%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU144+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 : n029.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 17:42:45 EDT 2023 % Result : Theorem 12.99s 2.57s % Output : Proof 15.39s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU144+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n029.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Wed Aug 23 17:57:08 EDT 2023 % 0.12/0.34 % CPUTime : % 0.20/0.64 ________ _____ % 0.20/0.64 ___ __ \_________(_)________________________________ % 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.64 % 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.64 (2023-06-19) % 0.20/0.64 % 0.20/0.64 (c) Philipp Rümmer, 2009-2023 % 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.64 Amanda Stjerna. % 0.20/0.64 Free software under BSD-3-Clause. % 0.20/0.64 % 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.64 % 0.20/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.66 Running up to 7 provers in parallel. % 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 3.03/1.16 Prover 1: Preprocessing ... % 3.03/1.16 Prover 4: Preprocessing ... % 3.03/1.19 Prover 5: Preprocessing ... % 3.03/1.19 Prover 6: Preprocessing ... % 3.03/1.19 Prover 2: Preprocessing ... % 3.03/1.19 Prover 0: Preprocessing ... % 3.03/1.19 Prover 3: Preprocessing ... % 7.91/1.85 Prover 1: Warning: ignoring some quantifiers % 8.06/1.86 Prover 5: Proving ... % 8.52/1.92 Prover 1: Constructing countermodel ... % 8.52/1.94 Prover 3: Warning: ignoring some quantifiers % 8.81/1.97 Prover 3: Constructing countermodel ... % 8.81/1.98 Prover 6: Proving ... % 8.81/2.05 Prover 2: Proving ... % 8.81/2.08 Prover 4: Warning: ignoring some quantifiers % 8.81/2.18 Prover 4: Constructing countermodel ... % 10.68/2.23 Prover 0: Proving ... % 11.68/2.36 Prover 3: gave up % 11.71/2.36 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.00/2.43 Prover 7: Preprocessing ... % 12.24/2.46 Prover 1: gave up % 12.24/2.47 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.99/2.55 Prover 8: Preprocessing ... % 12.99/2.57 Prover 0: proved (1897ms) % 12.99/2.57 % 12.99/2.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 12.99/2.57 % 12.99/2.57 Prover 7: Warning: ignoring some quantifiers % 12.99/2.57 Prover 6: stopped % 12.99/2.58 Prover 5: stopped % 12.99/2.58 Prover 2: stopped % 12.99/2.58 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.99/2.58 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.99/2.58 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.99/2.59 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 13.44/2.59 Prover 7: Constructing countermodel ... % 13.44/2.65 Prover 11: Preprocessing ... % 13.44/2.65 Prover 13: Preprocessing ... % 13.44/2.65 Prover 10: Preprocessing ... % 13.98/2.67 Prover 16: Preprocessing ... % 13.98/2.78 Prover 4: Found proof (size 57) % 13.98/2.78 Prover 4: proved (2106ms) % 13.98/2.78 Prover 11: stopped % 13.98/2.78 Prover 10: Warning: ignoring some quantifiers % 13.98/2.78 Prover 7: stopped % 13.98/2.79 Prover 10: Constructing countermodel ... % 13.98/2.80 Prover 8: Warning: ignoring some quantifiers % 13.98/2.81 Prover 10: stopped % 13.98/2.81 Prover 8: Constructing countermodel ... % 13.98/2.82 Prover 16: Warning: ignoring some quantifiers % 13.98/2.83 Prover 8: stopped % 13.98/2.83 Prover 16: Constructing countermodel ... % 13.98/2.84 Prover 13: Warning: ignoring some quantifiers % 13.98/2.84 Prover 16: stopped % 13.98/2.85 Prover 13: Constructing countermodel ... % 15.01/2.86 Prover 13: stopped % 15.01/2.86 % 15.01/2.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 15.01/2.86 % 15.01/2.87 % SZS output start Proof for theBenchmark % 15.01/2.88 Assumptions after simplification: % 15.01/2.88 --------------------------------- % 15.01/2.88 % 15.01/2.88 (d1_tarski) % 15.39/2.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) = v1) | % 15.39/2.90 ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! % 15.39/2.90 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) | ~ (in(v0, v1) = % 15.39/2.90 v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.39/2.90 (v2 = v0 | ~ (singleton(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 15.39/2.90 [v4: any] : (in(v3, v0) = v4 & $i(v3) & ( ~ (v4 = 0) | ~ (v3 = v1)) & (v4 = % 15.39/2.90 0 | v3 = v1))) % 15.39/2.90 % 15.39/2.90 (d3_tarski) % 15.39/2.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 15.39/2.91 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 15.39/2.91 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 15.39/2.91 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 15.39/2.91 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 15.39/2.91 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 15.39/2.91 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 15.39/2.91 $i(v0) | in(v2, v1) = 0) % 15.39/2.91 % 15.39/2.91 (d4_xboole_0) % 15.39/2.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 15.39/2.92 | ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~ % 15.39/2.92 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1) = % 15.39/2.92 v6 & in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: % 15.39/2.92 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 15.39/2.92 (set_difference(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) % 15.39/2.92 | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v6 & % 15.39/2.92 in(v3, v0) = v5 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : % 15.39/2.92 ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (set_difference(v0, v1) = v2) | % 15.39/2.92 ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? % 15.39/2.92 [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) % 15.39/2.92 | (v6 = 0 & ~ (v4 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 15.39/2.92 ! [v3: $i] : ! [v4: any] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) % 15.39/2.92 = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? % 15.39/2.92 [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ % 15.39/2.92 (v6 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : % 15.39/2.92 ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 15.39/2.92 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = % 15.39/2.92 v4 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 15.39/2.92 $i] : ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | % 15.39/2.92 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v2) % 15.39/2.92 = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : % 15.39/2.92 ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (set_difference(v1, v2) = v3) | ~ % 15.39/2.92 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : % 15.39/2.92 ? [v7: any] : (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) % 15.39/2.92 & ( ~ (v6 = 0) | ~ (v5 = 0) | v7 = 0) & (v5 = 0 | (v6 = 0 & ~ (v7 = % 15.39/2.92 0))))) % 15.39/2.92 % 15.39/2.92 (l2_zfmisc_1) % 15.39/2.92 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] : % 15.39/2.92 (singleton(v0) = v2 & subset(v2, v1) = v3 & in(v0, v1) = v4 & $i(v2) & $i(v1) % 15.39/2.92 & $i(v0) & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0)))) % 15.39/2.92 % 15.39/2.92 (l32_xboole_1) % 15.39/2.92 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~ % 15.39/2.92 (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ % 15.39/2.92 (v3 = 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 15.39/2.92 int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 15.39/2.92 $i] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3 & $i(v3))) & ! % 15.39/2.92 [v0: $i] : ! [v1: $i] : ( ~ (set_difference(v0, v1) = empty_set) | ~ $i(v1) % 15.39/2.92 | ~ $i(v0) | subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.39/2.92 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | set_difference(v0, v1) = % 15.39/2.92 empty_set) % 15.39/2.92 % 15.39/2.92 (t37_xboole_1) % 15.39/2.92 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = empty_set | ~ % 15.39/2.92 (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ % 15.39/2.92 (v3 = 0) & subset(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 15.39/2.92 int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 15.39/2.92 $i] : ( ~ (v3 = empty_set) & set_difference(v0, v1) = v3 & $i(v3))) & ! % 15.39/2.92 [v0: $i] : ! [v1: $i] : ( ~ (set_difference(v0, v1) = empty_set) | ~ $i(v1) % 15.39/2.92 | ~ $i(v0) | subset(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.39/2.92 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | set_difference(v0, v1) = % 15.39/2.92 empty_set) % 15.39/2.92 % 15.39/2.92 (t69_enumset1) % 15.39/2.93 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 15.39/2.93 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~ % 15.39/2.93 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1))) % 15.39/2.93 % 15.39/2.93 (function-axioms) % 15.39/2.93 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 15.39/2.93 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 15.39/2.93 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.39/2.93 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 15.39/2.93 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.39/2.93 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 15.39/2.93 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.39/2.93 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 15.39/2.93 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.39/2.93 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 15.39/2.93 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = % 15.39/2.93 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 15.39/2.93 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 15.39/2.93 (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) = v0)) & ! [v0: % 15.39/2.93 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 15.39/2.93 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 15.39/2.93 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 15.39/2.93 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 15.39/2.93 [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) % 15.39/2.93 % 15.39/2.93 Further assumptions not needed in the proof: % 15.39/2.93 -------------------------------------------- % 15.39/2.93 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski, % 15.39/2.93 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_xboole_0, % 15.39/2.93 d2_tarski, d2_xboole_0, d3_xboole_0, d7_xboole_0, d8_xboole_0, dt_k1_tarski, % 15.39/2.93 dt_k1_xboole_0, dt_k2_tarski, dt_k2_xboole_0, dt_k3_xboole_0, dt_k4_xboole_0, % 15.39/2.93 fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 15.39/2.93 idempotence_k3_xboole_0, irreflexivity_r2_xboole_0, l1_zfmisc_1, rc1_xboole_0, % 15.39/2.93 rc2_xboole_0, reflexivity_r1_tarski, symmetry_r1_xboole_0, t12_xboole_1, % 15.39/2.93 t17_xboole_1, t19_xboole_1, t1_boole, t1_xboole_1, t26_xboole_1, t28_xboole_1, % 15.39/2.93 t2_boole, t2_tarski, t2_xboole_1, t33_xboole_1, t36_xboole_1, t39_xboole_1, % 15.39/2.93 t3_boole, t3_xboole_0, t3_xboole_1, t40_xboole_1, t45_xboole_1, t48_xboole_1, % 15.39/2.93 t4_boole, t4_xboole_0, t60_xboole_1, t63_xboole_1, t6_boole, t7_boole, % 15.39/2.93 t7_xboole_1, t83_xboole_1, t8_boole, t8_xboole_1 % 15.39/2.93 % 15.39/2.93 Those formulas are unsatisfiable: % 15.39/2.93 --------------------------------- % 15.39/2.93 % 15.39/2.93 Begin of proof % 15.39/2.93 | % 15.39/2.93 | ALPHA: (d1_tarski) implies: % 15.39/2.93 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) % 15.39/2.93 | = v1) | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)) % 15.39/2.93 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (singleton(v0) % 15.39/2.93 | = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 15.39/2.93 | % 15.39/2.93 | ALPHA: (d3_tarski) implies: % 15.39/2.93 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 15.39/2.93 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 15.39/2.93 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 15.39/2.94 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 15.39/2.94 | (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 15.39/2.94 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) % 15.39/2.94 | % 15.39/2.94 | ALPHA: (d4_xboole_0) implies: % 15.39/2.94 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 15.39/2.94 | (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | ~ % 15.39/2.94 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 15.39/2.94 | (in(v3, v2) = v5 & in(v3, v1) = v4 & (v5 = 0 | v4 = 0))) % 15.39/2.94 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 15.39/2.94 | ( ~ (set_difference(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | % 15.39/2.94 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 15.39/2.94 | (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v4 = 0 & ~ (v6 % 15.39/2.94 | = 0))))) % 15.39/2.94 | % 15.39/2.94 | ALPHA: (t37_xboole_1) implies: % 15.39/2.94 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 15.39/2.94 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = empty_set) % 15.39/2.94 | & set_difference(v0, v1) = v3 & $i(v3))) % 15.39/2.94 | % 15.39/2.94 | ALPHA: (t69_enumset1) implies: % 15.39/2.94 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) | % 15.39/2.94 | (unordered_pair(v0, v0) = v1 & $i(v1))) % 15.39/2.94 | % 15.39/2.94 | ALPHA: (function-axioms) implies: % 15.39/2.94 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 15.39/2.94 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 15.39/2.94 | % 15.39/2.94 | DELTA: instantiating (l2_zfmisc_1) with fresh symbols all_66_0, all_66_1, % 15.39/2.94 | all_66_2, all_66_3, all_66_4 gives: % 15.39/2.94 | (10) singleton(all_66_4) = all_66_2 & subset(all_66_2, all_66_3) = all_66_1 % 15.39/2.94 | & in(all_66_4, all_66_3) = all_66_0 & $i(all_66_2) & $i(all_66_3) & % 15.39/2.94 | $i(all_66_4) & ((all_66_0 = 0 & ~ (all_66_1 = 0)) | (all_66_1 = 0 & % 15.39/2.94 | ~ (all_66_0 = 0))) % 15.39/2.94 | % 15.39/2.94 | ALPHA: (10) implies: % 15.39/2.94 | (11) $i(all_66_4) % 15.39/2.94 | (12) $i(all_66_3) % 15.39/2.94 | (13) $i(all_66_2) % 15.39/2.94 | (14) in(all_66_4, all_66_3) = all_66_0 % 15.39/2.94 | (15) subset(all_66_2, all_66_3) = all_66_1 % 15.39/2.94 | (16) singleton(all_66_4) = all_66_2 % 15.39/2.94 | (17) (all_66_0 = 0 & ~ (all_66_1 = 0)) | (all_66_1 = 0 & ~ (all_66_0 = % 15.39/2.94 | 0)) % 15.39/2.94 | % 15.39/2.95 | GROUND_INST: instantiating (3) with all_66_2, all_66_3, all_66_1, simplifying % 15.39/2.95 | with (12), (13), (15) gives: % 15.39/2.95 | (18) all_66_1 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 15.39/2.95 | all_66_2) = 0 & in(v0, all_66_3) = v1 & $i(v0)) % 15.39/2.95 | % 15.39/2.95 | GROUND_INST: instantiating (7) with all_66_2, all_66_3, all_66_1, simplifying % 15.39/2.95 | with (12), (13), (15) gives: % 15.39/2.95 | (19) all_66_1 = 0 | ? [v0: $i] : ( ~ (v0 = empty_set) & % 15.39/2.95 | set_difference(all_66_2, all_66_3) = v0 & $i(v0)) % 15.39/2.95 | % 15.39/2.95 | GROUND_INST: instantiating (8) with all_66_4, all_66_2, simplifying with (11), % 15.39/2.95 | (16) gives: % 15.39/2.95 | (20) unordered_pair(all_66_4, all_66_4) = all_66_2 & $i(all_66_2) % 15.39/2.95 | % 15.39/2.95 | BETA: splitting (17) gives: % 15.39/2.95 | % 15.39/2.95 | Case 1: % 15.39/2.95 | | % 15.39/2.95 | | (21) all_66_0 = 0 & ~ (all_66_1 = 0) % 15.39/2.95 | | % 15.39/2.95 | | ALPHA: (21) implies: % 15.39/2.95 | | (22) all_66_0 = 0 % 15.39/2.95 | | (23) ~ (all_66_1 = 0) % 15.39/2.95 | | % 15.39/2.95 | | REDUCE: (14), (22) imply: % 15.39/2.95 | | (24) in(all_66_4, all_66_3) = 0 % 15.39/2.95 | | % 15.39/2.95 | | BETA: splitting (19) gives: % 15.39/2.95 | | % 15.39/2.95 | | Case 1: % 15.39/2.95 | | | % 15.39/2.95 | | | (25) all_66_1 = 0 % 15.39/2.95 | | | % 15.39/2.95 | | | REDUCE: (23), (25) imply: % 15.39/2.95 | | | (26) $false % 15.39/2.95 | | | % 15.39/2.95 | | | CLOSE: (26) is inconsistent. % 15.39/2.95 | | | % 15.39/2.95 | | Case 2: % 15.39/2.95 | | | % 15.39/2.95 | | | (27) ? [v0: $i] : ( ~ (v0 = empty_set) & set_difference(all_66_2, % 15.39/2.95 | | | all_66_3) = v0 & $i(v0)) % 15.39/2.95 | | | % 15.39/2.95 | | | DELTA: instantiating (27) with fresh symbol all_107_0 gives: % 15.39/2.95 | | | (28) ~ (all_107_0 = empty_set) & set_difference(all_66_2, all_66_3) = % 15.39/2.95 | | | all_107_0 & $i(all_107_0) % 15.39/2.95 | | | % 15.39/2.95 | | | ALPHA: (28) implies: % 15.39/2.95 | | | (29) $i(all_107_0) % 15.39/2.95 | | | (30) set_difference(all_66_2, all_66_3) = all_107_0 % 15.39/2.95 | | | % 15.39/2.95 | | | BETA: splitting (18) gives: % 15.39/2.95 | | | % 15.39/2.95 | | | Case 1: % 15.39/2.95 | | | | % 15.39/2.95 | | | | (31) all_66_1 = 0 % 15.39/2.95 | | | | % 15.39/2.95 | | | | REDUCE: (23), (31) imply: % 15.39/2.95 | | | | (32) $false % 15.39/2.95 | | | | % 15.39/2.95 | | | | CLOSE: (32) is inconsistent. % 15.39/2.95 | | | | % 15.39/2.95 | | | Case 2: % 15.39/2.95 | | | | % 15.39/2.95 | | | | (33) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_66_2) = 0 % 15.39/2.95 | | | | & in(v0, all_66_3) = v1 & $i(v0)) % 15.39/2.95 | | | | % 15.39/2.95 | | | | DELTA: instantiating (33) with fresh symbols all_112_0, all_112_1 gives: % 15.39/2.95 | | | | (34) ~ (all_112_0 = 0) & in(all_112_1, all_66_2) = 0 & in(all_112_1, % 15.39/2.95 | | | | all_66_3) = all_112_0 & $i(all_112_1) % 15.39/2.95 | | | | % 15.39/2.95 | | | | ALPHA: (34) implies: % 15.39/2.95 | | | | (35) ~ (all_112_0 = 0) % 15.39/2.95 | | | | (36) $i(all_112_1) % 15.39/2.95 | | | | (37) in(all_112_1, all_66_3) = all_112_0 % 15.39/2.95 | | | | (38) in(all_112_1, all_66_2) = 0 % 15.39/2.95 | | | | % 15.39/2.96 | | | | GROUND_INST: instantiating (2) with all_66_4, all_66_2, all_112_1, % 15.39/2.96 | | | | simplifying with (11), (13), (16), (36), (38) gives: % 15.39/2.96 | | | | (39) all_112_1 = all_66_4 % 15.39/2.96 | | | | % 15.39/2.96 | | | | GROUND_INST: instantiating (5) with all_66_2, all_66_3, all_107_0, % 15.39/2.96 | | | | all_112_1, simplifying with (12), (13), (29), (30), (36), % 15.39/2.96 | | | | (38) gives: % 15.39/2.96 | | | | (40) ? [v0: any] : ? [v1: any] : (in(all_112_1, all_107_0) = v1 & % 15.39/2.96 | | | | in(all_112_1, all_66_3) = v0 & (v1 = 0 | v0 = 0)) % 15.39/2.96 | | | | % 15.39/2.96 | | | | GROUND_INST: instantiating (6) with all_66_2, all_66_3, all_107_0, % 15.39/2.96 | | | | all_112_1, 0, simplifying with (12), (13), (29), (30), % 15.39/2.96 | | | | (36), (38) gives: % 15.39/2.96 | | | | (41) ? [v0: any] : ? [v1: any] : (in(all_112_1, all_107_0) = v0 & % 15.39/2.96 | | | | in(all_112_1, all_66_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 15.39/2.96 | | | | % 15.39/2.96 | | | | DELTA: instantiating (40) with fresh symbols all_141_0, all_141_1 gives: % 15.39/2.96 | | | | (42) in(all_112_1, all_107_0) = all_141_0 & in(all_112_1, all_66_3) = % 15.39/2.96 | | | | all_141_1 & (all_141_0 = 0 | all_141_1 = 0) % 15.39/2.96 | | | | % 15.39/2.96 | | | | ALPHA: (42) implies: % 15.39/2.96 | | | | (43) in(all_112_1, all_66_3) = all_141_1 % 15.39/2.96 | | | | % 15.39/2.96 | | | | DELTA: instantiating (41) with fresh symbols all_143_0, all_143_1 gives: % 15.39/2.96 | | | | (44) in(all_112_1, all_107_0) = all_143_1 & in(all_112_1, all_66_3) = % 15.39/2.96 | | | | all_143_0 & ( ~ (all_143_0 = 0) | ~ (all_143_1 = 0)) % 15.39/2.96 | | | | % 15.39/2.96 | | | | ALPHA: (44) implies: % 15.39/2.96 | | | | (45) in(all_112_1, all_66_3) = all_143_0 % 15.39/2.96 | | | | % 15.39/2.96 | | | | REDUCE: (39), (45) imply: % 15.39/2.96 | | | | (46) in(all_66_4, all_66_3) = all_143_0 % 15.39/2.96 | | | | % 15.39/2.96 | | | | REDUCE: (39), (43) imply: % 15.39/2.96 | | | | (47) in(all_66_4, all_66_3) = all_141_1 % 15.39/2.96 | | | | % 15.39/2.96 | | | | REDUCE: (37), (39) imply: % 15.39/2.96 | | | | (48) in(all_66_4, all_66_3) = all_112_0 % 15.39/2.96 | | | | % 15.39/2.96 | | | | GROUND_INST: instantiating (9) with all_112_0, all_141_1, all_66_3, % 15.39/2.96 | | | | all_66_4, simplifying with (47), (48) gives: % 15.39/2.96 | | | | (49) all_141_1 = all_112_0 % 15.39/2.96 | | | | % 15.39/2.96 | | | | GROUND_INST: instantiating (9) with 0, all_143_0, all_66_3, all_66_4, % 15.39/2.96 | | | | simplifying with (24), (46) gives: % 15.39/2.96 | | | | (50) all_143_0 = 0 % 15.39/2.96 | | | | % 15.39/2.96 | | | | GROUND_INST: instantiating (9) with all_141_1, all_143_0, all_66_3, % 15.39/2.96 | | | | all_66_4, simplifying with (46), (47) gives: % 15.39/2.96 | | | | (51) all_143_0 = all_141_1 % 15.39/2.96 | | | | % 15.39/2.96 | | | | COMBINE_EQS: (50), (51) imply: % 15.39/2.96 | | | | (52) all_141_1 = 0 % 15.39/2.96 | | | | % 15.39/2.96 | | | | SIMP: (52) implies: % 15.39/2.96 | | | | (53) all_141_1 = 0 % 15.39/2.96 | | | | % 15.39/2.96 | | | | COMBINE_EQS: (49), (53) imply: % 15.39/2.96 | | | | (54) all_112_0 = 0 % 15.39/2.96 | | | | % 15.39/2.96 | | | | SIMP: (54) implies: % 15.39/2.96 | | | | (55) all_112_0 = 0 % 15.39/2.96 | | | | % 15.39/2.96 | | | | REDUCE: (35), (55) imply: % 15.39/2.96 | | | | (56) $false % 15.39/2.96 | | | | % 15.39/2.96 | | | | CLOSE: (56) is inconsistent. % 15.39/2.96 | | | | % 15.39/2.96 | | | End of split % 15.39/2.96 | | | % 15.39/2.96 | | End of split % 15.39/2.96 | | % 15.39/2.96 | Case 2: % 15.39/2.96 | | % 15.39/2.96 | | (57) all_66_1 = 0 & ~ (all_66_0 = 0) % 15.39/2.96 | | % 15.39/2.96 | | ALPHA: (57) implies: % 15.39/2.96 | | (58) all_66_1 = 0 % 15.39/2.96 | | (59) ~ (all_66_0 = 0) % 15.39/2.96 | | % 15.39/2.96 | | REDUCE: (15), (58) imply: % 15.39/2.97 | | (60) subset(all_66_2, all_66_3) = 0 % 15.39/2.97 | | % 15.39/2.97 | | GROUND_INST: instantiating (4) with all_66_2, all_66_3, all_66_4, all_66_0, % 15.39/2.97 | | simplifying with (11), (12), (13), (14), (60) gives: % 15.39/2.97 | | (61) all_66_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_66_4, all_66_2) % 15.39/2.97 | | = v0) % 15.39/2.97 | | % 15.39/2.97 | | BETA: splitting (61) gives: % 15.39/2.97 | | % 15.39/2.97 | | Case 1: % 15.39/2.97 | | | % 15.39/2.97 | | | (62) all_66_0 = 0 % 15.39/2.97 | | | % 15.39/2.97 | | | REDUCE: (59), (62) imply: % 15.39/2.97 | | | (63) $false % 15.39/2.97 | | | % 15.39/2.97 | | | CLOSE: (63) is inconsistent. % 15.39/2.97 | | | % 15.39/2.97 | | Case 2: % 15.39/2.97 | | | % 15.39/2.97 | | | (64) ? [v0: int] : ( ~ (v0 = 0) & in(all_66_4, all_66_2) = v0) % 15.39/2.97 | | | % 15.39/2.97 | | | DELTA: instantiating (64) with fresh symbol all_117_0 gives: % 15.39/2.97 | | | (65) ~ (all_117_0 = 0) & in(all_66_4, all_66_2) = all_117_0 % 15.39/2.97 | | | % 15.39/2.97 | | | ALPHA: (65) implies: % 15.39/2.97 | | | (66) ~ (all_117_0 = 0) % 15.39/2.97 | | | (67) in(all_66_4, all_66_2) = all_117_0 % 15.39/2.97 | | | % 15.39/2.97 | | | GROUND_INST: instantiating (1) with all_66_4, all_66_2, all_117_0, % 15.39/2.97 | | | simplifying with (11), (13), (16), (67) gives: % 15.39/2.97 | | | (68) all_117_0 = 0 % 15.39/2.97 | | | % 15.39/2.97 | | | REDUCE: (66), (68) imply: % 15.39/2.97 | | | (69) $false % 15.39/2.97 | | | % 15.39/2.97 | | | CLOSE: (69) is inconsistent. % 15.39/2.97 | | | % 15.39/2.97 | | End of split % 15.39/2.97 | | % 15.39/2.97 | End of split % 15.39/2.97 | % 15.39/2.97 End of proof % 15.39/2.97 % SZS output end Proof for theBenchmark % 15.39/2.97 % 15.39/2.97 2331ms %------------------------------------------------------------------------------