%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET938+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 : n021.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 15:27:08 EDT 2023 % Result : Theorem 10.00s 2.14s % Output : Proof 11.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.14 % Problem : SET938+1 : TPTP v8.1.2. Released v3.2.0. % 0.08/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.36 % Computer : n021.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.36 % CPULimit : 300 % 0.14/0.36 % WCLimit : 300 % 0.14/0.36 % DateTime : Sat Aug 26 08:35:42 EDT 2023 % 0.14/0.36 % CPUTime : % 0.22/0.64 ________ _____ % 0.22/0.64 ___ __ \_________(_)________________________________ % 0.22/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.22/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.22/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.22/0.64 % 0.22/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.22/0.64 (2023-06-19) % 0.22/0.64 % 0.22/0.64 (c) Philipp Rümmer, 2009-2023 % 0.22/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.22/0.64 Amanda Stjerna. % 0.22/0.64 Free software under BSD-3-Clause. % 0.22/0.64 % 0.22/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.22/0.64 % 0.22/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.22/0.65 Running up to 7 provers in parallel. % 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.22/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.22/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.22/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.22/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.22/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.22/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.26/1.04 Prover 1: Preprocessing ... % 2.26/1.04 Prover 4: Preprocessing ... % 2.67/1.09 Prover 0: Preprocessing ... % 2.67/1.09 Prover 2: Preprocessing ... % 2.67/1.09 Prover 3: Preprocessing ... % 2.67/1.09 Prover 5: Preprocessing ... % 2.67/1.09 Prover 6: Preprocessing ... % 4.26/1.41 Prover 1: Warning: ignoring some quantifiers % 4.87/1.42 Prover 3: Warning: ignoring some quantifiers % 4.87/1.44 Prover 5: Proving ... % 4.87/1.44 Prover 4: Warning: ignoring some quantifiers % 4.87/1.44 Prover 1: Constructing countermodel ... % 4.87/1.44 Prover 3: Constructing countermodel ... % 4.87/1.45 Prover 6: Proving ... % 4.87/1.45 Prover 2: Proving ... % 4.87/1.46 Prover 4: Constructing countermodel ... % 5.34/1.51 Prover 0: Proving ... % 8.17/1.90 Prover 1: gave up % 8.17/1.90 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.17/1.97 Prover 7: Preprocessing ... % 8.17/1.98 Prover 3: gave up % 8.17/1.98 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.17/2.01 Prover 8: Preprocessing ... % 9.12/2.04 Prover 7: Warning: ignoring some quantifiers % 9.33/2.05 Prover 7: Constructing countermodel ... % 9.33/2.09 Prover 8: Warning: ignoring some quantifiers % 9.33/2.10 Prover 8: Constructing countermodel ... % 10.00/2.14 Prover 0: proved (1483ms) % 10.00/2.14 % 10.00/2.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.00/2.14 % 10.00/2.14 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 10.00/2.14 Prover 6: stopped % 10.00/2.14 Prover 5: stopped % 10.00/2.14 Prover 2: stopped % 10.00/2.16 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 10.00/2.16 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 10.00/2.16 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 10.00/2.16 Prover 10: Preprocessing ... % 10.00/2.16 Prover 13: Preprocessing ... % 10.00/2.17 Prover 11: Preprocessing ... % 10.00/2.17 Prover 16: Preprocessing ... % 10.41/2.20 Prover 10: Warning: ignoring some quantifiers % 10.41/2.21 Prover 10: Constructing countermodel ... % 10.41/2.22 Prover 13: Warning: ignoring some quantifiers % 10.41/2.22 Prover 4: Found proof (size 103) % 10.41/2.22 Prover 4: proved (1563ms) % 10.41/2.22 Prover 16: Warning: ignoring some quantifiers % 10.41/2.22 Prover 7: stopped % 10.41/2.22 Prover 10: stopped % 10.41/2.23 Prover 8: stopped % 10.41/2.23 Prover 13: Constructing countermodel ... % 10.41/2.23 Prover 16: Constructing countermodel ... % 10.41/2.23 Prover 13: stopped % 10.41/2.23 Prover 16: stopped % 10.41/2.25 Prover 11: Warning: ignoring some quantifiers % 10.84/2.26 Prover 11: Constructing countermodel ... % 10.84/2.26 Prover 11: stopped % 10.84/2.26 % 10.84/2.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 10.84/2.26 % 10.84/2.27 % SZS output start Proof for theBenchmark % 10.84/2.28 Assumptions after simplification: % 10.84/2.28 --------------------------------- % 10.84/2.28 % 10.84/2.28 (commutativity_k2_xboole_0) % 10.84/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 10.84/2.30 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 10.84/2.30 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 10.84/2.30 | (set_union2(v1, v0) = v2 & $i(v2))) % 10.84/2.30 % 10.84/2.30 (commutativity_k5_xboole_0) % 11.06/2.30 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v1, v0) = % 11.06/2.30 v2) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v0, v1) = v2 & % 11.06/2.30 $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 11.06/2.30 (symmetric_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 11.06/2.30 (symmetric_difference(v1, v0) = v2 & $i(v2))) % 11.06/2.30 % 11.06/2.30 (d1_zfmisc_1) % 11.06/2.31 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 11.06/2.31 (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 11.06/2.31 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0: $i] : ! % 11.06/2.31 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ % 11.06/2.31 (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ % 11.06/2.31 (v4 = 0) & subset(v2, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 11.06/2.31 : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | % 11.06/2.31 ~ $i(v0) | in(v2, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 11.06/2.31 (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 11.06/2.31 $i(v0) | subset(v2, v0) = 0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 % 11.06/2.31 = v0 | ~ (powerset(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 11.06/2.31 [v4: any] : ? [v5: any] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & $i(v3) & % 11.06/2.31 ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) % 11.06/2.31 % 11.06/2.31 (d2_xboole_0) % 11.06/2.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 11.06/2.33 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~ % 11.06/2.33 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) % 11.06/2.33 & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0: $i] : ! % 11.06/2.33 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 11.06/2.33 (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 11.06/2.33 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & % 11.06/2.33 in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : % 11.06/2.33 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (set_union2(v0, v1) = % 11.06/2.33 v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 11.06/2.33 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 % 11.06/2.33 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 11.06/2.33 $i] : ! [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | % 11.06/2.33 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 11.06/2.33 (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = % 11.06/2.33 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 11.06/2.33 [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | % 11.06/2.33 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, % 11.06/2.33 v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & % 11.06/2.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) % 11.06/2.33 = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 11.06/2.33 $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v1) = v5 & in(v3, v0) = v4 & % 11.06/2.33 (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 11.06/2.33 $i] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 11.06/2.33 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, % 11.06/2.33 v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( % 11.06/2.33 ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) % 11.06/2.33 % 11.06/2.33 (d3_tarski) % 11.06/2.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 11.06/2.33 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 11.06/2.33 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 11.06/2.33 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 11.06/2.33 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 11.06/2.33 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 11.06/2.33 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 11.06/2.33 $i(v0) | in(v2, v1) = 0) % 11.06/2.33 % 11.06/2.33 (d6_xboole_0) % 11.06/2.33 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v1, v0) = v2) | % 11.06/2.33 ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (set_difference(v0, v1) = % 11.06/2.33 v4 & symmetric_difference(v0, v1) = v3 & set_union2(v4, v2) = v3 & $i(v4) % 11.06/2.33 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 11.06/2.33 (set_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 11.06/2.33 [v4: $i] : (set_difference(v1, v0) = v4 & symmetric_difference(v0, v1) = v3 % 11.06/2.33 & set_union2(v2, v4) = v3 & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: $i] % 11.06/2.33 : ! [v2: $i] : ( ~ (symmetric_difference(v0, v1) = v2) | ~ $i(v1) | ~ % 11.06/2.33 $i(v0) | ? [v3: $i] : ? [v4: $i] : (set_difference(v1, v0) = v4 & % 11.06/2.33 set_difference(v0, v1) = v3 & set_union2(v3, v4) = v2 & $i(v4) & $i(v3) & % 11.06/2.33 $i(v2))) % 11.06/2.33 % 11.06/2.33 (t86_zfmisc_1) % 11.06/2.34 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 11.06/2.34 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: int] : ( ~ (v9 = 0) % 11.06/2.34 & set_difference(v1, v0) = v4 & set_difference(v0, v1) = v2 & powerset(v7) = % 11.06/2.34 v8 & powerset(v4) = v5 & powerset(v2) = v3 & subset(v6, v8) = v9 & % 11.06/2.34 symmetric_difference(v0, v1) = v7 & set_union2(v3, v5) = v6 & $i(v8) & % 11.06/2.34 $i(v7) & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 11.06/2.34 % 11.06/2.34 (function-axioms) % 11.06/2.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.06/2.34 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0: % 11.06/2.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.06/2.34 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: % 11.06/2.34 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.06/2.34 (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = % 11.06/2.34 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 11.06/2.34 ~ (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: % 11.06/2.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.06/2.34 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 11.06/2.34 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 11.06/2.34 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 11.06/2.34 [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 11.06/2.34 % 11.06/2.34 Further assumptions not needed in the proof: % 11.06/2.34 -------------------------------------------- % 11.06/2.34 antisymmetry_r2_hidden, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 11.06/2.34 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski % 11.06/2.34 % 11.06/2.34 Those formulas are unsatisfiable: % 11.06/2.34 --------------------------------- % 11.06/2.34 % 11.06/2.34 Begin of proof % 11.26/2.34 | % 11.26/2.34 | ALPHA: (commutativity_k2_xboole_0) implies: % 11.26/2.34 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 11.26/2.34 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 11.26/2.34 | % 11.26/2.34 | ALPHA: (commutativity_k5_xboole_0) implies: % 11.26/2.34 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v1, % 11.26/2.34 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v0, v1) % 11.26/2.34 | = v2 & $i(v2))) % 11.26/2.34 | % 11.26/2.34 | ALPHA: (d1_zfmisc_1) implies: % 11.26/2.34 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v0) = v1) | ~ % 11.26/2.34 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | subset(v2, v0) % 11.26/2.34 | = 0) % 11.26/2.35 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 11.26/2.35 | (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 11.26/2.35 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) % 11.26/2.35 | % 11.26/2.35 | ALPHA: (d2_xboole_0) implies: % 11.26/2.35 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 11.26/2.35 | (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 11.26/2.35 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 11.26/2.35 | (in(v3, v1) = v5 & in(v3, v0) = v4 & (v5 = 0 | v4 = 0))) % 11.26/2.35 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : % 11.26/2.35 | (v4 = 0 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ % 11.26/2.35 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: % 11.26/2.35 | int] : ( ~ (v6 = 0) & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = % 11.26/2.35 | v5)) % 11.26/2.35 | % 11.26/2.35 | ALPHA: (d3_tarski) implies: % 11.26/2.35 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~ % 11.26/2.35 | (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v2, v1) = % 11.26/2.35 | 0) % 11.26/2.35 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 11.26/2.35 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 11.26/2.35 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 11.26/2.35 | % 11.26/2.35 | ALPHA: (d6_xboole_0) implies: % 11.26/2.35 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0, % 11.26/2.35 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 11.26/2.35 | (set_difference(v1, v0) = v4 & set_difference(v0, v1) = v3 & % 11.26/2.35 | set_union2(v3, v4) = v2 & $i(v4) & $i(v3) & $i(v2))) % 11.26/2.35 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v0, v1) % 11.26/2.35 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 11.26/2.35 | (set_difference(v1, v0) = v4 & symmetric_difference(v0, v1) = v3 & % 11.26/2.35 | set_union2(v2, v4) = v3 & $i(v4) & $i(v3))) % 11.26/2.35 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_difference(v1, v0) % 11.26/2.35 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 11.26/2.35 | (set_difference(v0, v1) = v4 & symmetric_difference(v0, v1) = v3 & % 11.26/2.35 | set_union2(v4, v2) = v3 & $i(v4) & $i(v3))) % 11.26/2.35 | % 11.26/2.35 | ALPHA: (function-axioms) implies: % 11.26/2.35 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 11.26/2.35 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 11.26/2.35 | v0)) % 11.26/2.36 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.26/2.36 | (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, % 11.26/2.36 | v2) = v0)) % 11.26/2.36 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.26/2.36 | (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) % 11.26/2.36 | % 11.26/2.36 | DELTA: instantiating (t86_zfmisc_1) with fresh symbols all_22_0, all_22_1, % 11.26/2.36 | all_22_2, all_22_3, all_22_4, all_22_5, all_22_6, all_22_7, all_22_8, % 11.26/2.36 | all_22_9 gives: % 11.26/2.36 | (15) ~ (all_22_0 = 0) & set_difference(all_22_8, all_22_9) = all_22_5 & % 11.26/2.36 | set_difference(all_22_9, all_22_8) = all_22_7 & powerset(all_22_2) = % 11.26/2.36 | all_22_1 & powerset(all_22_5) = all_22_4 & powerset(all_22_7) = % 11.26/2.36 | all_22_6 & subset(all_22_3, all_22_1) = all_22_0 & % 11.26/2.36 | symmetric_difference(all_22_9, all_22_8) = all_22_2 & % 11.26/2.36 | set_union2(all_22_6, all_22_4) = all_22_3 & $i(all_22_1) & % 11.26/2.36 | $i(all_22_2) & $i(all_22_3) & $i(all_22_4) & $i(all_22_5) & % 11.26/2.36 | $i(all_22_6) & $i(all_22_7) & $i(all_22_8) & $i(all_22_9) % 11.26/2.36 | % 11.26/2.36 | ALPHA: (15) implies: % 11.26/2.36 | (16) ~ (all_22_0 = 0) % 11.26/2.36 | (17) $i(all_22_9) % 11.26/2.36 | (18) $i(all_22_8) % 11.26/2.36 | (19) $i(all_22_6) % 11.26/2.36 | (20) $i(all_22_4) % 11.26/2.36 | (21) $i(all_22_1) % 11.26/2.36 | (22) set_union2(all_22_6, all_22_4) = all_22_3 % 11.26/2.36 | (23) symmetric_difference(all_22_9, all_22_8) = all_22_2 % 11.26/2.36 | (24) subset(all_22_3, all_22_1) = all_22_0 % 11.26/2.36 | (25) powerset(all_22_7) = all_22_6 % 11.26/2.36 | (26) powerset(all_22_5) = all_22_4 % 11.26/2.36 | (27) powerset(all_22_2) = all_22_1 % 11.26/2.36 | (28) set_difference(all_22_9, all_22_8) = all_22_7 % 11.26/2.36 | (29) set_difference(all_22_8, all_22_9) = all_22_5 % 11.26/2.36 | % 11.26/2.36 | GROUND_INST: instantiating (1) with all_22_4, all_22_6, all_22_3, simplifying % 11.26/2.36 | with (19), (20), (22) gives: % 11.26/2.36 | (30) set_union2(all_22_4, all_22_6) = all_22_3 & $i(all_22_3) % 11.26/2.36 | % 11.26/2.36 | ALPHA: (30) implies: % 11.26/2.36 | (31) $i(all_22_3) % 11.26/2.36 | (32) set_union2(all_22_4, all_22_6) = all_22_3 % 11.26/2.36 | % 11.26/2.36 | GROUND_INST: instantiating (2) with all_22_8, all_22_9, all_22_2, simplifying % 11.26/2.36 | with (17), (18), (23) gives: % 11.26/2.36 | (33) symmetric_difference(all_22_8, all_22_9) = all_22_2 & $i(all_22_2) % 11.26/2.36 | % 11.26/2.36 | ALPHA: (33) implies: % 11.26/2.36 | (34) symmetric_difference(all_22_8, all_22_9) = all_22_2 % 11.26/2.36 | % 11.26/2.36 | GROUND_INST: instantiating (9) with all_22_9, all_22_8, all_22_2, simplifying % 11.26/2.36 | with (17), (18), (23) gives: % 11.26/2.36 | (35) ? [v0: $i] : ? [v1: $i] : (set_difference(all_22_8, all_22_9) = v1 & % 11.26/2.36 | set_difference(all_22_9, all_22_8) = v0 & set_union2(v0, v1) = % 11.26/2.36 | all_22_2 & $i(v1) & $i(v0) & $i(all_22_2)) % 11.26/2.36 | % 11.26/2.36 | GROUND_INST: instantiating (8) with all_22_3, all_22_1, all_22_0, simplifying % 11.26/2.36 | with (21), (24), (31) gives: % 11.26/2.37 | (36) all_22_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 11.26/2.37 | all_22_1) = v1 & in(v0, all_22_3) = 0 & $i(v0)) % 11.26/2.37 | % 11.26/2.37 | GROUND_INST: instantiating (11) with all_22_8, all_22_9, all_22_7, simplifying % 11.26/2.37 | with (17), (18), (28) gives: % 11.26/2.37 | (37) ? [v0: $i] : ? [v1: $i] : (set_difference(all_22_8, all_22_9) = v1 & % 11.26/2.37 | symmetric_difference(all_22_8, all_22_9) = v0 & set_union2(v1, % 11.26/2.37 | all_22_7) = v0 & $i(v1) & $i(v0)) % 11.26/2.37 | % 11.26/2.37 | GROUND_INST: instantiating (10) with all_22_9, all_22_8, all_22_7, simplifying % 11.26/2.37 | with (17), (18), (28) gives: % 11.26/2.37 | (38) ? [v0: $i] : ? [v1: $i] : (set_difference(all_22_8, all_22_9) = v1 & % 11.26/2.37 | symmetric_difference(all_22_9, all_22_8) = v0 & set_union2(all_22_7, % 11.26/2.37 | v1) = v0 & $i(v1) & $i(v0)) % 11.26/2.37 | % 11.26/2.37 | GROUND_INST: instantiating (11) with all_22_9, all_22_8, all_22_5, simplifying % 11.26/2.37 | with (17), (18), (29) gives: % 11.26/2.37 | (39) ? [v0: $i] : ? [v1: $i] : (set_difference(all_22_9, all_22_8) = v1 & % 11.26/2.37 | symmetric_difference(all_22_9, all_22_8) = v0 & set_union2(v1, % 11.26/2.37 | all_22_5) = v0 & $i(v1) & $i(v0)) % 11.26/2.37 | % 11.26/2.37 | GROUND_INST: instantiating (10) with all_22_8, all_22_9, all_22_5, simplifying % 11.26/2.37 | with (17), (18), (29) gives: % 11.26/2.37 | (40) ? [v0: $i] : ? [v1: $i] : (set_difference(all_22_9, all_22_8) = v1 & % 11.26/2.37 | symmetric_difference(all_22_8, all_22_9) = v0 & set_union2(all_22_5, % 11.26/2.37 | v1) = v0 & $i(v1) & $i(v0)) % 11.26/2.37 | % 11.26/2.37 | DELTA: instantiating (40) with fresh symbols all_34_0, all_34_1 gives: % 11.26/2.37 | (41) set_difference(all_22_9, all_22_8) = all_34_0 & % 11.26/2.37 | symmetric_difference(all_22_8, all_22_9) = all_34_1 & % 11.26/2.37 | set_union2(all_22_5, all_34_0) = all_34_1 & $i(all_34_0) & % 11.26/2.37 | $i(all_34_1) % 11.26/2.37 | % 11.26/2.37 | ALPHA: (41) implies: % 11.26/2.37 | (42) $i(all_34_1) % 11.26/2.37 | (43) $i(all_34_0) % 11.26/2.37 | (44) symmetric_difference(all_22_8, all_22_9) = all_34_1 % 11.26/2.37 | (45) set_difference(all_22_9, all_22_8) = all_34_0 % 11.26/2.37 | % 11.26/2.37 | DELTA: instantiating (38) with fresh symbols all_36_0, all_36_1 gives: % 11.26/2.37 | (46) set_difference(all_22_8, all_22_9) = all_36_0 & % 11.26/2.37 | symmetric_difference(all_22_9, all_22_8) = all_36_1 & % 11.26/2.37 | set_union2(all_22_7, all_36_0) = all_36_1 & $i(all_36_0) & % 11.26/2.37 | $i(all_36_1) % 11.26/2.37 | % 11.26/2.37 | ALPHA: (46) implies: % 11.26/2.37 | (47) $i(all_36_0) % 11.26/2.37 | (48) set_union2(all_22_7, all_36_0) = all_36_1 % 11.26/2.37 | (49) symmetric_difference(all_22_9, all_22_8) = all_36_1 % 11.26/2.37 | (50) set_difference(all_22_8, all_22_9) = all_36_0 % 11.26/2.37 | % 11.26/2.37 | DELTA: instantiating (37) with fresh symbols all_38_0, all_38_1 gives: % 11.26/2.37 | (51) set_difference(all_22_8, all_22_9) = all_38_0 & % 11.26/2.38 | symmetric_difference(all_22_8, all_22_9) = all_38_1 & % 11.26/2.38 | set_union2(all_38_0, all_22_7) = all_38_1 & $i(all_38_0) & % 11.26/2.38 | $i(all_38_1) % 11.26/2.38 | % 11.26/2.38 | ALPHA: (51) implies: % 11.26/2.38 | (52) symmetric_difference(all_22_8, all_22_9) = all_38_1 % 11.26/2.38 | (53) set_difference(all_22_8, all_22_9) = all_38_0 % 11.26/2.38 | % 11.26/2.38 | DELTA: instantiating (39) with fresh symbols all_40_0, all_40_1 gives: % 11.26/2.38 | (54) set_difference(all_22_9, all_22_8) = all_40_0 & % 11.26/2.38 | symmetric_difference(all_22_9, all_22_8) = all_40_1 & % 11.26/2.38 | set_union2(all_40_0, all_22_5) = all_40_1 & $i(all_40_0) & % 11.26/2.38 | $i(all_40_1) % 11.26/2.38 | % 11.26/2.38 | ALPHA: (54) implies: % 11.26/2.38 | (55) symmetric_difference(all_22_9, all_22_8) = all_40_1 % 11.26/2.38 | (56) set_difference(all_22_9, all_22_8) = all_40_0 % 11.26/2.38 | % 11.26/2.38 | DELTA: instantiating (35) with fresh symbols all_42_0, all_42_1 gives: % 11.26/2.38 | (57) set_difference(all_22_8, all_22_9) = all_42_0 & % 11.26/2.38 | set_difference(all_22_9, all_22_8) = all_42_1 & set_union2(all_42_1, % 11.26/2.38 | all_42_0) = all_22_2 & $i(all_42_0) & $i(all_42_1) & $i(all_22_2) % 11.26/2.38 | % 11.26/2.38 | ALPHA: (57) implies: % 11.26/2.38 | (58) set_difference(all_22_9, all_22_8) = all_42_1 % 11.26/2.38 | (59) set_difference(all_22_8, all_22_9) = all_42_0 % 11.26/2.38 | % 11.26/2.38 | BETA: splitting (36) gives: % 11.26/2.38 | % 11.26/2.38 | Case 1: % 11.26/2.38 | | % 11.26/2.38 | | (60) all_22_0 = 0 % 11.26/2.38 | | % 11.26/2.38 | | REDUCE: (16), (60) imply: % 11.26/2.38 | | (61) $false % 11.26/2.38 | | % 11.26/2.38 | | CLOSE: (61) is inconsistent. % 11.26/2.38 | | % 11.26/2.38 | Case 2: % 11.26/2.38 | | % 11.26/2.38 | | (62) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_22_1) = v1 & % 11.26/2.38 | | in(v0, all_22_3) = 0 & $i(v0)) % 11.26/2.38 | | % 11.26/2.38 | | DELTA: instantiating (62) with fresh symbols all_48_0, all_48_1 gives: % 11.26/2.38 | | (63) ~ (all_48_0 = 0) & in(all_48_1, all_22_1) = all_48_0 & in(all_48_1, % 11.26/2.38 | | all_22_3) = 0 & $i(all_48_1) % 11.26/2.38 | | % 11.26/2.38 | | ALPHA: (63) implies: % 11.26/2.38 | | (64) ~ (all_48_0 = 0) % 11.26/2.38 | | (65) $i(all_48_1) % 11.26/2.38 | | (66) in(all_48_1, all_22_3) = 0 % 11.26/2.38 | | (67) in(all_48_1, all_22_1) = all_48_0 % 11.26/2.38 | | % 11.26/2.38 | | GROUND_INST: instantiating (13) with all_22_2, all_40_1, all_22_8, all_22_9, % 11.26/2.38 | | simplifying with (23), (55) gives: % 11.26/2.38 | | (68) all_40_1 = all_22_2 % 11.26/2.38 | | % 11.26/2.38 | | GROUND_INST: instantiating (13) with all_36_1, all_40_1, all_22_8, all_22_9, % 11.26/2.38 | | simplifying with (49), (55) gives: % 11.26/2.38 | | (69) all_40_1 = all_36_1 % 11.26/2.38 | | % 11.26/2.38 | | GROUND_INST: instantiating (13) with all_34_1, all_38_1, all_22_9, all_22_8, % 11.26/2.38 | | simplifying with (44), (52) gives: % 11.26/2.38 | | (70) all_38_1 = all_34_1 % 11.26/2.38 | | % 11.26/2.38 | | GROUND_INST: instantiating (13) with all_22_2, all_38_1, all_22_9, all_22_8, % 11.26/2.38 | | simplifying with (34), (52) gives: % 11.26/2.38 | | (71) all_38_1 = all_22_2 % 11.26/2.38 | | % 11.26/2.38 | | GROUND_INST: instantiating (14) with all_22_7, all_40_0, all_22_8, all_22_9, % 11.26/2.38 | | simplifying with (28), (56) gives: % 11.26/2.38 | | (72) all_40_0 = all_22_7 % 11.26/2.38 | | % 11.26/2.38 | | GROUND_INST: instantiating (14) with all_40_0, all_42_1, all_22_8, all_22_9, % 11.26/2.38 | | simplifying with (56), (58) gives: % 11.26/2.39 | | (73) all_42_1 = all_40_0 % 11.26/2.39 | | % 11.26/2.39 | | GROUND_INST: instantiating (14) with all_34_0, all_42_1, all_22_8, all_22_9, % 11.26/2.39 | | simplifying with (45), (58) gives: % 11.26/2.39 | | (74) all_42_1 = all_34_0 % 11.26/2.39 | | % 11.26/2.39 | | GROUND_INST: instantiating (14) with all_22_5, all_38_0, all_22_9, all_22_8, % 11.26/2.39 | | simplifying with (29), (53) gives: % 11.26/2.39 | | (75) all_38_0 = all_22_5 % 11.26/2.39 | | % 11.26/2.39 | | GROUND_INST: instantiating (14) with all_38_0, all_42_0, all_22_9, all_22_8, % 11.26/2.39 | | simplifying with (53), (59) gives: % 11.26/2.39 | | (76) all_42_0 = all_38_0 % 11.26/2.39 | | % 11.26/2.39 | | GROUND_INST: instantiating (14) with all_36_0, all_42_0, all_22_9, all_22_8, % 11.26/2.39 | | simplifying with (50), (59) gives: % 11.26/2.39 | | (77) all_42_0 = all_36_0 % 11.26/2.39 | | % 11.26/2.39 | | COMBINE_EQS: (76), (77) imply: % 11.26/2.39 | | (78) all_38_0 = all_36_0 % 11.26/2.39 | | % 11.26/2.39 | | SIMP: (78) implies: % 11.26/2.39 | | (79) all_38_0 = all_36_0 % 11.26/2.39 | | % 11.26/2.39 | | COMBINE_EQS: (73), (74) imply: % 11.26/2.39 | | (80) all_40_0 = all_34_0 % 11.26/2.39 | | % 11.26/2.39 | | SIMP: (80) implies: % 11.26/2.39 | | (81) all_40_0 = all_34_0 % 11.26/2.39 | | % 11.26/2.39 | | COMBINE_EQS: (72), (81) imply: % 11.26/2.39 | | (82) all_34_0 = all_22_7 % 11.26/2.39 | | % 11.26/2.39 | | COMBINE_EQS: (68), (69) imply: % 11.26/2.39 | | (83) all_36_1 = all_22_2 % 11.26/2.39 | | % 11.26/2.39 | | SIMP: (83) implies: % 11.26/2.39 | | (84) all_36_1 = all_22_2 % 11.26/2.39 | | % 11.26/2.39 | | COMBINE_EQS: (75), (79) imply: % 11.26/2.39 | | (85) all_36_0 = all_22_5 % 11.26/2.39 | | % 11.26/2.39 | | COMBINE_EQS: (70), (71) imply: % 11.26/2.39 | | (86) all_34_1 = all_22_2 % 11.26/2.39 | | % 11.26/2.39 | | SIMP: (86) implies: % 11.26/2.39 | | (87) all_34_1 = all_22_2 % 11.26/2.39 | | % 11.26/2.39 | | REDUCE: (48), (84), (85) imply: % 11.26/2.39 | | (88) set_union2(all_22_7, all_22_5) = all_22_2 % 11.26/2.39 | | % 11.26/2.39 | | REDUCE: (47), (85) imply: % 11.26/2.39 | | (89) $i(all_22_5) % 11.26/2.39 | | % 11.26/2.39 | | REDUCE: (43), (82) imply: % 11.26/2.39 | | (90) $i(all_22_7) % 11.26/2.39 | | % 11.26/2.39 | | REDUCE: (42), (87) imply: % 11.26/2.39 | | (91) $i(all_22_2) % 11.26/2.39 | | % 11.26/2.39 | | GROUND_INST: instantiating (5) with all_22_6, all_22_4, all_22_3, all_48_1, % 11.26/2.39 | | simplifying with (19), (20), (22), (31), (65), (66) gives: % 11.26/2.39 | | (92) ? [v0: any] : ? [v1: any] : (in(all_48_1, all_22_4) = v1 & % 11.26/2.39 | | in(all_48_1, all_22_6) = v0 & (v1 = 0 | v0 = 0)) % 11.26/2.39 | | % 11.26/2.39 | | GROUND_INST: instantiating (4) with all_22_2, all_22_1, all_48_1, all_48_0, % 11.26/2.39 | | simplifying with (21), (27), (65), (67), (91) gives: % 11.26/2.39 | | (93) all_48_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_48_1, % 11.26/2.39 | | all_22_2) = v0) % 11.26/2.39 | | % 11.26/2.39 | | GROUND_INST: instantiating (5) with all_22_4, all_22_6, all_22_3, all_48_1, % 11.26/2.39 | | simplifying with (19), (20), (31), (32), (65), (66) gives: % 11.26/2.39 | | (94) ? [v0: any] : ? [v1: any] : (in(all_48_1, all_22_4) = v0 & % 11.26/2.39 | | in(all_48_1, all_22_6) = v1 & (v1 = 0 | v0 = 0)) % 11.26/2.39 | | % 11.26/2.39 | | DELTA: instantiating (94) with fresh symbols all_63_0, all_63_1 gives: % 11.26/2.39 | | (95) in(all_48_1, all_22_4) = all_63_1 & in(all_48_1, all_22_6) = % 11.26/2.39 | | all_63_0 & (all_63_0 = 0 | all_63_1 = 0) % 11.26/2.39 | | % 11.26/2.39 | | ALPHA: (95) implies: % 11.26/2.39 | | (96) in(all_48_1, all_22_6) = all_63_0 % 11.26/2.39 | | (97) in(all_48_1, all_22_4) = all_63_1 % 11.26/2.39 | | (98) all_63_0 = 0 | all_63_1 = 0 % 11.26/2.39 | | % 11.26/2.39 | | DELTA: instantiating (92) with fresh symbols all_69_0, all_69_1 gives: % 11.26/2.40 | | (99) in(all_48_1, all_22_4) = all_69_0 & in(all_48_1, all_22_6) = % 11.26/2.40 | | all_69_1 & (all_69_0 = 0 | all_69_1 = 0) % 11.26/2.40 | | % 11.26/2.40 | | ALPHA: (99) implies: % 11.26/2.40 | | (100) in(all_48_1, all_22_6) = all_69_1 % 11.26/2.40 | | (101) in(all_48_1, all_22_4) = all_69_0 % 11.26/2.40 | | % 11.26/2.40 | | BETA: splitting (93) gives: % 11.26/2.40 | | % 11.26/2.40 | | Case 1: % 11.26/2.40 | | | % 11.26/2.40 | | | (102) all_48_0 = 0 % 11.26/2.40 | | | % 11.26/2.40 | | | REDUCE: (64), (102) imply: % 11.26/2.40 | | | (103) $false % 11.26/2.40 | | | % 11.26/2.40 | | | CLOSE: (103) is inconsistent. % 11.26/2.40 | | | % 11.26/2.40 | | Case 2: % 11.26/2.40 | | | % 11.26/2.40 | | | (104) ? [v0: int] : ( ~ (v0 = 0) & subset(all_48_1, all_22_2) = v0) % 11.26/2.40 | | | % 11.26/2.40 | | | DELTA: instantiating (104) with fresh symbol all_77_0 gives: % 11.26/2.40 | | | (105) ~ (all_77_0 = 0) & subset(all_48_1, all_22_2) = all_77_0 % 11.26/2.40 | | | % 11.26/2.40 | | | ALPHA: (105) implies: % 11.26/2.40 | | | (106) ~ (all_77_0 = 0) % 11.26/2.40 | | | (107) subset(all_48_1, all_22_2) = all_77_0 % 11.26/2.40 | | | % 11.26/2.40 | | | GROUND_INST: instantiating (12) with all_63_0, all_69_1, all_22_6, % 11.26/2.40 | | | all_48_1, simplifying with (96), (100) gives: % 11.26/2.40 | | | (108) all_69_1 = all_63_0 % 11.26/2.40 | | | % 11.26/2.40 | | | GROUND_INST: instantiating (12) with all_63_1, all_69_0, all_22_4, % 11.26/2.40 | | | all_48_1, simplifying with (97), (101) gives: % 11.26/2.40 | | | (109) all_69_0 = all_63_1 % 11.26/2.40 | | | % 11.26/2.40 | | | GROUND_INST: instantiating (8) with all_48_1, all_22_2, all_77_0, % 11.26/2.40 | | | simplifying with (65), (91), (107) gives: % 11.26/2.40 | | | (110) all_77_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 11.26/2.40 | | | all_48_1) = 0 & in(v0, all_22_2) = v1 & $i(v0)) % 11.26/2.40 | | | % 11.26/2.40 | | | BETA: splitting (110) gives: % 11.26/2.40 | | | % 11.26/2.40 | | | Case 1: % 11.26/2.40 | | | | % 11.26/2.40 | | | | (111) all_77_0 = 0 % 11.26/2.40 | | | | % 11.26/2.40 | | | | REDUCE: (106), (111) imply: % 11.26/2.40 | | | | (112) $false % 11.26/2.40 | | | | % 11.26/2.40 | | | | CLOSE: (112) is inconsistent. % 11.26/2.40 | | | | % 11.26/2.40 | | | Case 2: % 11.26/2.40 | | | | % 11.26/2.40 | | | | (113) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_48_1) = % 11.26/2.40 | | | | 0 & in(v0, all_22_2) = v1 & $i(v0)) % 11.26/2.40 | | | | % 11.26/2.40 | | | | DELTA: instantiating (113) with fresh symbols all_94_0, all_94_1 gives: % 11.26/2.40 | | | | (114) ~ (all_94_0 = 0) & in(all_94_1, all_48_1) = 0 & in(all_94_1, % 11.26/2.40 | | | | all_22_2) = all_94_0 & $i(all_94_1) % 11.26/2.40 | | | | % 11.26/2.40 | | | | ALPHA: (114) implies: % 11.26/2.40 | | | | (115) ~ (all_94_0 = 0) % 11.26/2.40 | | | | (116) $i(all_94_1) % 11.26/2.40 | | | | (117) in(all_94_1, all_22_2) = all_94_0 % 11.26/2.40 | | | | (118) in(all_94_1, all_48_1) = 0 % 11.26/2.40 | | | | % 11.26/2.40 | | | | GROUND_INST: instantiating (6) with all_22_7, all_22_5, all_22_2, % 11.26/2.40 | | | | all_94_1, all_94_0, simplifying with (88), (89), (90), % 11.26/2.40 | | | | (91), (116), (117) gives: % 11.26/2.40 | | | | (119) all_94_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ % 11.26/2.40 | | | | (v0 = 0) & in(all_94_1, all_22_5) = v1 & in(all_94_1, % 11.26/2.40 | | | | all_22_7) = v0) % 11.26/2.40 | | | | % 11.26/2.40 | | | | BETA: splitting (119) gives: % 11.26/2.40 | | | | % 11.26/2.40 | | | | Case 1: % 11.26/2.40 | | | | | % 11.26/2.40 | | | | | (120) all_94_0 = 0 % 11.26/2.40 | | | | | % 11.26/2.40 | | | | | REDUCE: (115), (120) imply: % 11.26/2.40 | | | | | (121) $false % 11.26/2.40 | | | | | % 11.26/2.40 | | | | | CLOSE: (121) is inconsistent. % 11.26/2.40 | | | | | % 11.26/2.40 | | | | Case 2: % 11.26/2.40 | | | | | % 11.26/2.40 | | | | | (122) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 11.26/2.40 | | | | | in(all_94_1, all_22_5) = v1 & in(all_94_1, all_22_7) = v0) % 11.26/2.40 | | | | | % 11.26/2.40 | | | | | DELTA: instantiating (122) with fresh symbols all_107_0, all_107_1 % 11.26/2.40 | | | | | gives: % 11.26/2.40 | | | | | (123) ~ (all_107_0 = 0) & ~ (all_107_1 = 0) & in(all_94_1, % 11.26/2.40 | | | | | all_22_5) = all_107_0 & in(all_94_1, all_22_7) = all_107_1 % 11.26/2.40 | | | | | % 11.26/2.40 | | | | | ALPHA: (123) implies: % 11.26/2.40 | | | | | (124) ~ (all_107_1 = 0) % 11.26/2.40 | | | | | (125) ~ (all_107_0 = 0) % 11.26/2.40 | | | | | (126) in(all_94_1, all_22_7) = all_107_1 % 11.26/2.40 | | | | | (127) in(all_94_1, all_22_5) = all_107_0 % 11.26/2.40 | | | | | % 11.26/2.40 | | | | | BETA: splitting (98) gives: % 11.26/2.40 | | | | | % 11.26/2.41 | | | | | Case 1: % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | | (128) all_63_0 = 0 % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | | REDUCE: (96), (128) imply: % 11.26/2.41 | | | | | | (129) in(all_48_1, all_22_6) = 0 % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | | GROUND_INST: instantiating (3) with all_22_7, all_22_6, all_48_1, % 11.26/2.41 | | | | | | simplifying with (19), (25), (65), (90), (129) gives: % 11.26/2.41 | | | | | | (130) subset(all_48_1, all_22_7) = 0 % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | | GROUND_INST: instantiating (7) with all_48_1, all_22_7, all_94_1, % 11.26/2.41 | | | | | | simplifying with (65), (90), (116), (118), (130) gives: % 11.26/2.41 | | | | | | (131) in(all_94_1, all_22_7) = 0 % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | | GROUND_INST: instantiating (12) with all_107_1, 0, all_22_7, % 11.26/2.41 | | | | | | all_94_1, simplifying with (126), (131) gives: % 11.26/2.41 | | | | | | (132) all_107_1 = 0 % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | | REDUCE: (124), (132) imply: % 11.26/2.41 | | | | | | (133) $false % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | | CLOSE: (133) is inconsistent. % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | Case 2: % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | | (134) all_63_1 = 0 % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | | REDUCE: (97), (134) imply: % 11.26/2.41 | | | | | | (135) in(all_48_1, all_22_4) = 0 % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | | GROUND_INST: instantiating (3) with all_22_5, all_22_4, all_48_1, % 11.26/2.41 | | | | | | simplifying with (20), (26), (65), (89), (135) gives: % 11.26/2.41 | | | | | | (136) subset(all_48_1, all_22_5) = 0 % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | | GROUND_INST: instantiating (7) with all_48_1, all_22_5, all_94_1, % 11.26/2.41 | | | | | | simplifying with (65), (89), (116), (118), (136) gives: % 11.26/2.41 | | | | | | (137) in(all_94_1, all_22_5) = 0 % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | | GROUND_INST: instantiating (12) with all_107_0, 0, all_22_5, % 11.26/2.41 | | | | | | all_94_1, simplifying with (127), (137) gives: % 11.26/2.41 | | | | | | (138) all_107_0 = 0 % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | | REDUCE: (125), (138) imply: % 11.26/2.41 | | | | | | (139) $false % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | | CLOSE: (139) is inconsistent. % 11.26/2.41 | | | | | | % 11.26/2.41 | | | | | End of split % 11.26/2.41 | | | | | % 11.26/2.41 | | | | End of split % 11.26/2.41 | | | | % 11.26/2.41 | | | End of split % 11.26/2.41 | | | % 11.26/2.41 | | End of split % 11.26/2.41 | | % 11.26/2.41 | End of split % 11.26/2.41 | % 11.26/2.41 End of proof % 11.26/2.41 % SZS output end Proof for theBenchmark % 11.26/2.41 % 11.26/2.41 1774ms %------------------------------------------------------------------------------