboole_0, % 14.27/2.70 reflexivity_r1_tarski, symmetry_r1_xboole_0, t17_xboole_1, t19_xboole_1, % 14.27/2.70 t1_boole, t1_xboole_1, t26_xboole_1, t2_boole, t2_tarski, t2_xboole_1, t3_boole, % 14.27/2.70 t3_xboole_0, t3_xboole_1, t4_boole, t4_xboole_0, t7_boole, t7_xboole_1, % 14.27/2.70 t8_boole, t8_xboole_1 % 14.27/2.70 % 14.27/2.70 Those formulas are unsatisfiable: % 14.27/2.70 --------------------------------- % 14.27/2.70 % 14.27/2.70 Begin of proof % 14.27/2.70 | % 14.27/2.71 | ALPHA: (commutativity_k2_xboole_0) implies: % 14.27/2.71 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 14.27/2.71 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 14.27/2.71 | % 14.27/2.71 | ALPHA: (commutativity_k3_xboole_0) implies: % 14.27/2.71 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v1, % 14.27/2.71 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (set_intersection2(v0, v1) = % 14.27/2.71 | v2 & $i(v2))) % 14.27/2.71 | % 14.27/2.71 | ALPHA: (d2_xboole_0) implies: % 14.27/2.71 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 14.27/2.71 | ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ % 14.27/2.71 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 14.27/2.71 | (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 % 14.27/2.71 | = 0))))) % 14.27/2.71 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 14.27/2.71 | ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 14.27/2.71 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 14.27/2.71 | (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 % 14.27/2.71 | = 0))))) % 14.27/2.71 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 14.27/2.71 | (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ % 14.27/2.71 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 14.27/2.71 | int] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = % 14.27/2.71 | v5)) % 14.27/2.71 | % 14.27/2.71 | ALPHA: (d3_tarski) implies: % 14.27/2.71 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 14.27/2.71 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 14.27/2.71 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 14.27/2.71 | % 14.27/2.71 | ALPHA: (d3_xboole_0) implies: % 14.27/2.71 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 14.27/2.71 | ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) % 14.27/2.71 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 14.27/2.71 | (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = % 14.27/2.71 | 0)))) % 14.27/2.71 | % 14.27/2.71 | ALPHA: (d4_xboole_0) implies: % 14.27/2.72 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 14.27/2.72 | (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | ~ % 14.27/2.72 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 14.27/2.72 | (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) % 14.27/2.72 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 14.27/2.72 | (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 14.27/2.72 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v3, % 14.27/2.72 | v1) = v4 & in(v3, v0) = 0)) % 14.27/2.72 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 14.27/2.72 | ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | % 14.27/2.72 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 14.27/2.72 | (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 % 14.27/2.72 | = 0))))) % 14.27/2.72 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 14.27/2.72 | (v4 = 0 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ % 14.27/2.72 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 14.27/2.72 | any] : (in(v3, v1) = v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = % 14.27/2.72 | 0))) % 14.27/2.72 | % 14.27/2.72 | ALPHA: (l32_xboole_1) implies: % 14.27/2.72 | (12) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 14.27/2.72 | $i(v0) | set_difference(v0, v1) = empty_set) % 14.27/2.72 | % 14.27/2.72 | ALPHA: (t12_xboole_1) implies: % 14.27/2.72 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 14.27/2.72 | $i(v0) | set_union2(v0, v1) = v1) % 14.27/2.72 | % 14.27/2.72 | ALPHA: (t28_xboole_1) implies: % 14.27/2.72 | (14) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ % 14.27/2.72 | $i(v0) | set_intersection2(v0, v1) = v0) % 14.27/2.72 | % 14.27/2.72 | ALPHA: (t6_boole) implies: % 14.27/2.72 | (15) ! [v0: $i] : (v0 = empty_set | ~ (empty(v0) = 0) | ~ $i(v0)) % 14.27/2.72 | % 14.27/2.72 | ALPHA: (function-axioms) implies: % 14.27/2.72 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 14.27/2.72 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 14.27/2.72 | v0)) % 14.27/2.72 | % 14.27/2.72 | DELTA: instantiating (rc1_xboole_0) with fresh symbol all_40_0 gives: % 14.27/2.72 | (17) empty(all_40_0) = 0 & $i(all_40_0) % 14.27/2.72 | % 14.27/2.72 | ALPHA: (17) implies: % 14.27/2.72 | (18) $i(all_40_0) % 14.27/2.72 | (19) empty(all_40_0) = 0 % 14.27/2.72 | % 14.27/2.72 | DELTA: instantiating (t33_xboole_1) with fresh symbols all_46_0, all_46_1, % 14.27/2.72 | all_46_2, all_46_3, all_46_4, all_46_5 gives: % 14.27/2.73 | (20) ~ (all_46_0 = 0) & set_difference(all_46_4, all_46_3) = all_46_1 & % 14.27/2.73 | set_difference(all_46_5, all_46_3) = all_46_2 & subset(all_46_2, % 14.27/2.73 | all_46_1) = all_46_0 & subset(all_46_5, all_46_4) = 0 & $i(all_46_1) % 14.27/2.73 | & $i(all_46_2) & $i(all_46_3) & $i(all_46_4) & $i(all_46_5) % 14.27/2.73 | % 14.27/2.73 | ALPHA: (20) implies: % 14.27/2.73 | (21) ~ (all_46_0 = 0) % 14.27/2.73 | (22) $i(all_46_5) % 14.27/2.73 | (23) $i(all_46_4) % 14.27/2.73 | (24) $i(all_46_3) % 14.27/2.73 | (25) $i(all_46_2) % 14.27/2.73 | (26) $i(all_46_1) % 14.27/2.73 | (27) subset(all_46_5, all_46_4) = 0 % 14.27/2.73 | (28) subset(all_46_2, all_46_1) = all_46_0 % 14.27/2.73 | (29) set_difference(all_46_5, all_46_3) = all_46_2 % 14.27/2.73 | (30) set_difference(all_46_4, all_46_3) = all_46_1 % 14.27/2.73 | % 14.27/2.73 | GROUND_INST: instantiating (12) with all_46_5, all_46_4, simplifying with % 14.27/2.73 | (22), (23), (27) gives: % 14.27/2.73 | (31) set_difference(all_46_5, all_46_4) = empty_set % 14.27/2.73 | % 14.27/2.73 | GROUND_INST: instantiating (14) with all_46_5, all_46_4, simplifying with % 14.27/2.73 | (22), (23), (27) gives: % 14.27/2.73 | (32) set_intersection2(all_46_5, all_46_4) = all_46_5 % 14.27/2.73 | % 14.27/2.73 | GROUND_INST: instantiating (13) with all_46_5, all_46_4, simplifying with % 14.27/2.73 | (22), (23), (27) gives: % 14.27/2.73 | (33) set_union2(all_46_5, all_46_4) = all_46_4 % 14.27/2.73 | % 14.27/2.73 | GROUND_INST: instantiating (6) with all_46_2, all_46_1, all_46_0, simplifying % 14.27/2.73 | with (25), (26), (28) gives: % 14.27/2.73 | (34) all_46_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 14.27/2.73 | all_46_1) = v1 & in(v0, all_46_2) = 0 & $i(v0)) % 14.27/2.73 | % 14.27/2.73 | GROUND_INST: instantiating (15) with all_40_0, simplifying with (18), (19) % 14.27/2.73 | gives: % 14.27/2.73 | (35) all_40_0 = empty_set % 14.27/2.73 | % 14.27/2.73 | REDUCE: (18), (35) imply: % 14.27/2.73 | (36) $i(empty_set) % 14.27/2.73 | % 14.27/2.73 | BETA: splitting (34) gives: % 14.27/2.73 | % 14.27/2.73 | Case 1: % 14.27/2.73 | | % 14.27/2.73 | | (37) all_46_0 = 0 % 14.27/2.73 | | % 14.27/2.73 | | REDUCE: (21), (37) imply: % 14.27/2.73 | | (38) $false % 14.27/2.73 | | % 14.27/2.73 | | CLOSE: (38) is inconsistent. % 14.27/2.73 | | % 14.27/2.73 | Case 2: % 14.27/2.73 | | % 14.27/2.73 | | (39) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_46_1) = v1 & % 14.27/2.73 | | in(v0, all_46_2) = 0 & $i(v0)) % 14.27/2.73 | | % 14.27/2.73 | | DELTA: instantiating (39) with fresh symbols all_69_0, all_69_1 gives: % 14.27/2.73 | | (40) ~ (all_69_0 = 0) & in(all_69_1, all_46_1) = all_69_0 & in(all_69_1, % 14.27/2.73 | | all_46_2) = 0 & $i(all_69_1) % 14.27/2.73 | | % 14.27/2.73 | | ALPHA: (40) implies: % 14.27/2.73 | | (41) ~ (all_69_0 = 0) % 14.27/2.73 | | (42) $i(all_69_1) % 14.27/2.73 | | (43) in(all_69_1, all_46_2) = 0 % 14.27/2.73 | | (44) in(all_69_1, all_46_1) = all_69_0 % 14.27/2.73 | | % 14.27/2.73 | | GROUND_INST: instantiating (9) with all_46_5, all_46_3, all_46_2, all_69_1, % 14.27/2.73 | | simplifying with (22), (24), (25), (29), (42), (43) gives: % 14.27/2.74 | | (45) ? [v0: int] : ( ~ (v0 = 0) & in(all_69_1, all_46_3) = v0 & % 14.27/2.74 | | in(all_69_1, all_46_5) = 0) % 14.27/2.74 | | % 14.27/2.74 | | GROUND_INST: instantiating (11) with all_46_4, all_46_3, all_46_1, all_69_1, % 14.27/2.74 | | all_69_0, simplifying with (23), (24), (26), (30), (42), (44) % 14.27/2.74 | | gives: % 14.27/2.74 | | (46) all_69_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_69_1, all_46_3) % 14.27/2.74 | | = v1 & in(all_69_1, all_46_4) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 14.27/2.74 | | % 14.27/2.74 | | GROUND_INST: instantiating (1) with all_46_4, all_46_5, all_46_4, % 14.27/2.74 | | simplifying with (22), (23), (33) gives: % 14.27/2.74 | | (47) set_union2(all_46_4, all_46_5) = all_46_4 % 14.27/2.74 | | % 14.27/2.74 | | GROUND_INST: instantiating (2) with all_46_4, all_46_5, all_46_5, % 14.27/2.74 | | simplifying with (22), (23), (32) gives: % 14.27/2.74 | | (48) set_intersection2(all_46_4, all_46_5) = all_46_5 % 14.27/2.74 | | % 14.27/2.74 | | DELTA: instantiating (45) with fresh symbol all_81_0 gives: % 14.27/2.74 | | (49) ~ (all_81_0 = 0) & in(all_69_1, all_46_3) = all_81_0 & in(all_69_1, % 14.27/2.74 | | all_46_5) = 0 % 14.27/2.74 | | % 14.27/2.74 | | ALPHA: (49) implies: % 14.27/2.74 | | (50) ~ (all_81_0 = 0) % 14.27/2.74 | | (51) in(all_69_1, all_46_5) = 0 % 14.27/2.74 | | (52) in(all_69_1, all_46_3) = all_81_0 % 14.27/2.74 | | % 14.27/2.74 | | BETA: splitting (46) gives: % 14.27/2.74 | | % 14.27/2.74 | | Case 1: % 14.27/2.74 | | | % 14.27/2.74 | | | (53) all_69_0 = 0 % 14.27/2.74 | | | % 14.27/2.74 | | | REDUCE: (41), (53) imply: % 14.27/2.74 | | | (54) $false % 14.27/2.74 | | | % 14.27/2.74 | | | CLOSE: (54) is inconsistent. % 14.27/2.74 | | | % 14.27/2.74 | | Case 2: % 14.27/2.74 | | | % 14.27/2.74 | | | (55) ? [v0: any] : ? [v1: any] : (in(all_69_1, all_46_3) = v1 & % 14.27/2.74 | | | in(all_69_1, all_46_4) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 14.27/2.74 | | | % 14.27/2.74 | | | DELTA: instantiating (55) with fresh symbols all_99_0, all_99_1 gives: % 14.27/2.74 | | | (56) in(all_69_1, all_46_3) = all_99_0 & in(all_69_1, all_46_4) = % 14.27/2.74 | | | all_99_1 & ( ~ (all_99_1 = 0) | all_99_0 = 0) % 14.27/2.74 | | | % 14.27/2.74 | | | ALPHA: (56) implies: % 14.27/2.74 | | | (57) in(all_69_1, all_46_4) = all_99_1 % 14.27/2.74 | | | (58) in(all_69_1, all_46_3) = all_99_0 % 14.27/2.74 | | | (59) ~ (all_99_1 = 0) | all_99_0 = 0 % 14.27/2.74 | | | % 14.27/2.74 | | | GROUND_INST: instantiating (16) with all_81_0, all_99_0, all_46_3, % 14.27/2.74 | | | all_69_1, simplifying with (52), (58) gives: % 14.27/2.74 | | | (60) all_99_0 = all_81_0 % 14.27/2.74 | | | % 14.27/2.74 | | | BETA: splitting (59) gives: % 14.27/2.74 | | | % 14.27/2.74 | | | Case 1: % 14.27/2.74 | | | | % 14.27/2.74 | | | | (61) ~ (all_99_1 = 0) % 14.27/2.74 | | | | % 14.27/2.74 | | | | GROUND_INST: instantiating (10) with all_46_5, all_46_4, empty_set, % 14.27/2.74 | | | | all_69_1, 0, simplifying with (22), (23), (31), (36), (42), % 14.27/2.74 | | | | (51) gives: % 14.27/2.74 | | | | (62) ? [v0: any] : ? [v1: any] : (in(all_69_1, all_46_4) = v1 & % 14.27/2.74 | | | | in(all_69_1, empty_set) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 14.27/2.74 | | | | % 14.27/2.74 | | | | GROUND_INST: instantiating (8) with all_46_5, all_46_4, empty_set, % 14.27/2.74 | | | | all_69_1, simplifying with (22), (23), (31), (36), (42), % 14.27/2.74 | | | | (51) gives: % 14.27/2.74 | | | | (63) ? [v0: any] : ? [v1: any] : (in(all_69_1, all_46_4) = v0 & % 14.27/2.74 | | | | in(all_69_1, empty_set) = v1 & (v1 = 0 | v0 = 0)) % 14.27/2.74 | | | | % 14.27/2.74 | | | | GROUND_INST: instantiating (5) with all_46_4, all_46_5, all_46_4, % 14.27/2.74 | | | | all_69_1, all_99_1, simplifying with (22), (23), (42), % 14.27/2.74 | | | | (47), (57) gives: % 14.27/2.74 | | | | (64) all_99_1 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ % 14.27/2.74 | | | | (v0 = 0) & in(all_69_1, all_46_4) = v0 & in(all_69_1, % 14.27/2.74 | | | | all_46_5) = v1) % 14.27/2.74 | | | | % 14.27/2.74 | | | | GROUND_INST: instantiating (3) with all_46_4, all_46_5, all_46_4, % 14.27/2.74 | | | | all_69_1, all_99_1, simplifying with (22), (23), (42), % 14.27/2.74 | | | | (47), (57) gives: % 14.27/2.74 | | | | (65) ? [v0: any] : ? [v1: any] : (in(all_69_1, all_46_4) = v1 & % 14.27/2.74 | | | | in(all_69_1, all_46_5) = v0 & (v1 = 0 | ( ~ (v0 = 0) & ~ % 14.27/2.74 | | | | (all_99_1 = 0)))) % 14.27/2.74 | | | | % 14.27/2.74 | | | | GROUND_INST: instantiating (4) with all_46_4, all_46_5, all_46_4, % 14.27/2.74 | | | | all_69_1, 0, simplifying with (22), (23), (42), (47), (51) % 14.27/2.74 | | | | gives: % 14.27/2.75 | | | | (66) ? [v0: MultipleValueBool] : (in(all_69_1, all_46_4) = v0 & % 14.27/2.75 | | | | in(all_69_1, all_46_4) = 0) % 14.27/2.75 | | | | % 14.27/2.75 | | | | GROUND_INST: instantiating (7) with all_46_4, all_46_5, all_46_5, % 14.27/2.75 | | | | all_69_1, 0, simplifying with (22), (23), (42), (48), (51) % 14.27/2.75 | | | | gives: % 14.27/2.75 | | | | (67) ? [v0: any] : ? [v1: any] : (in(all_69_1, all_46_4) = v1 & % 14.27/2.75 | | | | in(all_69_1, all_46_5) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 14.27/2.75 | | | | % 14.27/2.75 | | | | DELTA: instantiating (66) with fresh symbol all_141_0 gives: % 14.27/2.75 | | | | (68) in(all_69_1, all_46_4) = all_141_0 & in(all_69_1, all_46_4) = 0 % 14.27/2.75 | | | | % 14.27/2.75 | | | | ALPHA: (68) implies: % 14.27/2.75 | | | | (69) in(all_69_1, all_46_4) = 0 % 14.27/2.75 | | | | (70) in(all_69_1, all_46_4) = all_141_0 % 14.27/2.75 | | | | % 14.27/2.75 | | | | DELTA: instantiating (63) with fresh symbols all_145_0, all_145_1 gives: % 14.27/2.75 | | | | (71) in(all_69_1, all_46_4) = all_145_1 & in(all_69_1, empty_set) = % 14.27/2.75 | | | | all_145_0 & (all_145_0 = 0 | all_145_1 = 0) % 14.27/2.75 | | | | % 14.27/2.75 | | | | ALPHA: (71) implies: % 14.27/2.75 | | | | (72) in(all_69_1, all_46_4) = all_145_1 % 14.27/2.75 | | | | % 14.27/2.75 | | | | DELTA: instantiating (67) with fresh symbols all_147_0, all_147_1 gives: % 14.27/2.75 | | | | (73) in(all_69_1, all_46_4) = all_147_0 & in(all_69_1, all_46_5) = % 14.27/2.75 | | | | all_147_1 & ( ~ (all_147_1 = 0) | all_147_0 = 0) % 14.27/2.75 | | | | % 14.27/2.75 | | | | ALPHA: (73) implies: % 14.27/2.75 | | | | (74) in(all_69_1, all_46_4) = all_147_0 % 14.27/2.75 | | | | % 14.27/2.75 | | | | DELTA: instantiating (62) with fresh symbols all_149_0, all_149_1 gives: % 14.27/2.75 | | | | (75) in(all_69_1, all_46_4) = all_149_0 & in(all_69_1, empty_set) = % 14.27/2.75 | | | | all_149_1 & ( ~ (all_149_0 = 0) | ~ (all_149_1 = 0)) % 14.27/2.75 | | | | % 14.27/2.75 | | | | ALPHA: (75) implies: % 14.27/2.75 | | | | (76) in(all_69_1, all_46_4) = all_149_0 % 14.27/2.75 | | | | % 14.27/2.75 | | | | DELTA: instantiating (65) with fresh symbols all_151_0, all_151_1 gives: % 14.27/2.75 | | | | (77) in(all_69_1, all_46_4) = all_151_0 & in(all_69_1, all_46_5) = % 14.27/2.75 | | | | all_151_1 & (all_151_0 = 0 | ( ~ (all_151_1 = 0) & ~ (all_99_1 % 14.27/2.75 | | | | = 0))) % 14.27/2.75 | | | | % 14.27/2.75 | | | | ALPHA: (77) implies: % 14.27/2.75 | | | | (78) in(all_69_1, all_46_4) = all_151_0 % 14.27/2.75 | | | | % 14.27/2.75 | | | | BETA: splitting (64) gives: % 14.27/2.75 | | | | % 14.27/2.75 | | | | Case 1: % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | (79) all_99_1 = 0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | REDUCE: (61), (79) imply: % 14.27/2.75 | | | | | (80) $false % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | CLOSE: (80) is inconsistent. % 14.27/2.75 | | | | | % 14.27/2.75 | | | | Case 2: % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | (81) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 14.27/2.75 | | | | | in(all_69_1, all_46_4) = v0 & in(all_69_1, all_46_5) = v1) % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | DELTA: instantiating (81) with fresh symbols all_167_0, all_167_1 % 14.27/2.75 | | | | | gives: % 14.27/2.75 | | | | | (82) ~ (all_167_0 = 0) & ~ (all_167_1 = 0) & in(all_69_1, % 14.27/2.75 | | | | | all_46_4) = all_167_1 & in(all_69_1, all_46_5) = all_167_0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | ALPHA: (82) implies: % 14.27/2.75 | | | | | (83) in(all_69_1, all_46_4) = all_167_1 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | GROUND_INST: instantiating (16) with all_99_1, all_147_0, all_46_4, % 14.27/2.75 | | | | | all_69_1, simplifying with (57), (74) gives: % 14.27/2.75 | | | | | (84) all_147_0 = all_99_1 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | GROUND_INST: instantiating (16) with all_145_1, all_147_0, all_46_4, % 14.27/2.75 | | | | | all_69_1, simplifying with (72), (74) gives: % 14.27/2.75 | | | | | (85) all_147_0 = all_145_1 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | GROUND_INST: instantiating (16) with all_147_0, all_149_0, all_46_4, % 14.27/2.75 | | | | | all_69_1, simplifying with (74), (76) gives: % 14.27/2.75 | | | | | (86) all_149_0 = all_147_0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | GROUND_INST: instantiating (16) with all_149_0, all_151_0, all_46_4, % 14.27/2.75 | | | | | all_69_1, simplifying with (76), (78) gives: % 14.27/2.75 | | | | | (87) all_151_0 = all_149_0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | GROUND_INST: instantiating (16) with all_141_0, all_151_0, all_46_4, % 14.27/2.75 | | | | | all_69_1, simplifying with (70), (78) gives: % 14.27/2.75 | | | | | (88) all_151_0 = all_141_0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | GROUND_INST: instantiating (16) with all_147_0, all_167_1, all_46_4, % 14.27/2.75 | | | | | all_69_1, simplifying with (74), (83) gives: % 14.27/2.75 | | | | | (89) all_167_1 = all_147_0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | GROUND_INST: instantiating (16) with 0, all_167_1, all_46_4, all_69_1, % 14.27/2.75 | | | | | simplifying with (69), (83) gives: % 14.27/2.75 | | | | | (90) all_167_1 = 0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | COMBINE_EQS: (89), (90) imply: % 14.27/2.75 | | | | | (91) all_147_0 = 0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | SIMP: (91) implies: % 14.27/2.75 | | | | | (92) all_147_0 = 0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | COMBINE_EQS: (87), (88) imply: % 14.27/2.75 | | | | | (93) all_149_0 = all_141_0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | SIMP: (93) implies: % 14.27/2.75 | | | | | (94) all_149_0 = all_141_0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | COMBINE_EQS: (86), (94) imply: % 14.27/2.75 | | | | | (95) all_147_0 = all_141_0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | SIMP: (95) implies: % 14.27/2.75 | | | | | (96) all_147_0 = all_141_0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | COMBINE_EQS: (85), (92) imply: % 14.27/2.75 | | | | | (97) all_145_1 = 0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | COMBINE_EQS: (85), (96) imply: % 14.27/2.75 | | | | | (98) all_145_1 = all_141_0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | COMBINE_EQS: (84), (85) imply: % 14.27/2.75 | | | | | (99) all_145_1 = all_99_1 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | COMBINE_EQS: (98), (99) imply: % 14.27/2.75 | | | | | (100) all_141_0 = all_99_1 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | COMBINE_EQS: (97), (98) imply: % 14.27/2.75 | | | | | (101) all_141_0 = 0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | COMBINE_EQS: (100), (101) imply: % 14.27/2.75 | | | | | (102) all_99_1 = 0 % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | REDUCE: (61), (102) imply: % 14.27/2.75 | | | | | (103) $false % 14.27/2.75 | | | | | % 14.27/2.75 | | | | | CLOSE: (103) is inconsistent. % 14.27/2.75 | | | | | % 14.27/2.75 | | | | End of split % 14.27/2.75 | | | | % 14.27/2.75 | | | Case 2: % 14.27/2.75 | | | | % 14.27/2.75 | | | | (104) all_99_0 = 0 % 14.27/2.76 | | | | % 14.27/2.76 | | | | COMBINE_EQS: (60), (104) imply: % 14.27/2.76 | | | | (105) all_81_0 = 0 % 14.27/2.76 | | | | % 14.27/2.76 | | | | REDUCE: (50), (105) imply: % 14.27/2.76 | | | | (106) $false % 14.27/2.76 | | | | % 14.27/2.76 | | | | CLOSE: (106) is inconsistent. % 14.27/2.76 | | | | % 14.27/2.76 | | | End of split % 14.27/2.76 | | | % 14.27/2.76 | | End of split % 14.27/2.76 | | % 14.27/2.76 | End of split % 14.27/2.76 | % 14.27/2.76 End of proof % 14.27/2.76 % SZS output end Proof for theBenchmark % 14.27/2.76 % 14.27/2.76 2156ms %------------------------------------------------------------------------------