%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET945+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 : n005.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 15:27:09 EDT 2023 % Result : Theorem 8.86s 1.96s % Output : Proof 12.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.12 % Problem : SET945+1 : TPTP v8.1.2. Released v3.2.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n005.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Sat Aug 26 10:07:23 EDT 2023 % 0.12/0.34 % CPUTime : % 0.19/0.60 ________ _____ % 0.19/0.60 ___ __ \_________(_)________________________________ % 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.60 % 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.60 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.20/0.97 Prover 4: Preprocessing ... % 2.20/0.97 Prover 1: Preprocessing ... % 2.33/1.01 Prover 3: Preprocessing ... % 2.33/1.01 Prover 2: Preprocessing ... % 2.33/1.01 Prover 5: Preprocessing ... % 2.33/1.01 Prover 0: Preprocessing ... % 2.33/1.01 Prover 6: Preprocessing ... % 4.23/1.32 Prover 1: Warning: ignoring some quantifiers % 4.23/1.34 Prover 3: Warning: ignoring some quantifiers % 4.57/1.35 Prover 6: Proving ... % 4.57/1.35 Prover 5: Proving ... % 4.57/1.36 Prover 1: Constructing countermodel ... % 4.57/1.36 Prover 2: Proving ... % 4.57/1.36 Prover 3: Constructing countermodel ... % 4.57/1.36 Prover 4: Warning: ignoring some quantifiers % 4.57/1.38 Prover 4: Constructing countermodel ... % 5.31/1.43 Prover 0: Proving ... % 7.09/1.67 Prover 3: gave up % 7.09/1.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.09/1.69 Prover 7: Preprocessing ... % 7.81/1.76 Prover 7: Warning: ignoring some quantifiers % 7.81/1.77 Prover 7: Constructing countermodel ... % 8.02/1.82 Prover 7: gave up % 8.33/1.83 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.33/1.85 Prover 8: Preprocessing ... % 8.86/1.94 Prover 8: Warning: ignoring some quantifiers % 8.86/1.94 Prover 1: gave up % 8.86/1.94 Prover 8: Constructing countermodel ... % 8.86/1.95 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889 % 8.86/1.96 Prover 0: proved (1336ms) % 8.86/1.96 % 8.86/1.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.86/1.96 % 8.86/1.96 Prover 2: stopped % 8.86/1.96 Prover 5: stopped % 8.86/1.96 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.86/1.96 Prover 6: stopped % 8.86/1.97 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.86/1.97 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.86/1.97 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.86/1.98 Prover 9: Preprocessing ... % 8.86/1.99 Prover 13: Preprocessing ... % 8.86/1.99 Prover 11: Preprocessing ... % 8.86/1.99 Prover 10: Preprocessing ... % 8.86/2.00 Prover 16: Preprocessing ... % 8.86/2.03 Prover 10: Warning: ignoring some quantifiers % 8.86/2.03 Prover 16: Warning: ignoring some quantifiers % 8.86/2.04 Prover 10: Constructing countermodel ... % 8.86/2.04 Prover 16: Constructing countermodel ... % 9.70/2.08 Prover 10: gave up % 9.70/2.08 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 9.70/2.09 Prover 13: Warning: ignoring some quantifiers % 9.70/2.10 Prover 13: Constructing countermodel ... % 9.70/2.11 Prover 8: gave up % 9.70/2.12 Prover 9: Warning: ignoring some quantifiers % 9.70/2.12 Prover 19: Preprocessing ... % 9.70/2.12 Prover 9: Constructing countermodel ... % 9.70/2.13 Prover 9: stopped % 9.70/2.14 Prover 11: Warning: ignoring some quantifiers % 9.70/2.15 Prover 11: Constructing countermodel ... % 11.12/2.23 Prover 19: Warning: ignoring some quantifiers % 11.21/2.24 Prover 19: Constructing countermodel ... % 11.21/2.25 Prover 16: gave up % 11.74/2.31 Prover 4: Found proof (size 65) % 11.74/2.31 Prover 4: proved (1691ms) % 11.74/2.32 Prover 13: stopped % 11.74/2.32 Prover 11: stopped % 11.74/2.32 Prover 19: stopped % 11.74/2.32 % 11.74/2.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.74/2.32 % 11.74/2.33 % SZS output start Proof for theBenchmark % 11.74/2.33 Assumptions after simplification: % 11.74/2.33 --------------------------------- % 11.74/2.33 % 11.74/2.33 (d3_xboole_0) % 11.74/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 11.74/2.36 | ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = v4) | ~ $i(v3) | % 11.74/2.36 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v1) % 11.74/2.36 = v6 & in(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 11.74/2.36 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 11.74/2.36 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) | ~ % 11.74/2.36 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = % 11.74/2.36 v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : % 11.74/2.36 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ % 11.74/2.36 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) | ~ % 11.74/2.36 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (in(v3, v2) = % 11.74/2.36 v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : % 11.74/2.36 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) % 11.74/2.36 | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 11.74/2.36 (in(v3, v1) = 0 & in(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] % 11.74/2.36 : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | % 11.74/2.36 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 11.74/2.36 (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] % 11.74/2.36 : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (set_intersection2(v0, v1) = % 11.74/2.36 v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) % 11.74/2.36 | ? [v4: any] : ? [v5: any] : (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 % 11.74/2.36 = 0) | v5 = 0))) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 11.74/2.36 $i] : (v3 = v0 | ~ (set_intersection2(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) % 11.74/2.36 | ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : % 11.74/2.36 (in(v4, v2) = v7 & in(v4, v1) = v6 & in(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0) % 11.74/2.36 | ~ (v6 = 0) | ~ (v5 = 0)) & (v5 = 0 | (v7 = 0 & v6 = 0)))) % 11.74/2.37 % 11.74/2.37 (d4_tarski) % 12.06/2.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : ! [v4: $i] : (v3 = 0 % 12.06/2.37 | ~ (union(v0) = v1) | ~ (in(v4, v0) = 0) | ~ (in(v2, v1) = v3) | ~ % 12.06/2.37 $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: int] : ( ~ (v5 = 0) & % 12.06/2.37 in(v2, v4) = v5)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] % 12.06/2.37 : ! [v4: $i] : (v3 = 0 | ~ (union(v0) = v1) | ~ (in(v2, v4) = 0) | ~ % 12.06/2.37 (in(v2, v1) = v3) | ~ $i(v4) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: % 12.06/2.37 int] : ( ~ (v5 = 0) & in(v4, v0) = v5)) & ! [v0: $i] : ! [v1: $i] : ! % 12.06/2.37 [v2: $i] : ( ~ (union(v0) = v1) | ~ (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) % 12.06/2.37 | ~ $i(v0) | ? [v3: $i] : (in(v3, v0) = 0 & in(v2, v3) = 0 & $i(v3))) & ? % 12.06/2.37 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | ~ (union(v1) = v2) | ~ % 12.06/2.37 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: $i] : ? [v6: int] % 12.06/2.37 : ? [v7: int] : (in(v3, v0) = v4 & $i(v5) & $i(v3) & ( ~ (v4 = 0) | ( ! % 12.06/2.37 [v8: $i] : ( ~ (in(v8, v1) = 0) | ~ $i(v8) | ? [v9: int] : ( ~ (v9 = % 12.06/2.37 0) & in(v3, v8) = v9)) & ! [v8: $i] : ( ~ (in(v3, v8) = 0) | ~ % 12.06/2.37 $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & in(v8, v1) = v9)))) & (v4 = 0 % 12.06/2.37 | (v7 = 0 & v6 = 0 & in(v5, v1) = 0 & in(v3, v5) = 0)))) % 12.06/2.37 % 12.06/2.37 (symmetry_r1_xboole_0) % 12.06/2.37 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v1, v0) = % 12.06/2.37 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & disjoint(v0, % 12.06/2.37 v1) = v3)) & ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ % 12.06/2.37 $i(v1) | ~ $i(v0) | disjoint(v1, v0) = 0) % 12.06/2.37 % 12.06/2.37 (t4_xboole_0) % 12.06/2.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 12.06/2.38 (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | ~ % 12.06/2.38 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & disjoint(v0, v1) = v4)) & % 12.06/2.38 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) = % 12.06/2.38 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 12.06/2.38 (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0 & $i(v4) & $i(v3))) & ! % 12.06/2.38 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (set_intersection2(v0, v1) = v2) | % 12.06/2.38 ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ($i(v4) & % 12.06/2.38 ((v5 = 0 & in(v4, v2) = 0) | (v3 = 0 & disjoint(v0, v1) = 0)))) & ! [v0: % 12.06/2.38 $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 12.06/2.38 [v2: $i] : (set_intersection2(v0, v1) = v2 & $i(v2) & ! [v3: $i] : ( ~ % 12.06/2.38 (in(v3, v2) = 0) | ~ $i(v3)))) % 12.06/2.38 % 12.06/2.38 (t98_zfmisc_1) % 12.06/2.38 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 12.06/2.38 disjoint(v2, v1) = v3 & union(v0) = v2 & $i(v2) & $i(v1) & $i(v0) & ! [v4: % 12.06/2.38 $i] : ! [v5: int] : (v5 = 0 | ~ (disjoint(v4, v1) = v5) | ~ $i(v4) | ? % 12.06/2.38 [v6: int] : ( ~ (v6 = 0) & in(v4, v0) = v6)) & ! [v4: $i] : ( ~ (in(v4, % 12.06/2.38 v0) = 0) | ~ $i(v4) | disjoint(v4, v1) = 0)) % 12.06/2.38 % 12.06/2.38 (function-axioms) % 12.06/2.38 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 12.06/2.38 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 12.06/2.38 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 12.06/2.38 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & ! % 12.06/2.38 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 12.06/2.38 $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0: % 12.06/2.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | % 12.06/2.38 ~ (empty(v2) = v1) | ~ (empty(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! % 12.06/2.38 [v2: $i] : (v1 = v0 | ~ (union(v2) = v1) | ~ (union(v2) = v0)) % 12.06/2.38 % 12.06/2.38 Further assumptions not needed in the proof: % 12.06/2.38 -------------------------------------------- % 12.06/2.38 antisymmetry_r2_hidden, commutativity_k3_xboole_0, idempotence_k3_xboole_0, % 12.06/2.38 rc1_xboole_0, rc2_xboole_0 % 12.06/2.38 % 12.06/2.38 Those formulas are unsatisfiable: % 12.06/2.38 --------------------------------- % 12.06/2.38 % 12.06/2.38 Begin of proof % 12.06/2.38 | % 12.06/2.38 | ALPHA: (d3_xboole_0) implies: % 12.06/2.38 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 12.06/2.38 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = 0) | ~ $i(v3) | % 12.06/2.38 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 12.06/2.38 | (in(v3, v2) = v5 & in(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) % 12.06/2.38 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 12.06/2.38 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = 0) | ~ $i(v3) | % 12.06/2.38 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : % 12.06/2.38 | (in(v3, v2) = v5 & in(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) % 12.06/2.38 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 12.06/2.38 | (set_intersection2(v0, v1) = v2) | ~ (in(v3, v2) = 0) | ~ $i(v3) | % 12.06/2.38 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (in(v3, v1) = 0 & in(v3, v0) = 0)) % 12.06/2.38 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 12.06/2.38 | ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v0) = v4) | ~ $i(v3) % 12.06/2.38 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 12.06/2.38 | (in(v3, v2) = v5 & in(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = % 12.06/2.38 | 0)))) % 12.06/2.39 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : % 12.06/2.39 | ( ~ (set_intersection2(v0, v1) = v2) | ~ (in(v3, v1) = v4) | ~ $i(v3) % 12.06/2.39 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : % 12.06/2.39 | (in(v3, v2) = v5 & in(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 = % 12.06/2.39 | 0)))) % 12.06/2.39 | % 12.06/2.39 | ALPHA: (d4_tarski) implies: % 12.06/2.39 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (union(v0) = v1) | ~ % 12.06/2.39 | (in(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 12.06/2.39 | (in(v3, v0) = 0 & in(v2, v3) = 0 & $i(v3))) % 12.06/2.39 | % 12.06/2.39 | ALPHA: (symmetry_r1_xboole_0) implies: % 12.06/2.39 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v1, % 12.06/2.39 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & % 12.06/2.39 | disjoint(v0, v1) = v3)) % 12.06/2.39 | % 12.06/2.39 | ALPHA: (t4_xboole_0) implies: % 12.06/2.39 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ % 12.06/2.39 | $i(v0) | ? [v2: $i] : (set_intersection2(v0, v1) = v2 & $i(v2) & ! % 12.06/2.39 | [v3: $i] : ( ~ (in(v3, v2) = 0) | ~ $i(v3)))) % 12.06/2.39 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, % 12.06/2.39 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 12.06/2.39 | (set_intersection2(v0, v1) = v3 & in(v4, v3) = 0 & $i(v4) & $i(v3))) % 12.06/2.39 | % 12.06/2.39 | ALPHA: (function-axioms) implies: % 12.06/2.39 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 12.06/2.39 | : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = % 12.06/2.39 | v0)) % 12.06/2.39 | % 12.06/2.39 | DELTA: instantiating (t98_zfmisc_1) with fresh symbols all_14_0, all_14_1, % 12.06/2.39 | all_14_2, all_14_3 gives: % 12.06/2.39 | (11) ~ (all_14_0 = 0) & disjoint(all_14_1, all_14_2) = all_14_0 & % 12.06/2.39 | union(all_14_3) = all_14_1 & $i(all_14_1) & $i(all_14_2) & % 12.06/2.39 | $i(all_14_3) & ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (disjoint(v0, % 12.06/2.39 | all_14_2) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & % 12.06/2.39 | in(v0, all_14_3) = v2)) & ! [v0: $i] : ( ~ (in(v0, all_14_3) = 0) % 12.06/2.39 | | ~ $i(v0) | disjoint(v0, all_14_2) = 0) % 12.06/2.39 | % 12.06/2.39 | ALPHA: (11) implies: % 12.06/2.39 | (12) ~ (all_14_0 = 0) % 12.06/2.39 | (13) $i(all_14_3) % 12.06/2.39 | (14) $i(all_14_2) % 12.06/2.39 | (15) $i(all_14_1) % 12.06/2.39 | (16) union(all_14_3) = all_14_1 % 12.06/2.39 | (17) disjoint(all_14_1, all_14_2) = all_14_0 % 12.06/2.39 | (18) ! [v0: $i] : ( ~ (in(v0, all_14_3) = 0) | ~ $i(v0) | disjoint(v0, % 12.06/2.39 | all_14_2) = 0) % 12.06/2.39 | % 12.06/2.39 | GROUND_INST: instantiating (7) with all_14_2, all_14_1, all_14_0, simplifying % 12.06/2.39 | with (14), (15), (17) gives: % 12.06/2.39 | (19) all_14_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & disjoint(all_14_2, % 12.06/2.39 | all_14_1) = v0) % 12.06/2.39 | % 12.06/2.39 | GROUND_INST: instantiating (9) with all_14_1, all_14_2, all_14_0, simplifying % 12.06/2.39 | with (14), (15), (17) gives: % 12.06/2.40 | (20) all_14_0 = 0 | ? [v0: $i] : ? [v1: $i] : % 12.06/2.40 | (set_intersection2(all_14_1, all_14_2) = v0 & in(v1, v0) = 0 & $i(v1) % 12.06/2.40 | & $i(v0)) % 12.06/2.40 | % 12.06/2.40 | BETA: splitting (20) gives: % 12.06/2.40 | % 12.06/2.40 | Case 1: % 12.06/2.40 | | % 12.06/2.40 | | (21) all_14_0 = 0 % 12.06/2.40 | | % 12.06/2.40 | | REDUCE: (12), (21) imply: % 12.06/2.40 | | (22) $false % 12.06/2.40 | | % 12.06/2.40 | | CLOSE: (22) is inconsistent. % 12.06/2.40 | | % 12.06/2.40 | Case 2: % 12.06/2.40 | | % 12.06/2.40 | | (23) ? [v0: $i] : ? [v1: $i] : (set_intersection2(all_14_1, all_14_2) = % 12.06/2.40 | | v0 & in(v1, v0) = 0 & $i(v1) & $i(v0)) % 12.06/2.40 | | % 12.06/2.40 | | DELTA: instantiating (23) with fresh symbols all_28_0, all_28_1 gives: % 12.06/2.40 | | (24) set_intersection2(all_14_1, all_14_2) = all_28_1 & in(all_28_0, % 12.06/2.40 | | all_28_1) = 0 & $i(all_28_0) & $i(all_28_1) % 12.06/2.40 | | % 12.06/2.40 | | ALPHA: (24) implies: % 12.06/2.40 | | (25) $i(all_28_1) % 12.06/2.40 | | (26) $i(all_28_0) % 12.06/2.40 | | (27) in(all_28_0, all_28_1) = 0 % 12.06/2.40 | | (28) set_intersection2(all_14_1, all_14_2) = all_28_1 % 12.06/2.40 | | % 12.06/2.40 | | BETA: splitting (19) gives: % 12.06/2.40 | | % 12.06/2.40 | | Case 1: % 12.06/2.40 | | | % 12.06/2.40 | | | (29) all_14_0 = 0 % 12.06/2.40 | | | % 12.06/2.40 | | | REDUCE: (12), (29) imply: % 12.06/2.40 | | | (30) $false % 12.06/2.40 | | | % 12.06/2.40 | | | CLOSE: (30) is inconsistent. % 12.06/2.40 | | | % 12.06/2.40 | | Case 2: % 12.06/2.40 | | | % 12.06/2.40 | | | (31) ? [v0: int] : ( ~ (v0 = 0) & disjoint(all_14_2, all_14_1) = v0) % 12.06/2.40 | | | % 12.06/2.40 | | | DELTA: instantiating (31) with fresh symbol all_34_0 gives: % 12.06/2.40 | | | (32) ~ (all_34_0 = 0) & disjoint(all_14_2, all_14_1) = all_34_0 % 12.06/2.40 | | | % 12.06/2.40 | | | ALPHA: (32) implies: % 12.06/2.40 | | | (33) ~ (all_34_0 = 0) % 12.06/2.40 | | | (34) disjoint(all_14_2, all_14_1) = all_34_0 % 12.06/2.40 | | | % 12.06/2.40 | | | GROUND_INST: instantiating (3) with all_14_1, all_14_2, all_28_1, % 12.06/2.40 | | | all_28_0, simplifying with (14), (15), (25), (26), (27), (28) % 12.06/2.40 | | | gives: % 12.06/2.40 | | | (35) in(all_28_0, all_14_1) = 0 & in(all_28_0, all_14_2) = 0 % 12.06/2.40 | | | % 12.06/2.40 | | | ALPHA: (35) implies: % 12.06/2.40 | | | (36) in(all_28_0, all_14_2) = 0 % 12.06/2.40 | | | (37) in(all_28_0, all_14_1) = 0 % 12.06/2.40 | | | % 12.06/2.40 | | | GROUND_INST: instantiating (9) with all_14_2, all_14_1, all_34_0, % 12.06/2.40 | | | simplifying with (14), (15), (34) gives: % 12.06/2.40 | | | (38) all_34_0 = 0 | ? [v0: $i] : ? [v1: $i] : % 12.06/2.40 | | | (set_intersection2(all_14_2, all_14_1) = v0 & in(v1, v0) = 0 & % 12.06/2.40 | | | $i(v1) & $i(v0)) % 12.06/2.40 | | | % 12.06/2.40 | | | BETA: splitting (38) gives: % 12.06/2.40 | | | % 12.06/2.40 | | | Case 1: % 12.06/2.40 | | | | % 12.06/2.40 | | | | (39) all_34_0 = 0 % 12.06/2.40 | | | | % 12.06/2.40 | | | | REDUCE: (33), (39) imply: % 12.06/2.40 | | | | (40) $false % 12.06/2.40 | | | | % 12.06/2.40 | | | | CLOSE: (40) is inconsistent. % 12.06/2.40 | | | | % 12.06/2.40 | | | Case 2: % 12.06/2.40 | | | | % 12.06/2.40 | | | | % 12.06/2.40 | | | | GROUND_INST: instantiating (6) with all_14_3, all_14_1, all_28_0, % 12.06/2.40 | | | | simplifying with (13), (15), (16), (26), (37) gives: % 12.06/2.40 | | | | (41) ? [v0: $i] : (in(v0, all_14_3) = 0 & in(all_28_0, v0) = 0 & % 12.06/2.40 | | | | $i(v0)) % 12.06/2.40 | | | | % 12.06/2.40 | | | | DELTA: instantiating (41) with fresh symbol all_79_0 gives: % 12.06/2.40 | | | | (42) in(all_79_0, all_14_3) = 0 & in(all_28_0, all_79_0) = 0 & % 12.06/2.40 | | | | $i(all_79_0) % 12.06/2.40 | | | | % 12.06/2.40 | | | | ALPHA: (42) implies: % 12.06/2.40 | | | | (43) $i(all_79_0) % 12.06/2.40 | | | | (44) in(all_28_0, all_79_0) = 0 % 12.06/2.40 | | | | (45) in(all_79_0, all_14_3) = 0 % 12.06/2.40 | | | | % 12.06/2.40 | | | | GROUND_INST: instantiating (18) with all_79_0, simplifying with (43), % 12.06/2.41 | | | | (45) gives: % 12.06/2.41 | | | | (46) disjoint(all_79_0, all_14_2) = 0 % 12.06/2.41 | | | | % 12.06/2.41 | | | | GROUND_INST: instantiating (8) with all_79_0, all_14_2, simplifying with % 12.06/2.41 | | | | (14), (43), (46) gives: % 12.06/2.41 | | | | (47) ? [v0: $i] : (set_intersection2(all_79_0, all_14_2) = v0 & % 12.06/2.41 | | | | $i(v0) & ! [v1: $i] : ( ~ (in(v1, v0) = 0) | ~ $i(v1))) % 12.06/2.41 | | | | % 12.06/2.41 | | | | DELTA: instantiating (47) with fresh symbol all_131_0 gives: % 12.06/2.41 | | | | (48) set_intersection2(all_79_0, all_14_2) = all_131_0 & % 12.06/2.41 | | | | $i(all_131_0) & ! [v0: $i] : ( ~ (in(v0, all_131_0) = 0) | ~ % 12.06/2.41 | | | | $i(v0)) % 12.06/2.41 | | | | % 12.06/2.41 | | | | ALPHA: (48) implies: % 12.06/2.41 | | | | (49) $i(all_131_0) % 12.06/2.41 | | | | (50) set_intersection2(all_79_0, all_14_2) = all_131_0 % 12.06/2.41 | | | | (51) ! [v0: $i] : ( ~ (in(v0, all_131_0) = 0) | ~ $i(v0)) % 12.06/2.41 | | | | % 12.06/2.41 | | | | GROUND_INST: instantiating (1) with all_79_0, all_14_2, all_131_0, % 12.06/2.41 | | | | all_28_0, simplifying with (14), (26), (43), (44), (49), % 12.06/2.41 | | | | (50) gives: % 12.06/2.41 | | | | (52) ? [v0: any] : ? [v1: any] : (in(all_28_0, all_131_0) = v1 & % 12.06/2.41 | | | | in(all_28_0, all_14_2) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 12.06/2.41 | | | | % 12.06/2.41 | | | | GROUND_INST: instantiating (4) with all_79_0, all_14_2, all_131_0, % 12.06/2.41 | | | | all_28_0, 0, simplifying with (14), (26), (43), (44), (49), % 12.06/2.41 | | | | (50) gives: % 12.06/2.41 | | | | (53) ? [v0: any] : ? [v1: any] : (in(all_28_0, all_131_0) = v0 & % 12.06/2.41 | | | | in(all_28_0, all_14_2) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 12.06/2.41 | | | | % 12.06/2.41 | | | | GROUND_INST: instantiating (2) with all_79_0, all_14_2, all_131_0, % 12.06/2.41 | | | | all_28_0, simplifying with (14), (26), (36), (43), (49), % 12.06/2.41 | | | | (50) gives: % 12.06/2.41 | | | | (54) ? [v0: any] : ? [v1: any] : (in(all_28_0, all_131_0) = v1 & % 12.06/2.41 | | | | in(all_28_0, all_79_0) = v0 & ( ~ (v0 = 0) | v1 = 0)) % 12.06/2.41 | | | | % 12.06/2.41 | | | | GROUND_INST: instantiating (5) with all_79_0, all_14_2, all_131_0, % 12.06/2.41 | | | | all_28_0, 0, simplifying with (14), (26), (36), (43), (49), % 12.06/2.41 | | | | (50) gives: % 12.06/2.41 | | | | (55) ? [v0: any] : ? [v1: any] : (in(all_28_0, all_131_0) = v0 & % 12.06/2.41 | | | | in(all_28_0, all_79_0) = v1 & ( ~ (v0 = 0) | v1 = 0)) % 12.06/2.41 | | | | % 12.06/2.41 | | | | DELTA: instantiating (55) with fresh symbols all_144_0, all_144_1 gives: % 12.06/2.41 | | | | (56) in(all_28_0, all_131_0) = all_144_1 & in(all_28_0, all_79_0) = % 12.06/2.41 | | | | all_144_0 & ( ~ (all_144_1 = 0) | all_144_0 = 0) % 12.06/2.41 | | | | % 12.06/2.41 | | | | ALPHA: (56) implies: % 12.06/2.41 | | | | (57) in(all_28_0, all_131_0) = all_144_1 % 12.06/2.41 | | | | % 12.06/2.41 | | | | DELTA: instantiating (54) with fresh symbols all_146_0, all_146_1 gives: % 12.06/2.41 | | | | (58) in(all_28_0, all_131_0) = all_146_0 & in(all_28_0, all_79_0) = % 12.06/2.41 | | | | all_146_1 & ( ~ (all_146_1 = 0) | all_146_0 = 0) % 12.06/2.41 | | | | % 12.06/2.41 | | | | ALPHA: (58) implies: % 12.06/2.41 | | | | (59) in(all_28_0, all_131_0) = all_146_0 % 12.06/2.41 | | | | % 12.06/2.41 | | | | DELTA: instantiating (53) with fresh symbols all_148_0, all_148_1 gives: % 12.06/2.41 | | | | (60) in(all_28_0, all_131_0) = all_148_1 & in(all_28_0, all_14_2) = % 12.06/2.41 | | | | all_148_0 & ( ~ (all_148_1 = 0) | all_148_0 = 0) % 12.06/2.41 | | | | % 12.06/2.41 | | | | ALPHA: (60) implies: % 12.06/2.41 | | | | (61) in(all_28_0, all_131_0) = all_148_1 % 12.06/2.41 | | | | % 12.06/2.41 | | | | DELTA: instantiating (52) with fresh symbols all_154_0, all_154_1 gives: % 12.06/2.41 | | | | (62) in(all_28_0, all_131_0) = all_154_0 & in(all_28_0, all_14_2) = % 12.06/2.41 | | | | all_154_1 & ( ~ (all_154_1 = 0) | all_154_0 = 0) % 12.06/2.42 | | | | % 12.06/2.42 | | | | ALPHA: (62) implies: % 12.06/2.42 | | | | (63) in(all_28_0, all_14_2) = all_154_1 % 12.06/2.42 | | | | (64) in(all_28_0, all_131_0) = all_154_0 % 12.06/2.42 | | | | (65) ~ (all_154_1 = 0) | all_154_0 = 0 % 12.06/2.42 | | | | % 12.06/2.42 | | | | GROUND_INST: instantiating (10) with 0, all_154_1, all_14_2, all_28_0, % 12.06/2.42 | | | | simplifying with (36), (63) gives: % 12.06/2.42 | | | | (66) all_154_1 = 0 % 12.06/2.42 | | | | % 12.06/2.42 | | | | GROUND_INST: instantiating (10) with all_144_1, all_148_1, all_131_0, % 12.06/2.42 | | | | all_28_0, simplifying with (57), (61) gives: % 12.06/2.42 | | | | (67) all_148_1 = all_144_1 % 12.06/2.42 | | | | % 12.06/2.42 | | | | GROUND_INST: instantiating (10) with all_148_1, all_154_0, all_131_0, % 12.06/2.42 | | | | all_28_0, simplifying with (61), (64) gives: % 12.06/2.42 | | | | (68) all_154_0 = all_148_1 % 12.06/2.42 | | | | % 12.06/2.42 | | | | GROUND_INST: instantiating (10) with all_146_0, all_154_0, all_131_0, % 12.06/2.42 | | | | all_28_0, simplifying with (59), (64) gives: % 12.06/2.42 | | | | (69) all_154_0 = all_146_0 % 12.06/2.42 | | | | % 12.06/2.42 | | | | COMBINE_EQS: (68), (69) imply: % 12.06/2.42 | | | | (70) all_148_1 = all_146_0 % 12.06/2.42 | | | | % 12.06/2.42 | | | | SIMP: (70) implies: % 12.06/2.42 | | | | (71) all_148_1 = all_146_0 % 12.06/2.42 | | | | % 12.06/2.42 | | | | COMBINE_EQS: (67), (71) imply: % 12.06/2.42 | | | | (72) all_146_0 = all_144_1 % 12.06/2.42 | | | | % 12.06/2.42 | | | | SIMP: (72) implies: % 12.06/2.42 | | | | (73) all_146_0 = all_144_1 % 12.06/2.42 | | | | % 12.06/2.42 | | | | COMBINE_EQS: (69), (73) imply: % 12.06/2.42 | | | | (74) all_154_0 = all_144_1 % 12.06/2.42 | | | | % 12.06/2.42 | | | | BETA: splitting (65) gives: % 12.06/2.42 | | | | % 12.06/2.42 | | | | Case 1: % 12.06/2.42 | | | | | % 12.06/2.42 | | | | | (75) ~ (all_154_1 = 0) % 12.06/2.42 | | | | | % 12.06/2.42 | | | | | REDUCE: (66), (75) imply: % 12.06/2.42 | | | | | (76) $false % 12.06/2.42 | | | | | % 12.06/2.42 | | | | | CLOSE: (76) is inconsistent. % 12.06/2.42 | | | | | % 12.06/2.42 | | | | Case 2: % 12.06/2.42 | | | | | % 12.06/2.42 | | | | | (77) all_154_0 = 0 % 12.06/2.42 | | | | | % 12.06/2.42 | | | | | COMBINE_EQS: (74), (77) imply: % 12.06/2.42 | | | | | (78) all_144_1 = 0 % 12.06/2.42 | | | | | % 12.06/2.42 | | | | | SIMP: (78) implies: % 12.06/2.42 | | | | | (79) all_144_1 = 0 % 12.06/2.42 | | | | | % 12.06/2.42 | | | | | REDUCE: (57), (79) imply: % 12.06/2.42 | | | | | (80) in(all_28_0, all_131_0) = 0 % 12.06/2.42 | | | | | % 12.06/2.42 | | | | | GROUND_INST: instantiating (51) with all_28_0, simplifying with (26), % 12.06/2.42 | | | | | (80) gives: % 12.06/2.42 | | | | | (81) $false % 12.06/2.42 | | | | | % 12.06/2.42 | | | | | CLOSE: (81) is inconsistent. % 12.06/2.42 | | | | | % 12.06/2.42 | | | | End of split % 12.06/2.42 | | | | % 12.06/2.42 | | | End of split % 12.06/2.42 | | | % 12.06/2.42 | | End of split % 12.06/2.42 | | % 12.06/2.42 | End of split % 12.06/2.42 | % 12.06/2.42 End of proof % 12.06/2.42 % SZS output end Proof for theBenchmark % 12.06/2.42 % 12.06/2.42 1820ms %------------------------------------------------------------------------------