%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET934+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 : n010.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 15:27:07 EDT 2023 % Result : Theorem 7.71s 1.88s % Output : Proof 10.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET934+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n010.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Sat Aug 26 16:24:35 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.61 ________ _____ % 0.20/0.61 ___ __ \_________(_)________________________________ % 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.61 % 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.61 (2023-06-19) % 0.20/0.61 % 0.20/0.61 (c) Philipp Rümmer, 2009-2023 % 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.61 Amanda Stjerna. % 0.20/0.61 Free software under BSD-3-Clause. % 0.20/0.61 % 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.61 % 0.20/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.38/1.04 Prover 1: Preprocessing ... % 2.38/1.04 Prover 4: Preprocessing ... % 2.38/1.08 Prover 3: Preprocessing ... % 2.38/1.08 Prover 0: Preprocessing ... % 2.38/1.08 Prover 2: Preprocessing ... % 2.38/1.08 Prover 5: Preprocessing ... % 2.38/1.08 Prover 6: Preprocessing ... % 4.82/1.42 Prover 5: Proving ... % 4.82/1.42 Prover 2: Proving ... % 4.82/1.42 Prover 6: Proving ... % 4.82/1.42 Prover 3: Warning: ignoring some quantifiers % 4.82/1.43 Prover 1: Warning: ignoring some quantifiers % 4.82/1.43 Prover 3: Constructing countermodel ... % 4.82/1.44 Prover 4: Warning: ignoring some quantifiers % 4.82/1.45 Prover 0: Proving ... % 4.82/1.45 Prover 1: Constructing countermodel ... % 4.82/1.47 Prover 4: Constructing countermodel ... % 7.71/1.88 Prover 0: proved (1235ms) % 7.71/1.88 % 7.71/1.88 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 7.71/1.88 % 7.71/1.88 Prover 2: stopped % 7.71/1.88 Prover 5: stopped % 7.71/1.88 Prover 3: stopped % 7.71/1.88 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.71/1.88 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.71/1.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.36/1.89 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.36/1.89 Prover 6: stopped % 8.36/1.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.36/1.91 Prover 11: Preprocessing ... % 8.36/1.92 Prover 8: Preprocessing ... % 8.36/1.92 Prover 7: Preprocessing ... % 8.36/1.93 Prover 10: Preprocessing ... % 8.36/1.93 Prover 13: Preprocessing ... % 9.00/1.98 Prover 8: Warning: ignoring some quantifiers % 9.00/1.99 Prover 7: Warning: ignoring some quantifiers % 9.00/2.00 Prover 8: Constructing countermodel ... % 9.00/2.00 Prover 7: Constructing countermodel ... % 9.00/2.01 Prover 10: Warning: ignoring some quantifiers % 9.00/2.03 Prover 10: Constructing countermodel ... % 9.00/2.04 Prover 13: Warning: ignoring some quantifiers % 9.00/2.06 Prover 13: Constructing countermodel ... % 9.00/2.07 Prover 11: Warning: ignoring some quantifiers % 9.00/2.08 Prover 11: Constructing countermodel ... % 9.95/2.14 Prover 4: Found proof (size 76) % 9.95/2.14 Prover 4: proved (1499ms) % 9.95/2.14 Prover 13: stopped % 9.95/2.14 Prover 8: stopped % 9.95/2.14 Prover 11: stopped % 9.95/2.14 Prover 1: stopped % 9.95/2.14 Prover 7: stopped % 9.95/2.14 Prover 10: stopped % 9.95/2.14 % 9.95/2.14 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 9.95/2.14 % 9.95/2.15 % SZS output start Proof for theBenchmark % 9.95/2.16 Assumptions after simplification: % 9.95/2.16 --------------------------------- % 9.95/2.16 % 9.95/2.16 (commutativity_k2_xboole_0) % 9.95/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) | ~ % 9.95/2.19 $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : ! % 9.95/2.19 [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) % 9.95/2.19 | (set_union2(v1, v0) = v2 & $i(v2))) % 9.95/2.19 % 9.95/2.19 (d1_zfmisc_1) % 9.95/2.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 9.95/2.19 (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 9.95/2.19 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v1) = v4)) & ! [v0: $i] : ! % 9.95/2.19 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (powerset(v0) = v1) | ~ % 9.95/2.19 (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ % 9.95/2.19 (v4 = 0) & subset(v2, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 9.95/2.19 : ( ~ (powerset(v0) = v1) | ~ (subset(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | % 9.95/2.19 ~ $i(v0) | in(v2, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 9.95/2.19 (powerset(v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 9.95/2.19 $i(v0) | subset(v2, v0) = 0) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 % 9.95/2.19 = v0 | ~ (powerset(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? % 9.95/2.19 [v4: any] : ? [v5: any] : (subset(v3, v1) = v5 & in(v3, v0) = v4 & $i(v3) & % 9.95/2.20 ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 | v4 = 0))) % 9.95/2.20 % 9.95/2.20 (d2_xboole_0) % 10.47/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 10.47/2.21 | ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | ~ % 10.47/2.21 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) % 10.47/2.21 & ~ (v5 = 0) & in(v3, v1) = v6 & in(v3, v0) = v5)) & ! [v0: $i] : ! % 10.47/2.21 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ % 10.47/2.21 (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) | % 10.47/2.21 ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & % 10.47/2.21 in(v3, v0) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : % 10.47/2.21 ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (set_union2(v0, v1) = % 10.47/2.21 v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 10.47/2.21 | ? [v5: any] : ? [v6: any] : (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 % 10.47/2.21 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 10.47/2.21 $i] : ! [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | % 10.47/2.21 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 10.47/2.21 (in(v3, v2) = v6 & in(v3, v0) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = % 10.47/2.21 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! % 10.47/2.21 [v4: any] : ( ~ (set_union2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | % 10.47/2.21 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, % 10.47/2.21 v2) = v6 & in(v3, v1) = v5 & (v6 = 0 | ( ~ (v5 = 0) & ~ (v4 = 0))))) & % 10.47/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_union2(v0, v1) % 10.47/2.21 = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 10.47/2.21 $i(v0) | ? [v4: any] : ? [v5: any] : (in(v3, v1) = v5 & in(v3, v0) = v4 & % 10.47/2.21 (v5 = 0 | v4 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 10.47/2.21 $i] : (v3 = v0 | ~ (set_union2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 10.47/2.21 $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (in(v4, % 10.47/2.21 v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v5 = 0) | ( % 10.47/2.21 ~ (v7 = 0) & ~ (v6 = 0))) & (v7 = 0 | v6 = 0 | v5 = 0))) % 10.47/2.21 % 10.47/2.21 (d3_tarski) % 10.47/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.47/2.21 (subset(v0, v1) = 0) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 10.47/2.21 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v0) = v4)) & ! [v0: $i] : ! % 10.47/2.21 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ % 10.47/2.21 $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3, v1) = v4 & % 10.47/2.21 in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 10.47/2.21 (subset(v0, v1) = 0) | ~ (in(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ % 10.47/2.21 $i(v0) | in(v2, v1) = 0) % 10.47/2.21 % 10.47/2.21 (t1_xboole_1) % 10.47/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.47/2.21 (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 10.47/2.21 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = v4)) & ! [v0: $i] : % 10.47/2.21 ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (subset(v0, v2) = v3) % 10.47/2.21 | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] % 10.47/2.21 : ( ~ (v4 = 0) & subset(v1, v2) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: % 10.47/2.21 $i] : ( ~ (subset(v1, v2) = 0) | ~ (subset(v0, v1) = 0) | ~ $i(v2) | ~ % 10.47/2.21 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0) % 10.47/2.21 % 10.47/2.21 (t7_xboole_1) % 10.47/2.21 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v0, v1) = v2) | ~ % 10.47/2.21 $i(v1) | ~ $i(v0) | subset(v0, v2) = 0) % 10.47/2.21 % 10.47/2.21 (t81_zfmisc_1) % 10.47/2.21 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 10.47/2.21 $i] : ? [v6: $i] : ? [v7: int] : ( ~ (v7 = 0) & powerset(v5) = v6 & % 10.47/2.21 powerset(v1) = v3 & powerset(v0) = v2 & subset(v4, v6) = v7 & set_union2(v2, % 10.47/2.21 v3) = v4 & set_union2(v0, v1) = v5 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & % 10.47/2.21 $i(v2) & $i(v1) & $i(v0)) % 10.47/2.21 % 10.47/2.21 (function-axioms) % 10.47/2.22 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 10.47/2.22 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 10.47/2.22 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 10.47/2.22 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0: % 10.47/2.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 10.47/2.22 : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 10.47/2.22 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 10.47/2.22 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 10.47/2.22 [v2: $i] : (v1 = v0 | ~ (powerset(v2) = v1) | ~ (powerset(v2) = v0)) % 10.47/2.22 % 10.47/2.22 Further assumptions not needed in the proof: % 10.47/2.22 -------------------------------------------- % 10.47/2.22 antisymmetry_r2_hidden, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 10.47/2.22 rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski % 10.47/2.22 % 10.47/2.22 Those formulas are unsatisfiable: % 10.47/2.22 --------------------------------- % 10.47/2.22 % 10.47/2.22 Begin of proof % 10.47/2.22 | % 10.47/2.22 | ALPHA: (commutativity_k2_xboole_0) implies: % 10.47/2.22 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_union2(v1, v0) = v2) % 10.47/2.22 | | ~ $i(v1) | ~ $i(v0) | (set_union2(v0, v1) = v2 & $i(v2))) % 10.47/2.22 | % 10.47/2.22 | ALPHA: (d1_zfmisc_1) implies: % 10.47/2.22 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.47/2.22 | (powerset(v0) = v1) | ~ (in(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 10.47/2.22 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v2, v0) = v4)) % 10.47/2.22 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.47/2.22 | (powerset(v0) = v1) | ~ (subset(v2, v0) = v3) | ~ $i(v2) | ~ % 10.47/2.22 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & in(v2, v1) = v4)) % 10.47/2.22 | % 10.47/2.22 | ALPHA: (d2_xboole_0) implies: % 10.47/2.22 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.47/2.22 | (set_union2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 10.47/2.22 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 10.47/2.22 | (in(v3, v1) = v5 & in(v3, v0) = v4 & (v5 = 0 | v4 = 0))) % 10.47/2.22 | % 10.47/2.22 | ALPHA: (d3_tarski) implies: % 10.47/2.22 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) % 10.47/2.22 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ % 10.47/2.22 | (v4 = 0) & in(v3, v1) = v4 & in(v3, v0) = 0 & $i(v3))) % 10.47/2.22 | % 10.47/2.22 | ALPHA: (t1_xboole_1) implies: % 10.47/2.22 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 10.47/2.22 | (subset(v1, v2) = 0) | ~ (subset(v0, v2) = v3) | ~ $i(v2) | ~ % 10.47/2.22 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & subset(v0, v1) = % 10.47/2.22 | v4)) % 10.47/2.22 | % 10.47/2.22 | ALPHA: (function-axioms) implies: % 10.47/2.22 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 10.47/2.22 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) % 10.47/2.22 | % 10.47/2.23 | DELTA: instantiating (t81_zfmisc_1) with fresh symbols all_20_0, all_20_1, % 10.47/2.23 | all_20_2, all_20_3, all_20_4, all_20_5, all_20_6, all_20_7 gives: % 10.47/2.23 | (8) ~ (all_20_0 = 0) & powerset(all_20_2) = all_20_1 & powerset(all_20_6) % 10.47/2.23 | = all_20_4 & powerset(all_20_7) = all_20_5 & subset(all_20_3, all_20_1) % 10.47/2.23 | = all_20_0 & set_union2(all_20_5, all_20_4) = all_20_3 & % 10.47/2.23 | set_union2(all_20_7, all_20_6) = all_20_2 & $i(all_20_1) & $i(all_20_2) % 10.47/2.23 | & $i(all_20_3) & $i(all_20_4) & $i(all_20_5) & $i(all_20_6) & % 10.47/2.23 | $i(all_20_7) % 10.47/2.23 | % 10.47/2.23 | ALPHA: (8) implies: % 10.47/2.23 | (9) ~ (all_20_0 = 0) % 10.47/2.23 | (10) $i(all_20_7) % 10.47/2.23 | (11) $i(all_20_6) % 10.47/2.23 | (12) $i(all_20_5) % 10.47/2.23 | (13) $i(all_20_4) % 10.47/2.23 | (14) $i(all_20_1) % 10.47/2.23 | (15) set_union2(all_20_7, all_20_6) = all_20_2 % 10.47/2.23 | (16) set_union2(all_20_5, all_20_4) = all_20_3 % 10.47/2.23 | (17) subset(all_20_3, all_20_1) = all_20_0 % 10.47/2.23 | (18) powerset(all_20_7) = all_20_5 % 10.47/2.23 | (19) powerset(all_20_6) = all_20_4 % 10.47/2.23 | (20) powerset(all_20_2) = all_20_1 % 10.47/2.23 | % 10.47/2.23 | GROUND_INST: instantiating (1) with all_20_6, all_20_7, all_20_2, simplifying % 10.47/2.23 | with (10), (11), (15) gives: % 10.47/2.23 | (21) set_union2(all_20_6, all_20_7) = all_20_2 & $i(all_20_2) % 10.47/2.23 | % 10.47/2.23 | ALPHA: (21) implies: % 10.47/2.23 | (22) $i(all_20_2) % 10.47/2.23 | (23) set_union2(all_20_6, all_20_7) = all_20_2 % 10.47/2.23 | % 10.47/2.23 | GROUND_INST: instantiating (t7_xboole_1) with all_20_7, all_20_6, all_20_2, % 10.47/2.23 | simplifying with (10), (11), (15) gives: % 10.47/2.23 | (24) subset(all_20_7, all_20_2) = 0 % 10.47/2.23 | % 10.47/2.23 | GROUND_INST: instantiating (1) with all_20_4, all_20_5, all_20_3, simplifying % 10.47/2.23 | with (12), (13), (16) gives: % 10.47/2.23 | (25) set_union2(all_20_4, all_20_5) = all_20_3 & $i(all_20_3) % 10.47/2.23 | % 10.47/2.23 | ALPHA: (25) implies: % 10.47/2.23 | (26) $i(all_20_3) % 10.47/2.23 | (27) set_union2(all_20_4, all_20_5) = all_20_3 % 10.47/2.23 | % 10.47/2.23 | GROUND_INST: instantiating (5) with all_20_3, all_20_1, all_20_0, simplifying % 10.47/2.23 | with (14), (17), (26) gives: % 10.47/2.23 | (28) all_20_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, % 10.47/2.23 | all_20_1) = v1 & in(v0, all_20_3) = 0 & $i(v0)) % 10.47/2.23 | % 10.47/2.23 | BETA: splitting (28) gives: % 10.47/2.23 | % 10.47/2.23 | Case 1: % 10.47/2.23 | | % 10.47/2.23 | | (29) all_20_0 = 0 % 10.47/2.23 | | % 10.47/2.23 | | REDUCE: (9), (29) imply: % 10.47/2.23 | | (30) $false % 10.47/2.23 | | % 10.47/2.23 | | CLOSE: (30) is inconsistent. % 10.47/2.23 | | % 10.47/2.24 | Case 2: % 10.47/2.24 | | % 10.47/2.24 | | (31) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & in(v0, all_20_1) = v1 & % 10.47/2.24 | | in(v0, all_20_3) = 0 & $i(v0)) % 10.47/2.24 | | % 10.47/2.24 | | DELTA: instantiating (31) with fresh symbols all_42_0, all_42_1 gives: % 10.47/2.24 | | (32) ~ (all_42_0 = 0) & in(all_42_1, all_20_1) = all_42_0 & in(all_42_1, % 10.47/2.24 | | all_20_3) = 0 & $i(all_42_1) % 10.47/2.24 | | % 10.47/2.24 | | ALPHA: (32) implies: % 10.47/2.24 | | (33) ~ (all_42_0 = 0) % 10.47/2.24 | | (34) $i(all_42_1) % 10.47/2.24 | | (35) in(all_42_1, all_20_3) = 0 % 10.47/2.24 | | (36) in(all_42_1, all_20_1) = all_42_0 % 10.47/2.24 | | % 10.47/2.24 | | GROUND_INST: instantiating (4) with all_20_5, all_20_4, all_20_3, all_42_1, % 10.47/2.24 | | simplifying with (12), (13), (16), (26), (34), (35) gives: % 10.47/2.24 | | (37) ? [v0: any] : ? [v1: any] : (in(all_42_1, all_20_4) = v1 & % 10.47/2.24 | | in(all_42_1, all_20_5) = v0 & (v1 = 0 | v0 = 0)) % 10.47/2.24 | | % 10.47/2.24 | | GROUND_INST: instantiating (2) with all_20_2, all_20_1, all_42_1, all_42_0, % 10.47/2.24 | | simplifying with (14), (20), (22), (34), (36) gives: % 10.47/2.24 | | (38) all_42_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_42_1, % 10.47/2.24 | | all_20_2) = v0) % 10.47/2.24 | | % 10.47/2.24 | | GROUND_INST: instantiating (t7_xboole_1) with all_20_6, all_20_7, all_20_2, % 10.47/2.24 | | simplifying with (10), (11), (23) gives: % 10.47/2.24 | | (39) subset(all_20_6, all_20_2) = 0 % 10.47/2.24 | | % 10.47/2.24 | | GROUND_INST: instantiating (4) with all_20_4, all_20_5, all_20_3, all_42_1, % 10.47/2.24 | | simplifying with (12), (13), (26), (27), (34), (35) gives: % 10.47/2.24 | | (40) ? [v0: any] : ? [v1: any] : (in(all_42_1, all_20_4) = v0 & % 10.47/2.24 | | in(all_42_1, all_20_5) = v1 & (v1 = 0 | v0 = 0)) % 10.47/2.24 | | % 10.47/2.24 | | DELTA: instantiating (40) with fresh symbols all_62_0, all_62_1 gives: % 10.47/2.24 | | (41) in(all_42_1, all_20_4) = all_62_1 & in(all_42_1, all_20_5) = % 10.47/2.24 | | all_62_0 & (all_62_0 = 0 | all_62_1 = 0) % 10.47/2.24 | | % 10.47/2.24 | | ALPHA: (41) implies: % 10.47/2.24 | | (42) in(all_42_1, all_20_5) = all_62_0 % 10.47/2.24 | | (43) in(all_42_1, all_20_4) = all_62_1 % 10.47/2.24 | | % 10.47/2.24 | | DELTA: instantiating (37) with fresh symbols all_66_0, all_66_1 gives: % 10.47/2.24 | | (44) in(all_42_1, all_20_4) = all_66_0 & in(all_42_1, all_20_5) = % 10.47/2.24 | | all_66_1 & (all_66_0 = 0 | all_66_1 = 0) % 10.47/2.24 | | % 10.47/2.24 | | ALPHA: (44) implies: % 10.47/2.24 | | (45) in(all_42_1, all_20_5) = all_66_1 % 10.47/2.24 | | (46) in(all_42_1, all_20_4) = all_66_0 % 10.47/2.24 | | (47) all_66_0 = 0 | all_66_1 = 0 % 10.47/2.24 | | % 10.47/2.24 | | BETA: splitting (38) gives: % 10.47/2.24 | | % 10.47/2.24 | | Case 1: % 10.47/2.24 | | | % 10.47/2.24 | | | (48) all_42_0 = 0 % 10.47/2.24 | | | % 10.47/2.24 | | | REDUCE: (33), (48) imply: % 10.47/2.24 | | | (49) $false % 10.47/2.24 | | | % 10.47/2.24 | | | CLOSE: (49) is inconsistent. % 10.47/2.24 | | | % 10.47/2.24 | | Case 2: % 10.47/2.24 | | | % 10.47/2.24 | | | (50) ? [v0: int] : ( ~ (v0 = 0) & subset(all_42_1, all_20_2) = v0) % 10.47/2.25 | | | % 10.47/2.25 | | | DELTA: instantiating (50) with fresh symbol all_72_0 gives: % 10.47/2.25 | | | (51) ~ (all_72_0 = 0) & subset(all_42_1, all_20_2) = all_72_0 % 10.47/2.25 | | | % 10.47/2.25 | | | ALPHA: (51) implies: % 10.47/2.25 | | | (52) ~ (all_72_0 = 0) % 10.47/2.25 | | | (53) subset(all_42_1, all_20_2) = all_72_0 % 10.47/2.25 | | | % 10.47/2.25 | | | GROUND_INST: instantiating (7) with all_62_0, all_66_1, all_20_5, % 10.47/2.25 | | | all_42_1, simplifying with (42), (45) gives: % 10.47/2.25 | | | (54) all_66_1 = all_62_0 % 10.47/2.25 | | | % 10.47/2.25 | | | GROUND_INST: instantiating (7) with all_62_1, all_66_0, all_20_4, % 10.47/2.25 | | | all_42_1, simplifying with (43), (46) gives: % 10.47/2.25 | | | (55) all_66_0 = all_62_1 % 10.47/2.25 | | | % 10.47/2.25 | | | GROUND_INST: instantiating (6) with all_42_1, all_20_7, all_20_2, % 10.47/2.25 | | | all_72_0, simplifying with (10), (22), (24), (34), (53) % 10.47/2.25 | | | gives: % 10.47/2.25 | | | (56) all_72_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_42_1, % 10.47/2.25 | | | all_20_7) = v0) % 10.47/2.25 | | | % 10.47/2.25 | | | GROUND_INST: instantiating (6) with all_42_1, all_20_6, all_20_2, % 10.47/2.25 | | | all_72_0, simplifying with (11), (22), (34), (39), (53) % 10.47/2.25 | | | gives: % 10.47/2.25 | | | (57) all_72_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & subset(all_42_1, % 10.47/2.25 | | | all_20_6) = v0) % 10.47/2.25 | | | % 10.47/2.25 | | | BETA: splitting (57) gives: % 10.47/2.25 | | | % 10.47/2.25 | | | Case 1: % 10.47/2.25 | | | | % 10.47/2.25 | | | | (58) all_72_0 = 0 % 10.47/2.25 | | | | % 10.47/2.25 | | | | REDUCE: (52), (58) imply: % 10.47/2.25 | | | | (59) $false % 10.47/2.25 | | | | % 10.47/2.25 | | | | CLOSE: (59) is inconsistent. % 10.47/2.25 | | | | % 10.47/2.25 | | | Case 2: % 10.47/2.25 | | | | % 10.47/2.25 | | | | (60) ? [v0: int] : ( ~ (v0 = 0) & subset(all_42_1, all_20_6) = v0) % 10.47/2.25 | | | | % 10.47/2.25 | | | | DELTA: instantiating (60) with fresh symbol all_95_0 gives: % 10.47/2.25 | | | | (61) ~ (all_95_0 = 0) & subset(all_42_1, all_20_6) = all_95_0 % 10.47/2.25 | | | | % 10.47/2.25 | | | | ALPHA: (61) implies: % 10.47/2.25 | | | | (62) ~ (all_95_0 = 0) % 10.47/2.25 | | | | (63) subset(all_42_1, all_20_6) = all_95_0 % 10.47/2.25 | | | | % 10.47/2.25 | | | | BETA: splitting (56) gives: % 10.47/2.25 | | | | % 10.47/2.25 | | | | Case 1: % 10.47/2.25 | | | | | % 10.47/2.25 | | | | | (64) all_72_0 = 0 % 10.47/2.25 | | | | | % 10.47/2.25 | | | | | REDUCE: (52), (64) imply: % 10.47/2.25 | | | | | (65) $false % 10.47/2.25 | | | | | % 10.47/2.25 | | | | | CLOSE: (65) is inconsistent. % 10.47/2.25 | | | | | % 10.47/2.25 | | | | Case 2: % 10.47/2.25 | | | | | % 10.47/2.25 | | | | | (66) ? [v0: int] : ( ~ (v0 = 0) & subset(all_42_1, all_20_7) = v0) % 10.47/2.25 | | | | | % 10.47/2.25 | | | | | DELTA: instantiating (66) with fresh symbol all_100_0 gives: % 10.47/2.25 | | | | | (67) ~ (all_100_0 = 0) & subset(all_42_1, all_20_7) = all_100_0 % 10.47/2.25 | | | | | % 10.47/2.25 | | | | | ALPHA: (67) implies: % 10.47/2.25 | | | | | (68) ~ (all_100_0 = 0) % 10.47/2.25 | | | | | (69) subset(all_42_1, all_20_7) = all_100_0 % 10.47/2.25 | | | | | % 10.47/2.25 | | | | | GROUND_INST: instantiating (3) with all_20_7, all_20_5, all_42_1, % 10.47/2.25 | | | | | all_100_0, simplifying with (10), (12), (18), (34), (69) % 10.47/2.25 | | | | | gives: % 10.47/2.25 | | | | | (70) all_100_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_42_1, % 10.47/2.25 | | | | | all_20_5) = v0) % 10.47/2.25 | | | | | % 10.47/2.25 | | | | | GROUND_INST: instantiating (3) with all_20_6, all_20_4, all_42_1, % 10.47/2.25 | | | | | all_95_0, simplifying with (11), (13), (19), (34), (63) % 10.47/2.25 | | | | | gives: % 10.47/2.25 | | | | | (71) all_95_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & in(all_42_1, % 10.47/2.25 | | | | | all_20_4) = v0) % 10.47/2.25 | | | | | % 10.47/2.26 | | | | | BETA: splitting (70) gives: % 10.47/2.26 | | | | | % 10.47/2.26 | | | | | Case 1: % 10.47/2.26 | | | | | | % 10.47/2.26 | | | | | | (72) all_100_0 = 0 % 10.47/2.26 | | | | | | % 10.47/2.26 | | | | | | REDUCE: (68), (72) imply: % 10.47/2.26 | | | | | | (73) $false % 10.47/2.26 | | | | | | % 10.47/2.26 | | | | | | CLOSE: (73) is inconsistent. % 10.47/2.26 | | | | | | % 10.47/2.26 | | | | | Case 2: % 10.47/2.26 | | | | | | % 10.47/2.26 | | | | | | (74) ? [v0: int] : ( ~ (v0 = 0) & in(all_42_1, all_20_5) = v0) % 10.47/2.26 | | | | | | % 10.47/2.26 | | | | | | DELTA: instantiating (74) with fresh symbol all_117_0 gives: % 10.47/2.26 | | | | | | (75) ~ (all_117_0 = 0) & in(all_42_1, all_20_5) = all_117_0 % 10.47/2.26 | | | | | | % 10.47/2.26 | | | | | | ALPHA: (75) implies: % 10.47/2.26 | | | | | | (76) ~ (all_117_0 = 0) % 10.47/2.26 | | | | | | (77) in(all_42_1, all_20_5) = all_117_0 % 10.47/2.26 | | | | | | % 10.47/2.26 | | | | | | BETA: splitting (71) gives: % 10.47/2.26 | | | | | | % 10.47/2.26 | | | | | | Case 1: % 10.47/2.26 | | | | | | | % 10.47/2.26 | | | | | | | (78) all_95_0 = 0 % 10.47/2.26 | | | | | | | % 10.47/2.26 | | | | | | | REDUCE: (62), (78) imply: % 10.47/2.26 | | | | | | | (79) $false % 10.47/2.26 | | | | | | | % 10.47/2.26 | | | | | | | CLOSE: (79) is inconsistent. % 10.47/2.26 | | | | | | | % 10.47/2.26 | | | | | | Case 2: % 10.47/2.26 | | | | | | | % 10.47/2.26 | | | | | | | (80) ? [v0: int] : ( ~ (v0 = 0) & in(all_42_1, all_20_4) = v0) % 10.47/2.26 | | | | | | | % 10.47/2.26 | | | | | | | DELTA: instantiating (80) with fresh symbol all_138_0 gives: % 10.47/2.26 | | | | | | | (81) ~ (all_138_0 = 0) & in(all_42_1, all_20_4) = all_138_0 % 10.47/2.26 | | | | | | | % 10.47/2.26 | | | | | | | ALPHA: (81) implies: % 10.47/2.26 | | | | | | | (82) ~ (all_138_0 = 0) % 10.47/2.26 | | | | | | | (83) in(all_42_1, all_20_4) = all_138_0 % 10.47/2.26 | | | | | | | % 10.47/2.26 | | | | | | | GROUND_INST: instantiating (7) with all_62_0, all_117_0, all_20_5, % 10.47/2.26 | | | | | | | all_42_1, simplifying with (42), (77) gives: % 10.47/2.26 | | | | | | | (84) all_117_0 = all_62_0 % 10.47/2.26 | | | | | | | % 10.47/2.26 | | | | | | | GROUND_INST: instantiating (7) with all_62_1, all_138_0, all_20_4, % 10.47/2.26 | | | | | | | all_42_1, simplifying with (43), (83) gives: % 10.47/2.26 | | | | | | | (85) all_138_0 = all_62_1 % 10.47/2.26 | | | | | | | % 10.47/2.26 | | | | | | | REDUCE: (82), (85) imply: % 10.47/2.26 | | | | | | | (86) ~ (all_62_1 = 0) % 10.47/2.26 | | | | | | | % 10.47/2.26 | | | | | | | REDUCE: (76), (84) imply: % 10.47/2.26 | | | | | | | (87) ~ (all_62_0 = 0) % 10.47/2.26 | | | | | | | % 10.47/2.26 | | | | | | | BETA: splitting (47) gives: % 10.47/2.26 | | | | | | | % 10.47/2.26 | | | | | | | Case 1: % 10.47/2.26 | | | | | | | | % 10.47/2.26 | | | | | | | | (88) all_66_0 = 0 % 10.47/2.26 | | | | | | | | % 10.47/2.26 | | | | | | | | COMBINE_EQS: (55), (88) imply: % 10.47/2.26 | | | | | | | | (89) all_62_1 = 0 % 10.47/2.26 | | | | | | | | % 10.47/2.26 | | | | | | | | SIMP: (89) implies: % 10.47/2.26 | | | | | | | | (90) all_62_1 = 0 % 10.47/2.26 | | | | | | | | % 10.47/2.26 | | | | | | | | REDUCE: (86), (90) imply: % 10.47/2.26 | | | | | | | | (91) $false % 10.47/2.26 | | | | | | | | % 10.47/2.26 | | | | | | | | CLOSE: (91) is inconsistent. % 10.47/2.26 | | | | | | | | % 10.47/2.26 | | | | | | | Case 2: % 10.47/2.26 | | | | | | | | % 10.47/2.26 | | | | | | | | (92) all_66_1 = 0 % 10.47/2.26 | | | | | | | | % 10.47/2.26 | | | | | | | | COMBINE_EQS: (54), (92) imply: % 10.47/2.26 | | | | | | | | (93) all_62_0 = 0 % 10.47/2.26 | | | | | | | | % 10.47/2.26 | | | | | | | | SIMP: (93) implies: % 10.47/2.26 | | | | | | | | (94) all_62_0 = 0 % 10.47/2.26 | | | | | | | | % 10.47/2.26 | | | | | | | | REDUCE: (87), (94) imply: % 10.47/2.26 | | | | | | | | (95) $false % 10.47/2.26 | | | | | | | | % 10.47/2.26 | | | | | | | | CLOSE: (95) is inconsistent. % 10.47/2.26 | | | | | | | | % 10.47/2.26 | | | | | | | End of split % 10.47/2.26 | | | | | | | % 10.47/2.26 | | | | | | End of split % 10.47/2.26 | | | | | | % 10.47/2.26 | | | | | End of split % 10.47/2.26 | | | | | % 10.47/2.26 | | | | End of split % 10.47/2.26 | | | | % 10.47/2.26 | | | End of split % 10.47/2.26 | | | % 10.47/2.26 | | End of split % 10.47/2.26 | | % 10.47/2.26 | End of split % 10.47/2.26 | % 10.47/2.26 End of proof % 10.47/2.26 % SZS output end Proof for theBenchmark % 10.47/2.26 % 10.47/2.26 1648ms %------------------------------------------------------------------------------