%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET952+1 : TPTP v8.1.2. Released v3.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n007.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 15:27:11 EDT 2023 % Result : Theorem 18.26s 3.19s % Output : Proof 24.03s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET952+1 : TPTP v8.1.2. Released v3.2.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n007.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 : Sat Aug 26 08:54:11 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.65 ________ _____ % 0.20/0.65 ___ __ \_________(_)________________________________ % 0.20/0.65 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.65 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.65 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.65 % 0.20/0.65 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.65 (2023-06-19) % 0.20/0.65 % 0.20/0.65 (c) Philipp Rümmer, 2009-2023 % 0.20/0.65 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.65 Amanda Stjerna. % 0.20/0.65 Free software under BSD-3-Clause. % 0.20/0.65 % 0.20/0.65 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.65 % 0.20/0.65 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.67 Running up to 7 provers in parallel. % 0.20/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.60/1.06 Prover 1: Preprocessing ... % 2.60/1.06 Prover 4: Preprocessing ... % 2.74/1.09 Prover 5: Preprocessing ... % 2.74/1.09 Prover 2: Preprocessing ... % 2.74/1.09 Prover 3: Preprocessing ... % 2.74/1.09 Prover 6: Preprocessing ... % 2.74/1.09 Prover 0: Preprocessing ... % 5.92/1.54 Prover 3: Warning: ignoring some quantifiers % 5.92/1.56 Prover 6: Proving ... % 5.92/1.56 Prover 3: Constructing countermodel ... % 5.92/1.58 Prover 1: Warning: ignoring some quantifiers % 5.92/1.58 Prover 5: Proving ... % 6.39/1.59 Prover 4: Warning: ignoring some quantifiers % 6.39/1.61 Prover 1: Constructing countermodel ... % 6.39/1.62 Prover 4: Constructing countermodel ... % 6.98/1.67 Prover 0: Proving ... % 7.08/1.68 Prover 2: Proving ... % 9.94/2.09 Prover 3: gave up % 9.94/2.09 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 10.53/2.13 Prover 7: Preprocessing ... % 11.48/2.27 Prover 7: Warning: ignoring some quantifiers % 11.48/2.30 Prover 7: Constructing countermodel ... % 12.43/2.41 Prover 1: gave up % 12.71/2.43 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.78/2.45 Prover 8: Preprocessing ... % 13.76/2.58 Prover 8: Warning: ignoring some quantifiers % 13.76/2.59 Prover 8: Constructing countermodel ... % 16.54/2.99 Prover 7: gave up % 16.54/3.01 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 17.23/3.02 Prover 8: gave up % 17.23/3.04 Prover 9: Preprocessing ... % 17.23/3.04 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 17.23/3.07 Prover 10: Preprocessing ... % 18.26/3.17 Prover 10: Warning: ignoring some quantifiers % 18.26/3.18 Prover 10: Constructing countermodel ... % 18.26/3.19 Prover 0: proved (2521ms) % 18.26/3.19 % 18.26/3.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.26/3.19 % 18.26/3.21 Prover 9: Warning: ignoring some quantifiers % 18.26/3.21 Prover 2: stopped % 18.26/3.22 Prover 5: stopped % 18.26/3.22 Prover 9: Constructing countermodel ... % 18.26/3.22 Prover 9: stopped % 18.26/3.23 Prover 6: stopped % 18.26/3.23 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 18.26/3.23 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 18.26/3.23 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 18.26/3.23 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 18.75/3.24 Prover 11: Preprocessing ... % 18.75/3.25 Prover 16: Preprocessing ... % 18.75/3.25 Prover 19: Preprocessing ... % 18.75/3.25 Prover 13: Preprocessing ... % 19.24/3.31 Prover 16: Warning: ignoring some quantifiers % 19.24/3.31 Prover 10: gave up % 19.24/3.31 Prover 16: Constructing countermodel ... % 19.43/3.33 Prover 11: Warning: ignoring some quantifiers % 19.43/3.34 Prover 11: Constructing countermodel ... % 19.43/3.36 Prover 13: Warning: ignoring some quantifiers % 19.43/3.36 Prover 19: Warning: ignoring some quantifiers % 19.43/3.37 Prover 19: Constructing countermodel ... % 19.43/3.37 Prover 13: Constructing countermodel ... % 21.70/3.65 Prover 13: gave up % 23.39/3.87 Prover 4: Found proof (size 149) % 23.39/3.87 Prover 4: proved (3185ms) % 23.39/3.87 Prover 19: stopped % 23.39/3.87 Prover 16: stopped % 23.39/3.87 Prover 11: stopped % 23.39/3.87 % 23.39/3.87 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 23.39/3.87 % 23.39/3.88 % SZS output start Proof for theBenchmark % 23.39/3.88 Assumptions after simplification: % 23.39/3.88 --------------------------------- % 23.39/3.88 % 23.39/3.88 (antisymmetry_r2_hidden) % 23.39/3.91 ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 23.39/3.91 [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : ( % 23.39/3.91 ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 23.39/3.91 in(v1, v0) = v2)) % 23.39/3.91 % 23.39/3.91 (commutativity_k2_tarski) % 23.39/3.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | % 23.39/3.91 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & $i(v2))) & ! [v0: $i] % 23.39/3.91 : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | % 23.39/3.91 ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 23.39/3.91 % 23.39/3.91 (commutativity_k2_xboole_0) % 23.39/3.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 23.39/3.91 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 23.39/3.91 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 23.39/3.91 | (set_union2(v1, v0) = v2 & $i(v2))) % 23.39/3.91 % 23.39/3.91 (d1_zfmisc_1) % 23.39/3.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 23.39/3.92 (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 23.39/3.92 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0: $i] : ! % 23.39/3.92 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ % 23.39/3.92 (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ % 23.39/3.92 (v4 = 0) & subset(v2, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 23.39/3.92 : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | % 23.39/3.92 ~ $i(v0) | in(v2, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 23.39/3.92 (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 23.39/3.92 $i(v0) | subset(v2, v0) = 0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 % 23.39/3.92 = v0 | ~ (powerset(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 23.39/3.92 [v4: any] : ? [v5: any] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & $i(v3) & % 23.39/3.92 ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) % 23.39/3.92 % 23.39/3.92 (d2_tarski) % 23.39/3.92 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | % 23.39/3.92 ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 23.39/3.92 $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.39/3.92 ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v1, v2) = % 23.39/3.92 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! % 23.39/3.92 [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ % 23.39/3.92 (in(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ? [v0: $i] : ! % 23.39/3.92 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = % 23.39/3.92 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : % 23.39/3.92 (in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( ~ (v4 = v2) & ~ (v4 = v1))) & % 23.39/3.92 (v5 = 0 | v4 = v2 | v4 = v1))) % 23.39/3.92 % 23.39/3.92 (d2_xboole_0) % 23.39/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 23.39/3.93 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~ % 23.39/3.93 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) % 23.39/3.93 & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0: $i] : ! % 23.39/3.93 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 23.39/3.93 (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 23.39/3.93 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & % 23.39/3.93 in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : % 23.39/3.93 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (set_union2(v0, v1) = % 23.39/3.93 v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 23.39/3.93 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 % 23.39/3.93 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 23.39/3.93 $i] : ! [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | % 23.39/3.93 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 23.39/3.93 (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = % 23.39/3.93 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 23.39/3.93 [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | % 23.39/3.93 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, % 23.39/3.93 v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & % 23.39/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) % 23.39/3.93 = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 23.39/3.93 $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v1) = v5 & in(v3, v0) = v4 & % 23.39/3.93 (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 23.39/3.93 $i] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 23.39/3.93 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, % 23.39/3.93 v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( % 23.39/3.93 ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) % 23.39/3.93 % 23.39/3.93 (d2_zfmisc_1) % 23.39/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : ! [v5: % 23.39/3.93 $i] : ! [v6: $i] : (v4 = 0 | ~ (cartesian_product2(v0, v1) = v2) | ~ % 23.39/3.93 (ordered_pair(v5, v6) = v3) | ~ (in(v3, v2) = v4) | ~ $i(v6) | ~ $i(v5) | % 23.39/3.93 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ? [v8: any] % 23.39/3.93 : (in(v6, v1) = v8 & in(v5, v0) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! % 23.39/3.93 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 23.39/3.93 (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 23.39/3.93 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : % 23.39/3.93 (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0 & $i(v5) & % 23.39/3.93 $i(v4))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = % 23.39/3.93 v0 | ~ (cartesian_product2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 23.39/3.93 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: $i] : ? [v7: $i] : ? [v8: % 23.39/3.93 int] : ? [v9: int] : ? [v10: $i] : (in(v4, v0) = v5 & $i(v7) & $i(v6) & % 23.39/3.93 $i(v4) & ( ~ (v5 = 0) | ! [v11: $i] : ! [v12: $i] : ( ~ % 23.39/3.93 (ordered_pair(v11, v12) = v4) | ~ $i(v12) | ~ $i(v11) | ? [v13: % 23.39/3.93 any] : ? [v14: any] : (in(v12, v2) = v14 & in(v11, v1) = v13 & ( ~ % 23.39/3.93 (v14 = 0) | ~ (v13 = 0))))) & (v5 = 0 | (v10 = v4 & v9 = 0 & v8 = % 23.39/3.93 0 & ordered_pair(v6, v7) = v4 & in(v7, v2) = 0 & in(v6, v1) = 0)))) % 23.39/3.93 % 23.39/3.93 (d3_tarski) % 23.39/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 23.39/3.93 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 23.39/3.93 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 23.39/3.93 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 23.39/3.93 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 23.39/3.93 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 23.39/3.93 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 23.39/3.93 $i(v0) | in(v2, v1) = 0) % 23.39/3.93 % 23.39/3.93 (d5_tarski) % 23.39/3.93 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ % 23.39/3.93 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (singleton(v0) = v4 & % 23.39/3.93 unordered_pair(v3, v4) = v2 & unordered_pair(v0, v1) = v3 & $i(v4) & % 23.39/3.93 $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 23.39/3.93 (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 23.39/3.93 [v4: $i] : (singleton(v0) = v4 & ordered_pair(v0, v1) = v3 & % 23.39/3.93 unordered_pair(v2, v4) = v3 & $i(v4) & $i(v3))) % 23.39/3.93 % 23.39/3.93 (l2_zfmisc_1) % 23.39/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 23.39/3.94 (singleton(v0) = v2) | ~ (subset(v2, v1) = v3) | ~ $i(v1) | ~ $i(v0) | ? % 23.39/3.94 [v4: int] : ( ~ (v4 = 0) & in(v0, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : % 23.39/3.94 ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: % 23.39/3.94 $i] : ? [v4: int] : ( ~ (v4 = 0) & singleton(v0) = v3 & subset(v3, v1) = % 23.39/3.94 v4 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 23.39/3.94 (singleton(v0) = v2) | ~ (subset(v2, v1) = 0) | ~ $i(v1) | ~ $i(v0) | % 23.39/3.94 in(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ % 23.39/3.94 $i(v1) | ~ $i(v0) | ? [v2: $i] : (singleton(v0) = v2 & subset(v2, v1) = 0 % 23.39/3.94 & $i(v2))) % 23.39/3.94 % 23.39/3.94 (t105_zfmisc_1) % 23.39/3.94 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 23.39/3.94 $i] : ? [v6: int] : ( ~ (v6 = 0) & cartesian_product2(v0, v1) = v2 & % 23.39/3.94 powerset(v4) = v5 & powerset(v3) = v4 & subset(v2, v5) = v6 & set_union2(v0, % 23.39/3.94 v1) = v3 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 23.39/3.94 % 23.39/3.94 (t1_xboole_1) % 23.39/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 23.39/3.94 (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 23.39/3.94 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : % 23.39/3.94 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (subset(v0, v2) = v3) % 23.39/3.94 | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] % 23.39/3.94 : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 23.39/3.94 $i] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ % 23.39/3.94 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0) % 23.39/3.94 % 23.39/3.94 (t38_zfmisc_1) % 23.74/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 23.74/3.94 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) | ~ $i(v2) | % 23.74/3.94 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v1, v2) = v6 & % 23.74/3.94 in(v0, v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! [v1: % 23.75/3.94 $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (subset(v3, v2) = 0) | ~ % 23.75/3.94 (unordered_pair(v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v1, % 23.75/3.94 v2) = 0 & in(v0, v2) = 0)) % 23.75/3.94 % 23.75/3.94 (t7_xboole_1) % 23.75/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ % 23.75/3.94 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0) % 23.75/3.94 % 23.75/3.94 (function-axioms) % 23.75/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.75/3.94 (cartesian_product2(v3, v2) = v1) | ~ (cartesian_product2(v3, v2) = v0)) & % 23.75/3.94 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.75/3.94 (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & ! [v0: % 23.75/3.94 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 23.75/3.94 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 23.75/3.94 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 23.75/3.94 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: $i] : ! % 23.75/3.94 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = % 23.75/3.94 v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! % 23.75/3.94 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, % 23.75/3.94 v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: % 23.75/3.94 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (empty(v2) = v1) | ~ % 23.75/3.94 (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ % 23.75/3.94 (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] % 23.75/3.94 : ! [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 23.75/3.94 % 23.75/3.94 Further assumptions not needed in the proof: % 23.75/3.94 -------------------------------------------- % 23.75/3.94 fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, rc1_xboole_0, % 23.75/3.94 rc2_xboole_0, reflexivity_r1_tarski % 23.75/3.94 % 23.75/3.94 Those formulas are unsatisfiable: % 23.75/3.94 --------------------------------- % 23.75/3.94 % 23.75/3.94 Begin of proof % 23.75/3.95 | % 23.75/3.95 | ALPHA: (antisymmetry_r2_hidden) implies: % 23.75/3.95 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1) | ~ % 23.75/3.95 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & in(v0, v1) = v2)) % 23.75/3.95 | % 23.75/3.95 | ALPHA: (commutativity_k2_tarski) implies: % 23.75/3.95 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = % 23.75/3.95 | v2) | ~ $i(v1) | ~ $i(v0) | (unordered_pair(v0, v1) = v2 & % 23.75/3.95 | $i(v2))) % 23.75/3.95 | % 23.75/3.95 | ALPHA: (commutativity_k2_xboole_0) implies: % 23.75/3.95 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 23.75/3.95 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 23.75/3.95 | % 23.75/3.95 | ALPHA: (d1_zfmisc_1) implies: % 23.75/3.95 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v1) | ~ % 23.75/3.95 | (subset(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) % 23.75/3.95 | = 0) % 23.75/3.95 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 23.75/3.95 | (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 23.75/3.95 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) % 23.75/3.95 | % 23.75/3.95 | ALPHA: (d2_tarski) implies: % 23.75/3.95 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = % 23.75/3.95 | v0 | ~ (unordered_pair(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ % 23.75/3.95 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) % 23.75/3.95 | % 23.75/3.95 | ALPHA: (d2_xboole_0) implies: % 23.75/3.95 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 23.75/3.95 | ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ % 23.75/3.95 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 23.75/3.95 | (in(v3, v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 % 23.75/3.95 | = 0))))) % 23.75/3.95 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 23.75/3.95 | ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 23.75/3.95 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 23.75/3.95 | (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 % 23.75/3.95 | = 0))))) % 23.75/3.95 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 23.75/3.95 | (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ % 23.75/3.95 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: % 23.75/3.95 | any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | v6 = % 23.75/3.95 | 0))) % 23.75/3.95 | % 23.75/3.95 | ALPHA: (d2_zfmisc_1) implies: % 23.75/3.96 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 23.75/3.96 | (cartesian_product2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) % 23.75/3.96 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : % 23.75/3.96 | (ordered_pair(v4, v5) = v3 & in(v5, v1) = 0 & in(v4, v0) = 0 & % 23.75/3.96 | $i(v5) & $i(v4))) % 23.75/3.96 | % 23.75/3.96 | ALPHA: (d3_tarski) implies: % 23.75/3.96 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, % 23.75/3.96 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : % 23.75/3.96 | ( ~ (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 23.75/3.96 | % 23.75/3.96 | ALPHA: (d5_tarski) implies: % 23.75/3.96 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = % 23.75/3.96 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 23.75/3.96 | (singleton(v0) = v4 & unordered_pair(v3, v4) = v2 & % 23.75/3.96 | unordered_pair(v0, v1) = v3 & $i(v4) & $i(v3) & $i(v2))) % 23.75/3.96 | % 23.75/3.96 | ALPHA: (l2_zfmisc_1) implies: % 23.75/3.96 | (13) ! [v0: $i] : ! [v1: $i] : ( ~ (in(v0, v1) = 0) | ~ $i(v1) | ~ % 23.75/3.96 | $i(v0) | ? [v2: $i] : (singleton(v0) = v2 & subset(v2, v1) = 0 & % 23.75/3.96 | $i(v2))) % 23.75/3.96 | % 23.75/3.96 | ALPHA: (t1_xboole_1) implies: % 23.75/3.96 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 23.75/3.96 | (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ~ $i(v2) | ~ % 23.75/3.96 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = % 23.75/3.96 | v4)) % 23.75/3.96 | % 23.75/3.96 | ALPHA: (t38_zfmisc_1) implies: % 23.75/3.96 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 23.75/3.96 | (v4 = 0 | ~ (subset(v3, v2) = v4) | ~ (unordered_pair(v0, v1) = v3) % 23.75/3.96 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 23.75/3.96 | (in(v1, v2) = v6 & in(v0, v2) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) % 23.75/3.96 | % 23.75/3.96 | ALPHA: (function-axioms) implies: % 23.75/3.96 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) % 23.75/3.96 | = v1) | ~ (singleton(v2) = v0)) % 23.75/3.96 | (17) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 23.75/3.96 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 23.75/3.96 | v0)) % 23.75/3.96 | (18) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 23.75/3.96 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, % 23.75/3.96 | v2) = v0)) % 23.75/3.96 | % 23.75/3.96 | DELTA: instantiating (t105_zfmisc_1) with fresh symbols all_27_0, all_27_1, % 23.75/3.96 | all_27_2, all_27_3, all_27_4, all_27_5, all_27_6 gives: % 23.75/3.96 | (19) ~ (all_27_0 = 0) & cartesian_product2(all_27_6, all_27_5) = all_27_4 % 23.75/3.96 | & powerset(all_27_2) = all_27_1 & powerset(all_27_3) = all_27_2 & % 23.75/3.96 | subset(all_27_4, all_27_1) = all_27_0 & set_union2(all_27_6, all_27_5) % 23.75/3.96 | = all_27_3 & $i(all_27_1) & $i(all_27_2) & $i(all_27_3) & $i(all_27_4) % 23.75/3.96 | & $i(all_27_5) & $i(all_27_6) % 23.75/3.96 | % 23.75/3.96 | ALPHA: (19) implies: % 23.75/3.96 | (20) ~ (all_27_0 = 0) % 23.75/3.96 | (21) $i(all_27_6) % 23.75/3.96 | (22) $i(all_27_5) % 23.75/3.96 | (23) $i(all_27_4) % 23.75/3.96 | (24) $i(all_27_2) % 23.75/3.96 | (25) $i(all_27_1) % 23.75/3.96 | (26) set_union2(all_27_6, all_27_5) = all_27_3 % 23.75/3.96 | (27) subset(all_27_4, all_27_1) = all_27_0 % 23.75/3.96 | (28) powerset(all_27_3) = all_27_2 % 23.75/3.97 | (29) powerset(all_27_2) = all_27_1 % 23.75/3.97 | (30) cartesian_product2(all_27_6, all_27_5) = all_27_4 % 23.75/3.97 | % 23.75/3.97 | GROUND_INST: instantiating (3) with all_27_5, all_27_6, all_27_3, simplifying % 23.75/3.97 | with (21), (22), (26) gives: % 23.75/3.97 | (31) set_union2(all_27_5, all_27_6) = all_27_3 & $i(all_27_3) % 23.75/3.97 | % 23.75/3.97 | ALPHA: (31) implies: % 23.75/3.97 | (32) $i(all_27_3) % 23.75/3.97 | (33) set_union2(all_27_5, all_27_6) = all_27_3 % 23.75/3.97 | % 23.75/3.97 | GROUND_INST: instantiating (t7_xboole_1) with all_27_6, all_27_5, all_27_3, % 23.75/3.97 | simplifying with (21), (22), (26) gives: % 23.75/3.97 | (34) subset(all_27_6, all_27_3) = 0 % 23.75/3.97 | % 23.75/3.97 | GROUND_INST: instantiating (11) with all_27_4, all_27_1, all_27_0, simplifying % 23.75/3.97 | with (23), (25), (27) gives: % 23.75/3.97 | (35) all_27_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 23.75/3.97 | all_27_1) = v1 & in(v0, all_27_4) = 0 & $i(v0)) % 23.75/3.97 | % 23.75/3.97 | BETA: splitting (35) gives: % 23.75/3.97 | % 23.75/3.97 | Case 1: % 23.75/3.97 | | % 23.75/3.97 | | (36) all_27_0 = 0 % 23.75/3.97 | | % 23.75/3.97 | | REDUCE: (20), (36) imply: % 23.75/3.97 | | (37) $false % 23.75/3.97 | | % 23.75/3.97 | | CLOSE: (37) is inconsistent. % 23.75/3.97 | | % 23.75/3.97 | Case 2: % 23.75/3.97 | | % 23.75/3.97 | | (38) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_27_1) = v1 & % 23.75/3.97 | | in(v0, all_27_4) = 0 & $i(v0)) % 23.75/3.97 | | % 23.75/3.97 | | DELTA: instantiating (38) with fresh symbols all_49_0, all_49_1 gives: % 23.75/3.97 | | (39) ~ (all_49_0 = 0) & in(all_49_1, all_27_1) = all_49_0 & in(all_49_1, % 23.75/3.97 | | all_27_4) = 0 & $i(all_49_1) % 23.75/3.97 | | % 23.75/3.97 | | ALPHA: (39) implies: % 23.75/3.97 | | (40) ~ (all_49_0 = 0) % 23.75/3.97 | | (41) $i(all_49_1) % 23.75/3.97 | | (42) in(all_49_1, all_27_4) = 0 % 23.75/3.97 | | (43) in(all_49_1, all_27_1) = all_49_0 % 23.75/3.97 | | % 23.75/3.97 | | GROUND_INST: instantiating (10) with all_27_6, all_27_5, all_27_4, all_49_1, % 23.75/3.97 | | simplifying with (21), (22), (23), (30), (41), (42) gives: % 23.75/3.97 | | (44) ? [v0: $i] : ? [v1: $i] : (ordered_pair(v0, v1) = all_49_1 & % 23.75/3.97 | | in(v1, all_27_5) = 0 & in(v0, all_27_6) = 0 & $i(v1) & $i(v0)) % 23.75/3.97 | | % 23.75/3.97 | | GROUND_INST: instantiating (5) with all_27_2, all_27_1, all_49_1, all_49_0, % 23.75/3.97 | | simplifying with (24), (25), (29), (41), (43) gives: % 23.75/3.97 | | (45) all_49_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_49_1, % 23.75/3.97 | | all_27_2) = v0) % 23.75/3.97 | | % 23.75/3.97 | | GROUND_INST: instantiating (t7_xboole_1) with all_27_5, all_27_6, all_27_3, % 23.75/3.97 | | simplifying with (21), (22), (33) gives: % 23.75/3.97 | | (46) subset(all_27_5, all_27_3) = 0 % 23.75/3.97 | | % 23.75/3.97 | | GROUND_INST: instantiating (4) with all_27_3, all_27_2, all_27_6, % 23.75/3.97 | | simplifying with (21), (24), (28), (32), (34) gives: % 23.75/3.97 | | (47) in(all_27_6, all_27_2) = 0 % 23.75/3.97 | | % 23.75/3.97 | | DELTA: instantiating (44) with fresh symbols all_69_0, all_69_1 gives: % 23.75/3.98 | | (48) ordered_pair(all_69_1, all_69_0) = all_49_1 & in(all_69_0, all_27_5) % 23.75/3.98 | | = 0 & in(all_69_1, all_27_6) = 0 & $i(all_69_0) & $i(all_69_1) % 23.75/3.98 | | % 23.75/3.98 | | ALPHA: (48) implies: % 23.75/3.98 | | (49) $i(all_69_1) % 23.75/3.98 | | (50) $i(all_69_0) % 23.75/3.98 | | (51) in(all_69_1, all_27_6) = 0 % 23.75/3.98 | | (52) in(all_69_0, all_27_5) = 0 % 23.75/3.98 | | (53) ordered_pair(all_69_1, all_69_0) = all_49_1 % 23.75/3.98 | | % 23.75/3.98 | | BETA: splitting (45) gives: % 23.75/3.98 | | % 23.75/3.98 | | Case 1: % 23.75/3.98 | | | % 23.75/3.98 | | | (54) all_49_0 = 0 % 23.75/3.98 | | | % 23.75/3.98 | | | REDUCE: (40), (54) imply: % 23.75/3.98 | | | (55) $false % 23.75/3.98 | | | % 23.75/3.98 | | | CLOSE: (55) is inconsistent. % 23.75/3.98 | | | % 23.75/3.98 | | Case 2: % 23.75/3.98 | | | % 23.75/3.98 | | | (56) ? [v0: int] : ( ~ (v0 = 0) & subset(all_49_1, all_27_2) = v0) % 23.75/3.98 | | | % 23.75/3.98 | | | DELTA: instantiating (56) with fresh symbol all_80_0 gives: % 23.75/3.98 | | | (57) ~ (all_80_0 = 0) & subset(all_49_1, all_27_2) = all_80_0 % 23.75/3.98 | | | % 23.75/3.98 | | | ALPHA: (57) implies: % 23.75/3.98 | | | (58) ~ (all_80_0 = 0) % 23.75/3.98 | | | (59) subset(all_49_1, all_27_2) = all_80_0 % 23.75/3.98 | | | % 23.75/3.98 | | | GROUND_INST: instantiating (1) with all_27_2, all_27_6, simplifying with % 23.75/3.98 | | | (21), (24), (47) gives: % 23.75/3.98 | | | (60) ? [v0: int] : ( ~ (v0 = 0) & in(all_27_2, all_27_6) = v0) % 23.75/3.98 | | | % 23.75/3.98 | | | GROUND_INST: instantiating (7) with all_27_6, all_27_5, all_27_3, % 23.75/3.98 | | | all_69_1, 0, simplifying with (21), (22), (26), (32), (49), % 23.75/3.98 | | | (51) gives: % 23.75/3.98 | | | (61) ? [v0: MultipleValueBool] : (in(all_69_1, all_27_3) = 0 & % 23.75/3.98 | | | in(all_69_1, all_27_5) = v0) % 23.75/3.98 | | | % 23.75/3.98 | | | GROUND_INST: instantiating (13) with all_69_1, all_27_6, simplifying with % 23.75/3.98 | | | (21), (49), (51) gives: % 23.75/3.98 | | | (62) ? [v0: $i] : (singleton(all_69_1) = v0 & subset(v0, all_27_6) = 0 % 23.75/3.98 | | | & $i(v0)) % 23.75/3.98 | | | % 23.75/3.98 | | | GROUND_INST: instantiating (8) with all_27_6, all_27_5, all_27_3, % 23.75/3.98 | | | all_69_0, 0, simplifying with (21), (22), (26), (32), (50), % 23.75/3.98 | | | (52) gives: % 23.75/3.98 | | | (63) ? [v0: MultipleValueBool] : (in(all_69_0, all_27_3) = 0 & % 23.75/3.98 | | | in(all_69_0, all_27_6) = v0) % 23.75/3.98 | | | % 23.75/3.98 | | | GROUND_INST: instantiating (4) with all_27_3, all_27_2, all_27_5, % 23.75/3.98 | | | simplifying with (22), (24), (28), (32), (46) gives: % 23.75/3.98 | | | (64) in(all_27_5, all_27_2) = 0 % 23.75/3.98 | | | % 23.75/3.98 | | | GROUND_INST: instantiating (11) with all_49_1, all_27_2, all_80_0, % 23.75/3.98 | | | simplifying with (24), (41), (59) gives: % 23.75/3.98 | | | (65) all_80_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 23.75/3.98 | | | all_49_1) = 0 & in(v0, all_27_2) = v1 & $i(v0)) % 23.75/3.98 | | | % 23.75/3.98 | | | GROUND_INST: instantiating (12) with all_69_1, all_69_0, all_49_1, % 23.75/3.98 | | | simplifying with (49), (50), (53) gives: % 23.75/3.98 | | | (66) ? [v0: $i] : ? [v1: $i] : (singleton(all_69_1) = v1 & % 23.75/3.98 | | | unordered_pair(v0, v1) = all_49_1 & unordered_pair(all_69_1, % 23.75/3.98 | | | all_69_0) = v0 & $i(v1) & $i(v0) & $i(all_49_1)) % 23.75/3.98 | | | % 23.75/3.98 | | | DELTA: instantiating (63) with fresh symbol all_94_0 gives: % 23.75/3.98 | | | (67) in(all_69_0, all_27_3) = 0 & in(all_69_0, all_27_6) = all_94_0 % 23.75/3.98 | | | % 23.75/3.98 | | | ALPHA: (67) implies: % 23.75/3.98 | | | (68) in(all_69_0, all_27_3) = 0 % 23.75/3.98 | | | % 23.75/3.98 | | | DELTA: instantiating (61) with fresh symbol all_100_0 gives: % 23.75/3.98 | | | (69) in(all_69_1, all_27_3) = 0 & in(all_69_1, all_27_5) = all_100_0 % 23.75/3.98 | | | % 23.75/3.98 | | | ALPHA: (69) implies: % 23.75/3.98 | | | (70) in(all_69_1, all_27_3) = 0 % 23.75/3.98 | | | % 23.75/3.98 | | | DELTA: instantiating (60) with fresh symbol all_102_0 gives: % 23.75/3.98 | | | (71) ~ (all_102_0 = 0) & in(all_27_2, all_27_6) = all_102_0 % 23.75/3.98 | | | % 23.75/3.98 | | | ALPHA: (71) implies: % 23.75/3.98 | | | (72) ~ (all_102_0 = 0) % 23.75/3.98 | | | (73) in(all_27_2, all_27_6) = all_102_0 % 23.75/3.98 | | | % 23.75/3.98 | | | DELTA: instantiating (62) with fresh symbol all_106_0 gives: % 23.75/3.98 | | | (74) singleton(all_69_1) = all_106_0 & subset(all_106_0, all_27_6) = 0 % 23.75/3.98 | | | & $i(all_106_0) % 23.75/3.98 | | | % 23.75/3.98 | | | ALPHA: (74) implies: % 23.75/3.98 | | | (75) singleton(all_69_1) = all_106_0 % 23.75/3.98 | | | % 23.75/3.98 | | | DELTA: instantiating (66) with fresh symbols all_110_0, all_110_1 gives: % 23.75/3.98 | | | (76) singleton(all_69_1) = all_110_0 & unordered_pair(all_110_1, % 23.75/3.98 | | | all_110_0) = all_49_1 & unordered_pair(all_69_1, all_69_0) = % 23.75/3.98 | | | all_110_1 & $i(all_110_0) & $i(all_110_1) & $i(all_49_1) % 23.75/3.98 | | | % 23.75/3.98 | | | ALPHA: (76) implies: % 23.75/3.98 | | | (77) $i(all_110_0) % 23.75/3.98 | | | (78) unordered_pair(all_69_1, all_69_0) = all_110_1 % 23.75/3.98 | | | (79) unordered_pair(all_110_1, all_110_0) = all_49_1 % 23.75/3.98 | | | (80) singleton(all_69_1) = all_110_0 % 23.75/3.98 | | | % 23.75/3.98 | | | BETA: splitting (65) gives: % 23.75/3.98 | | | % 23.75/3.98 | | | Case 1: % 23.75/3.98 | | | | % 23.75/3.98 | | | | (81) all_80_0 = 0 % 23.75/3.98 | | | | % 23.75/3.98 | | | | REDUCE: (58), (81) imply: % 23.75/3.98 | | | | (82) $false % 23.75/3.98 | | | | % 23.75/3.98 | | | | CLOSE: (82) is inconsistent. % 23.75/3.98 | | | | % 23.75/3.98 | | | Case 2: % 23.75/3.98 | | | | % 23.75/3.98 | | | | (83) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_49_1) = 0 % 23.75/3.98 | | | | & in(v0, all_27_2) = v1 & $i(v0)) % 23.75/3.98 | | | | % 23.75/3.98 | | | | DELTA: instantiating (83) with fresh symbols all_126_0, all_126_1 gives: % 23.75/3.98 | | | | (84) ~ (all_126_0 = 0) & in(all_126_1, all_49_1) = 0 & in(all_126_1, % 23.75/3.98 | | | | all_27_2) = all_126_0 & $i(all_126_1) % 23.75/3.98 | | | | % 23.75/3.98 | | | | ALPHA: (84) implies: % 23.75/3.99 | | | | (85) ~ (all_126_0 = 0) % 23.75/3.99 | | | | (86) $i(all_126_1) % 23.75/3.99 | | | | (87) in(all_126_1, all_27_2) = all_126_0 % 23.75/3.99 | | | | (88) in(all_126_1, all_49_1) = 0 % 23.75/3.99 | | | | % 23.75/3.99 | | | | GROUND_INST: instantiating (16) with all_106_0, all_110_0, all_69_1, % 23.75/3.99 | | | | simplifying with (75), (80) gives: % 23.75/3.99 | | | | (89) all_110_0 = all_106_0 % 23.75/3.99 | | | | % 23.75/3.99 | | | | REDUCE: (79), (89) imply: % 23.75/3.99 | | | | (90) unordered_pair(all_110_1, all_106_0) = all_49_1 % 23.75/3.99 | | | | % 23.75/3.99 | | | | REDUCE: (77), (89) imply: % 23.75/3.99 | | | | (91) $i(all_106_0) % 23.75/3.99 | | | | % 23.75/3.99 | | | | GROUND_INST: instantiating (1) with all_27_2, all_27_5, simplifying with % 23.75/3.99 | | | | (22), (24), (64) gives: % 23.75/3.99 | | | | (92) ? [v0: int] : ( ~ (v0 = 0) & in(all_27_2, all_27_5) = v0) % 23.75/3.99 | | | | % 23.75/3.99 | | | | GROUND_INST: instantiating (9) with all_27_6, all_27_5, all_27_3, % 23.75/3.99 | | | | all_27_2, all_102_0, simplifying with (21), (22), (24), % 23.75/3.99 | | | | (26), (32), (73) gives: % 23.75/3.99 | | | | (93) all_102_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_27_2, % 23.75/3.99 | | | | all_27_3) = v0 & in(all_27_2, all_27_5) = v1 & ( ~ (v0 = 0) % 23.75/3.99 | | | | | v1 = 0)) % 23.75/3.99 | | | | % 23.75/3.99 | | | | GROUND_INST: instantiating (7) with all_27_6, all_27_5, all_27_3, % 23.75/3.99 | | | | all_27_2, all_102_0, simplifying with (21), (22), (24), % 23.75/3.99 | | | | (26), (32), (73) gives: % 23.75/3.99 | | | | (94) ? [v0: any] : ? [v1: any] : (in(all_27_2, all_27_3) = v1 & % 23.75/3.99 | | | | in(all_27_2, all_27_5) = v0 & (v1 = 0 | ( ~ (v0 = 0) & ~ % 23.75/3.99 | | | | (all_102_0 = 0)))) % 23.75/3.99 | | | | % 23.75/3.99 | | | | GROUND_INST: instantiating (13) with all_69_1, all_27_3, simplifying % 23.75/3.99 | | | | with (32), (49), (70) gives: % 23.75/3.99 | | | | (95) ? [v0: $i] : (singleton(all_69_1) = v0 & subset(v0, all_27_3) = % 23.75/3.99 | | | | 0 & $i(v0)) % 23.75/3.99 | | | | % 23.75/3.99 | | | | GROUND_INST: instantiating (5) with all_27_3, all_27_2, all_126_1, % 23.75/3.99 | | | | all_126_0, simplifying with (24), (28), (32), (86), (87) % 23.75/3.99 | | | | gives: % 23.75/3.99 | | | | (96) all_126_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_126_1, % 23.75/3.99 | | | | all_27_3) = v0) % 23.75/3.99 | | | | % 23.75/3.99 | | | | GROUND_INST: instantiating (2) with all_69_0, all_69_1, all_110_1, % 23.75/3.99 | | | | simplifying with (49), (50), (78) gives: % 23.75/3.99 | | | | (97) unordered_pair(all_69_0, all_69_1) = all_110_1 & $i(all_110_1) % 23.75/3.99 | | | | % 23.75/3.99 | | | | ALPHA: (97) implies: % 23.75/3.99 | | | | (98) $i(all_110_1) % 23.75/3.99 | | | | % 23.75/3.99 | | | | GROUND_INST: instantiating (15) with all_110_1, all_106_0, all_27_2, % 23.75/3.99 | | | | all_49_1, all_80_0, simplifying with (24), (59), (90), % 23.75/3.99 | | | | (91), (98) gives: % 23.75/3.99 | | | | (99) all_80_0 = 0 | ? [v0: any] : ? [v1: any] : (in(all_110_1, % 23.75/3.99 | | | | all_27_2) = v0 & in(all_106_0, all_27_2) = v1 & ( ~ (v1 = 0) % 23.75/3.99 | | | | | ~ (v0 = 0))) % 23.75/3.99 | | | | % 23.75/3.99 | | | | GROUND_INST: instantiating (2) with all_106_0, all_110_1, all_49_1, % 23.75/3.99 | | | | simplifying with (90), (91), (98) gives: % 23.75/3.99 | | | | (100) unordered_pair(all_106_0, all_110_1) = all_49_1 & $i(all_49_1) % 23.75/3.99 | | | | % 23.75/3.99 | | | | ALPHA: (100) implies: % 23.75/3.99 | | | | (101) unordered_pair(all_106_0, all_110_1) = all_49_1 % 23.75/3.99 | | | | % 23.75/3.99 | | | | DELTA: instantiating (92) with fresh symbol all_140_0 gives: % 23.75/3.99 | | | | (102) ~ (all_140_0 = 0) & in(all_27_2, all_27_5) = all_140_0 % 23.75/3.99 | | | | % 23.75/3.99 | | | | ALPHA: (102) implies: % 23.75/3.99 | | | | (103) ~ (all_140_0 = 0) % 23.75/3.99 | | | | (104) in(all_27_2, all_27_5) = all_140_0 % 23.75/3.99 | | | | % 23.75/3.99 | | | | DELTA: instantiating (95) with fresh symbol all_150_0 gives: % 23.75/3.99 | | | | (105) singleton(all_69_1) = all_150_0 & subset(all_150_0, all_27_3) = % 23.75/3.99 | | | | 0 & $i(all_150_0) % 23.75/3.99 | | | | % 23.75/3.99 | | | | ALPHA: (105) implies: % 23.75/3.99 | | | | (106) $i(all_150_0) % 23.75/3.99 | | | | (107) subset(all_150_0, all_27_3) = 0 % 23.75/3.99 | | | | (108) singleton(all_69_1) = all_150_0 % 23.75/3.99 | | | | % 23.75/3.99 | | | | DELTA: instantiating (94) with fresh symbols all_166_0, all_166_1 gives: % 23.75/3.99 | | | | (109) in(all_27_2, all_27_3) = all_166_0 & in(all_27_2, all_27_5) = % 23.75/3.99 | | | | all_166_1 & (all_166_0 = 0 | ( ~ (all_166_1 = 0) & ~ % 23.75/3.99 | | | | (all_102_0 = 0))) % 23.75/3.99 | | | | % 23.75/3.99 | | | | ALPHA: (109) implies: % 23.75/3.99 | | | | (110) in(all_27_2, all_27_5) = all_166_1 % 23.75/3.99 | | | | % 23.75/3.99 | | | | BETA: splitting (96) gives: % 23.75/3.99 | | | | % 23.75/3.99 | | | | Case 1: % 23.75/3.99 | | | | | % 23.75/3.99 | | | | | (111) all_126_0 = 0 % 23.75/3.99 | | | | | % 23.75/3.99 | | | | | REDUCE: (85), (111) imply: % 23.75/3.99 | | | | | (112) $false % 23.75/3.99 | | | | | % 23.75/3.99 | | | | | CLOSE: (112) is inconsistent. % 23.75/3.99 | | | | | % 23.75/3.99 | | | | Case 2: % 23.75/3.99 | | | | | % 23.75/3.99 | | | | | (113) ? [v0: int] : ( ~ (v0 = 0) & subset(all_126_1, all_27_3) = % 23.75/3.99 | | | | | v0) % 23.75/3.99 | | | | | % 23.75/3.99 | | | | | DELTA: instantiating (113) with fresh symbol all_214_0 gives: % 23.75/3.99 | | | | | (114) ~ (all_214_0 = 0) & subset(all_126_1, all_27_3) = all_214_0 % 23.75/3.99 | | | | | % 23.75/3.99 | | | | | ALPHA: (114) implies: % 23.75/3.99 | | | | | (115) ~ (all_214_0 = 0) % 23.75/3.99 | | | | | (116) subset(all_126_1, all_27_3) = all_214_0 % 23.75/3.99 | | | | | % 23.75/3.99 | | | | | BETA: splitting (99) gives: % 23.75/3.99 | | | | | % 23.75/3.99 | | | | | Case 1: % 23.75/3.99 | | | | | | % 23.75/3.99 | | | | | | (117) all_80_0 = 0 % 23.75/3.99 | | | | | | % 23.75/3.99 | | | | | | REDUCE: (58), (117) imply: % 23.75/3.99 | | | | | | (118) $false % 23.75/3.99 | | | | | | % 23.75/3.99 | | | | | | CLOSE: (118) is inconsistent. % 23.75/3.99 | | | | | | % 23.75/3.99 | | | | | Case 2: % 23.75/3.99 | | | | | | % 23.75/3.99 | | | | | | (119) ? [v0: any] : ? [v1: any] : (in(all_110_1, all_27_2) = v0 % 23.75/3.99 | | | | | | & in(all_106_0, all_27_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = % 23.75/3.99 | | | | | | 0))) % 23.75/3.99 | | | | | | % 23.75/3.99 | | | | | | DELTA: instantiating (119) with fresh symbols all_229_0, all_229_1 % 23.75/3.99 | | | | | | gives: % 23.75/3.99 | | | | | | (120) in(all_110_1, all_27_2) = all_229_1 & in(all_106_0, % 23.75/3.99 | | | | | | all_27_2) = all_229_0 & ( ~ (all_229_0 = 0) | ~ % 23.75/3.99 | | | | | | (all_229_1 = 0)) % 23.75/3.99 | | | | | | % 23.75/3.99 | | | | | | ALPHA: (120) implies: % 23.75/3.99 | | | | | | (121) in(all_106_0, all_27_2) = all_229_0 % 23.75/3.99 | | | | | | (122) in(all_110_1, all_27_2) = all_229_1 % 23.75/3.99 | | | | | | (123) ~ (all_229_0 = 0) | ~ (all_229_1 = 0) % 23.75/3.99 | | | | | | % 23.75/3.99 | | | | | | GROUND_INST: instantiating (17) with all_140_0, all_166_1, all_27_5, % 23.75/3.99 | | | | | | all_27_2, simplifying with (104), (110) gives: % 23.75/3.99 | | | | | | (124) all_166_1 = all_140_0 % 23.75/3.99 | | | | | | % 23.75/4.00 | | | | | | GROUND_INST: instantiating (16) with all_106_0, all_150_0, all_69_1, % 23.75/4.00 | | | | | | simplifying with (75), (108) gives: % 23.75/4.00 | | | | | | (125) all_150_0 = all_106_0 % 23.75/4.00 | | | | | | % 23.75/4.00 | | | | | | REDUCE: (107), (125) imply: % 23.75/4.00 | | | | | | (126) subset(all_106_0, all_27_3) = 0 % 23.75/4.00 | | | | | | % 23.75/4.00 | | | | | | BETA: splitting (93) gives: % 23.75/4.00 | | | | | | % 23.75/4.00 | | | | | | Case 1: % 23.75/4.00 | | | | | | | % 23.75/4.00 | | | | | | | (127) all_102_0 = 0 % 23.75/4.00 | | | | | | | % 23.75/4.00 | | | | | | | REDUCE: (72), (127) imply: % 23.75/4.00 | | | | | | | (128) $false % 23.75/4.00 | | | | | | | % 23.75/4.00 | | | | | | | CLOSE: (128) is inconsistent. % 23.75/4.00 | | | | | | | % 23.75/4.00 | | | | | | Case 2: % 23.75/4.00 | | | | | | | % 23.75/4.00 | | | | | | | (129) ? [v0: any] : ? [v1: any] : (in(all_27_2, all_27_3) = % 23.75/4.00 | | | | | | | v0 & in(all_27_2, all_27_5) = v1 & ( ~ (v0 = 0) | v1 = % 23.75/4.00 | | | | | | | 0)) % 23.75/4.00 | | | | | | | % 23.75/4.00 | | | | | | | DELTA: instantiating (129) with fresh symbols all_239_0, all_239_1 % 23.75/4.00 | | | | | | | gives: % 23.75/4.00 | | | | | | | (130) in(all_27_2, all_27_3) = all_239_1 & in(all_27_2, % 23.75/4.00 | | | | | | | all_27_5) = all_239_0 & ( ~ (all_239_1 = 0) | all_239_0 % 23.75/4.00 | | | | | | | = 0) % 23.75/4.00 | | | | | | | % 23.75/4.00 | | | | | | | ALPHA: (130) implies: % 23.75/4.00 | | | | | | | (131) in(all_27_2, all_27_5) = all_239_0 % 23.75/4.00 | | | | | | | (132) ~ (all_239_1 = 0) | all_239_0 = 0 % 23.75/4.00 | | | | | | | % 23.75/4.00 | | | | | | | GROUND_INST: instantiating (17) with all_140_0, all_239_0, % 23.75/4.00 | | | | | | | all_27_5, all_27_2, simplifying with (104), (131) % 23.75/4.00 | | | | | | | gives: % 23.75/4.00 | | | | | | | (133) all_239_0 = all_140_0 % 23.75/4.00 | | | | | | | % 23.75/4.00 | | | | | | | BETA: splitting (132) gives: % 23.75/4.00 | | | | | | | % 23.75/4.00 | | | | | | | Case 1: % 23.75/4.00 | | | | | | | | % 23.75/4.00 | | | | | | | | % 23.75/4.00 | | | | | | | | GROUND_INST: instantiating (5) with all_27_3, all_27_2, % 23.75/4.00 | | | | | | | | all_110_1, all_229_1, simplifying with (24), (28), % 23.75/4.00 | | | | | | | | (32), (98), (122) gives: % 23.75/4.00 | | | | | | | | (134) all_229_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 23.75/4.00 | | | | | | | | subset(all_110_1, all_27_3) = v0) % 23.75/4.00 | | | | | | | | % 23.75/4.00 | | | | | | | | GROUND_INST: instantiating (6) with all_106_0, all_110_1, % 23.75/4.00 | | | | | | | | all_49_1, all_126_1, simplifying with (41), (86), % 23.75/4.00 | | | | | | | | (88), (91), (98), (101) gives: % 24.03/4.00 | | | | | | | | (135) all_126_1 = all_110_1 | all_126_1 = all_106_0 % 24.03/4.00 | | | | | | | | % 24.03/4.00 | | | | | | | | GROUND_INST: instantiating (4) with all_27_3, all_27_2, % 24.03/4.00 | | | | | | | | all_106_0, simplifying with (24), (28), (32), (91), % 24.03/4.00 | | | | | | | | (126) gives: % 24.03/4.00 | | | | | | | | (136) in(all_106_0, all_27_2) = 0 % 24.03/4.00 | | | | | | | | % 24.03/4.00 | | | | | | | | GROUND_INST: instantiating (14) with all_126_1, all_27_5, % 24.03/4.00 | | | | | | | | all_27_3, all_214_0, simplifying with (22), (32), % 24.03/4.00 | | | | | | | | (46), (86), (116) gives: % 24.03/4.00 | | | | | | | | (137) all_214_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & % 24.03/4.00 | | | | | | | | subset(all_126_1, all_27_5) = v0) % 24.03/4.00 | | | | | | | | % 24.03/4.00 | | | | | | | | BETA: splitting (137) gives: % 24.03/4.00 | | | | | | | | % 24.03/4.00 | | | | | | | | Case 1: % 24.03/4.00 | | | | | | | | | % 24.03/4.00 | | | | | | | | | (138) all_214_0 = 0 % 24.03/4.00 | | | | | | | | | % 24.03/4.00 | | | | | | | | | REDUCE: (115), (138) imply: % 24.03/4.00 | | | | | | | | | (139) $false % 24.03/4.00 | | | | | | | | | % 24.03/4.00 | | | | | | | | | CLOSE: (139) is inconsistent. % 24.03/4.00 | | | | | | | | | % 24.03/4.00 | | | | | | | | Case 2: % 24.03/4.00 | | | | | | | | | % 24.03/4.00 | | | | | | | | | % 24.03/4.00 | | | | | | | | | GROUND_INST: instantiating (17) with all_229_0, 0, all_27_2, % 24.03/4.00 | | | | | | | | | all_106_0, simplifying with (121), (136) gives: % 24.03/4.00 | | | | | | | | | (140) all_229_0 = 0 % 24.03/4.00 | | | | | | | | | % 24.03/4.00 | | | | | | | | | BETA: splitting (123) gives: % 24.03/4.00 | | | | | | | | | % 24.03/4.00 | | | | | | | | | Case 1: % 24.03/4.00 | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | (141) ~ (all_229_0 = 0) % 24.03/4.00 | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | REDUCE: (140), (141) imply: % 24.03/4.00 | | | | | | | | | | (142) $false % 24.03/4.00 | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | CLOSE: (142) is inconsistent. % 24.03/4.00 | | | | | | | | | | % 24.03/4.00 | | | | | | | | | Case 2: % 24.03/4.00 | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | (143) ~ (all_229_1 = 0) % 24.03/4.00 | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | BETA: splitting (134) gives: % 24.03/4.00 | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | Case 1: % 24.03/4.00 | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | (144) all_229_1 = 0 % 24.03/4.00 | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | REDUCE: (143), (144) imply: % 24.03/4.00 | | | | | | | | | | | (145) $false % 24.03/4.00 | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | CLOSE: (145) is inconsistent. % 24.03/4.00 | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | Case 2: % 24.03/4.00 | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | (146) ? [v0: int] : ( ~ (v0 = 0) & subset(all_110_1, % 24.03/4.00 | | | | | | | | | | | all_27_3) = v0) % 24.03/4.00 | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | DELTA: instantiating (146) with fresh symbol all_485_0 % 24.03/4.00 | | | | | | | | | | | gives: % 24.03/4.00 | | | | | | | | | | | (147) ~ (all_485_0 = 0) & subset(all_110_1, all_27_3) = % 24.03/4.00 | | | | | | | | | | | all_485_0 % 24.03/4.00 | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | ALPHA: (147) implies: % 24.03/4.00 | | | | | | | | | | | (148) ~ (all_485_0 = 0) % 24.03/4.00 | | | | | | | | | | | (149) subset(all_110_1, all_27_3) = all_485_0 % 24.03/4.00 | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | BETA: splitting (135) gives: % 24.03/4.00 | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | Case 1: % 24.03/4.00 | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | (150) all_126_1 = all_110_1 % 24.03/4.00 | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | REDUCE: (116), (150) imply: % 24.03/4.00 | | | | | | | | | | | | (151) subset(all_110_1, all_27_3) = all_214_0 % 24.03/4.00 | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | GROUND_INST: instantiating (18) with all_485_0, all_214_0, % 24.03/4.00 | | | | | | | | | | | | all_27_3, all_110_1, simplifying with (149), (151) % 24.03/4.00 | | | | | | | | | | | | gives: % 24.03/4.00 | | | | | | | | | | | | (152) all_485_0 = all_214_0 % 24.03/4.00 | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_69_1, all_69_0, % 24.03/4.00 | | | | | | | | | | | | all_27_3, all_110_1, all_214_0, simplifying with % 24.03/4.00 | | | | | | | | | | | | (32), (49), (50), (78), (151) gives: % 24.03/4.00 | | | | | | | | | | | | (153) all_214_0 = 0 | ? [v0: any] : ? [v1: any] : % 24.03/4.00 | | | | | | | | | | | | (in(all_69_0, all_27_3) = v1 & in(all_69_1, % 24.03/4.00 | | | | | | | | | | | | all_27_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) % 24.03/4.00 | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | BETA: splitting (153) gives: % 24.03/4.00 | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | Case 1: % 24.03/4.00 | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | (154) all_214_0 = 0 % 24.03/4.00 | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | REDUCE: (115), (154) imply: % 24.03/4.00 | | | | | | | | | | | | | (155) $false % 24.03/4.00 | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | CLOSE: (155) is inconsistent. % 24.03/4.00 | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | Case 2: % 24.03/4.00 | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | (156) ? [v0: any] : ? [v1: any] : (in(all_69_0, % 24.03/4.00 | | | | | | | | | | | | | all_27_3) = v1 & in(all_69_1, all_27_3) = v0 & % 24.03/4.00 | | | | | | | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) % 24.03/4.00 | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | DELTA: instantiating (156) with fresh symbols all_637_0, % 24.03/4.00 | | | | | | | | | | | | | all_637_1 gives: % 24.03/4.00 | | | | | | | | | | | | | (157) in(all_69_0, all_27_3) = all_637_0 & in(all_69_1, % 24.03/4.00 | | | | | | | | | | | | | all_27_3) = all_637_1 & ( ~ (all_637_0 = 0) | ~ % 24.03/4.00 | | | | | | | | | | | | | (all_637_1 = 0)) % 24.03/4.00 | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | ALPHA: (157) implies: % 24.03/4.00 | | | | | | | | | | | | | (158) in(all_69_1, all_27_3) = all_637_1 % 24.03/4.00 | | | | | | | | | | | | | (159) in(all_69_0, all_27_3) = all_637_0 % 24.03/4.00 | | | | | | | | | | | | | (160) ~ (all_637_0 = 0) | ~ (all_637_1 = 0) % 24.03/4.00 | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_637_1, all_27_3, % 24.03/4.00 | | | | | | | | | | | | | all_69_1, simplifying with (70), (158) gives: % 24.03/4.00 | | | | | | | | | | | | | (161) all_637_1 = 0 % 24.03/4.00 | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_637_0, all_27_3, % 24.03/4.00 | | | | | | | | | | | | | all_69_0, simplifying with (68), (159) gives: % 24.03/4.00 | | | | | | | | | | | | | (162) all_637_0 = 0 % 24.03/4.00 | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | BETA: splitting (160) gives: % 24.03/4.00 | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | Case 1: % 24.03/4.00 | | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | | (163) ~ (all_637_0 = 0) % 24.03/4.00 | | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | | REDUCE: (162), (163) imply: % 24.03/4.00 | | | | | | | | | | | | | | (164) $false % 24.03/4.00 | | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | | CLOSE: (164) is inconsistent. % 24.03/4.00 | | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | Case 2: % 24.03/4.00 | | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | | (165) ~ (all_637_1 = 0) % 24.03/4.00 | | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | | REDUCE: (161), (165) imply: % 24.03/4.00 | | | | | | | | | | | | | | (166) $false % 24.03/4.00 | | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | | CLOSE: (166) is inconsistent. % 24.03/4.00 | | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | | End of split % 24.03/4.00 | | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | End of split % 24.03/4.00 | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | Case 2: % 24.03/4.00 | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | (167) all_126_1 = all_106_0 % 24.03/4.00 | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | REDUCE: (87), (167) imply: % 24.03/4.00 | | | | | | | | | | | | (168) in(all_106_0, all_27_2) = all_126_0 % 24.03/4.00 | | | | | | | | | | | | % 24.03/4.00 | | | | | | | | | | | | GROUND_INST: instantiating (17) with 0, all_126_0, all_27_2, % 24.03/4.00 | | | | | | | | | | | | all_106_0, simplifying with (136), (168) gives: % 24.03/4.00 | | | | | | | | | | | | (169) all_126_0 = 0 % 24.03/4.00 | | | | | | | | | | | | % 24.03/4.01 | | | | | | | | | | | | REDUCE: (85), (169) imply: % 24.03/4.01 | | | | | | | | | | | | (170) $false % 24.03/4.01 | | | | | | | | | | | | % 24.03/4.01 | | | | | | | | | | | | CLOSE: (170) is inconsistent. % 24.03/4.01 | | | | | | | | | | | | % 24.03/4.01 | | | | | | | | | | | End of split % 24.03/4.01 | | | | | | | | | | | % 24.03/4.01 | | | | | | | | | | End of split % 24.03/4.01 | | | | | | | | | | % 24.03/4.01 | | | | | | | | | End of split % 24.03/4.01 | | | | | | | | | % 24.03/4.01 | | | | | | | | End of split % 24.03/4.01 | | | | | | | | % 24.03/4.01 | | | | | | | Case 2: % 24.03/4.01 | | | | | | | | % 24.03/4.01 | | | | | | | | (171) all_239_0 = 0 % 24.03/4.01 | | | | | | | | % 24.03/4.01 | | | | | | | | COMBINE_EQS: (133), (171) imply: % 24.03/4.01 | | | | | | | | (172) all_140_0 = 0 % 24.03/4.01 | | | | | | | | % 24.03/4.01 | | | | | | | | REDUCE: (103), (172) imply: % 24.03/4.01 | | | | | | | | (173) $false % 24.03/4.01 | | | | | | | | % 24.03/4.01 | | | | | | | | CLOSE: (173) is inconsistent. % 24.03/4.01 | | | | | | | | % 24.03/4.01 | | | | | | | End of split % 24.03/4.01 | | | | | | | % 24.03/4.01 | | | | | | End of split % 24.03/4.01 | | | | | | % 24.03/4.01 | | | | | End of split % 24.03/4.01 | | | | | % 24.03/4.01 | | | | End of split % 24.03/4.01 | | | | % 24.03/4.01 | | | End of split % 24.03/4.01 | | | % 24.03/4.01 | | End of split % 24.03/4.01 | | % 24.03/4.01 | End of split % 24.03/4.01 | % 24.03/4.01 End of proof % 24.03/4.01 % SZS output end Proof for theBenchmark % 24.03/4.01 % 24.03/4.01 3352ms %------------------------------------------------------------------------------