%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET630+3 : TPTP v8.1.2. Released v2.2.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n004.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 15:25:45 EDT 2023 % Result : Theorem 7.78s 1.99s % Output : Proof 11.29s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SET630+3 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.31 % Computer : n004.cluster.edu % 0.11/0.31 % Model : x86_64 x86_64 % 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.31 % Memory : 8042.1875MB % 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.31 % CPULimit : 300 % 0.11/0.31 % WCLimit : 300 % 0.11/0.31 % DateTime : Sat Aug 26 13:25:52 EDT 2023 % 0.11/0.32 % CPUTime : % 0.17/0.60 ________ _____ % 0.17/0.60 ___ __ \_________(_)________________________________ % 0.17/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.60 % 0.17/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.60 (2023-06-19) % 0.17/0.60 % 0.17/0.60 (c) Philipp Rümmer, 2009-2023 % 0.17/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.60 Amanda Stjerna. % 0.17/0.60 Free software under BSD-3-Clause. % 0.17/0.60 % 0.17/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.60 % 0.17/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.17/0.61 Running up to 7 provers in parallel. % 0.17/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.17/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 2.25/1.09 Prover 1: Preprocessing ... % 2.25/1.09 Prover 4: Preprocessing ... % 2.75/1.15 Prover 0: Preprocessing ... % 2.75/1.15 Prover 6: Preprocessing ... % 2.75/1.15 Prover 3: Preprocessing ... % 2.75/1.15 Prover 5: Preprocessing ... % 2.75/1.15 Prover 2: Preprocessing ... % 5.08/1.54 Prover 3: Warning: ignoring some quantifiers % 5.08/1.55 Prover 1: Warning: ignoring some quantifiers % 5.08/1.56 Prover 6: Proving ... % 5.60/1.57 Prover 5: Proving ... % 5.60/1.58 Prover 1: Constructing countermodel ... % 5.60/1.58 Prover 3: Constructing countermodel ... % 5.79/1.60 Prover 2: Proving ... % 5.79/1.61 Prover 4: Warning: ignoring some quantifiers % 5.79/1.62 Prover 0: Proving ... % 5.79/1.63 Prover 4: Constructing countermodel ... % 7.78/1.91 Prover 3: gave up % 7.78/1.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.78/1.92 Prover 1: gave up % 7.78/1.92 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.78/1.96 Prover 7: Preprocessing ... % 7.78/1.97 Prover 8: Preprocessing ... % 7.78/1.99 Prover 0: proved (1362ms) % 7.78/1.99 % 7.78/1.99 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 7.78/1.99 % 7.78/2.00 Prover 5: stopped % 7.78/2.00 Prover 2: stopped % 7.78/2.01 Prover 6: stopped % 7.78/2.02 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 7.78/2.02 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 7.78/2.02 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 7.78/2.02 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 7.78/2.03 Prover 10: Preprocessing ... % 7.78/2.05 Prover 7: Warning: ignoring some quantifiers % 7.78/2.05 Prover 13: Preprocessing ... % 7.78/2.06 Prover 7: Constructing countermodel ... % 8.11/2.06 Prover 11: Preprocessing ... % 8.11/2.07 Prover 16: Preprocessing ... % 8.11/2.12 Prover 13: Warning: ignoring some quantifiers % 8.11/2.12 Prover 13: Constructing countermodel ... % 8.11/2.13 Prover 8: Warning: ignoring some quantifiers % 8.11/2.13 Prover 10: Warning: ignoring some quantifiers % 8.11/2.15 Prover 8: Constructing countermodel ... % 9.62/2.16 Prover 16: Warning: ignoring some quantifiers % 9.62/2.16 Prover 10: Constructing countermodel ... % 9.62/2.18 Prover 16: Constructing countermodel ... % 9.62/2.22 Prover 4: Found proof (size 68) % 9.62/2.22 Prover 4: proved (1588ms) % 9.62/2.22 Prover 10: gave up % 9.62/2.22 Prover 16: stopped % 9.62/2.22 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 9.62/2.22 Prover 8: stopped % 9.62/2.22 Prover 13: stopped % 9.62/2.22 Prover 7: stopped % 10.13/2.23 Prover 19: Preprocessing ... % 10.13/2.24 Prover 11: Warning: ignoring some quantifiers % 10.13/2.24 Prover 11: Constructing countermodel ... % 10.13/2.25 Prover 11: stopped % 10.34/2.31 Prover 19: Warning: ignoring some quantifiers % 10.34/2.32 Prover 19: Constructing countermodel ... % 10.34/2.33 Prover 19: stopped % 10.34/2.33 % 10.34/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.34/2.33 % 10.68/2.34 % SZS output start Proof for theBenchmark % 10.68/2.35 Assumptions after simplification: % 10.68/2.35 --------------------------------- % 10.68/2.35 % 10.68/2.35 (commutativity_of_intersection) % 10.83/2.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = v2) | ~ % 10.83/2.39 $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : % 10.83/2.39 ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ $i(v1) | ~ % 10.83/2.39 $i(v0) | (intersection(v1, v0) = v2 & $i(v2))) % 10.83/2.39 % 10.83/2.39 (commutativity_of_symmetric_difference) % 10.83/2.39 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v1, v0) = % 10.83/2.39 v2) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v0, v1) = v2 & % 10.83/2.39 $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 10.83/2.39 (symmetric_difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | % 10.83/2.39 (symmetric_difference(v1, v0) = v2 & $i(v2))) % 10.83/2.39 % 10.83/2.39 (disjoint_defn) % 10.83/2.40 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) = % 10.83/2.40 v2) | ~ $i(v1) | ~ $i(v0) | intersect(v0, v1) = 0) & ! [v0: $i] : ! % 10.83/2.40 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0, v1) = v2) | ~ $i(v1) | % 10.83/2.40 ~ $i(v0) | disjoint(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 10.83/2.40 (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) % 10.83/2.40 & intersect(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 10.83/2.40 (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 10.83/2.40 0) & disjoint(v0, v1) = v2)) % 10.83/2.40 % 10.83/2.40 (intersect_with_union) % 10.83/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 10.83/2.41 | ~ (intersect(v0, v3) = v4) | ~ (union(v1, v2) = v3) | ~ $i(v2) | ~ % 10.83/2.41 $i(v1) | ~ $i(v0) | ? [v5: int] : ? [v6: int] : ( ~ (v6 = 0) & ~ (v5 = % 10.83/2.41 0) & intersect(v0, v2) = v6 & intersect(v0, v1) = v5)) & ! [v0: $i] : % 10.83/2.41 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersect(v0, v3) = 0) | ~ % 10.83/2.41 (union(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? % 10.83/2.41 [v5: any] : (intersect(v0, v2) = v5 & intersect(v0, v1) = v4 & (v5 = 0 | v4 % 10.83/2.41 = 0))) % 10.83/2.41 % 10.83/2.41 (intersection_and_union_disjoint) % 10.83/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ % 10.83/2.41 $i(v1) | ~ $i(v0) | ? [v3: $i] : (disjoint(v2, v3) = 0 & difference(v0, % 10.83/2.41 v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 10.83/2.41 (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : % 10.83/2.41 (intersection(v0, v1) = v3 & disjoint(v3, v2) = 0 & $i(v3))) % 10.83/2.41 % 10.83/2.42 (prove_intersection_and_symmetric_difference_disjoint) % 10.83/2.42 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 10.83/2.42 = 0) & intersection(v0, v1) = v2 & disjoint(v2, v3) = v4 & % 10.83/2.42 symmetric_difference(v0, v1) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 10.83/2.42 % 10.83/2.42 (symmetric_difference_defn) % 10.83/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0, v1) = % 10.83/2.42 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (difference(v1, % 10.83/2.42 v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = v2 & $i(v4) & % 10.83/2.43 $i(v3) & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 10.83/2.43 (difference(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: % 10.83/2.43 $i] : (symmetric_difference(v0, v1) = v3 & difference(v0, v1) = v4 & % 10.83/2.43 union(v4, v2) = v3 & $i(v4) & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! % 10.83/2.43 [v2: $i] : ( ~ (difference(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] % 10.83/2.43 : ? [v4: $i] : (symmetric_difference(v0, v1) = v3 & difference(v1, v0) = v4 % 10.83/2.43 & union(v2, v4) = v3 & $i(v4) & $i(v3))) % 10.83/2.43 % 10.83/2.43 (function-axioms) % 11.14/2.43 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 11.14/2.43 [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & % 11.14/2.43 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.14/2.43 (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0: % 11.14/2.43 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 11.14/2.43 : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! % 11.14/2.43 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 11.14/2.43 $i] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) = v0)) % 11.14/2.43 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.14/2.43 (symmetric_difference(v3, v2) = v1) | ~ (symmetric_difference(v3, v2) = % 11.14/2.43 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 11.14/2.43 ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : % 11.14/2.43 ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | % 11.14/2.43 ~ (union(v3, v2) = v0)) % 11.14/2.43 % 11.14/2.43 Further assumptions not needed in the proof: % 11.14/2.43 -------------------------------------------- % 11.14/2.43 commutativity_of_union, equal_member_defn, intersect_defn, intersection_defn, % 11.14/2.43 symmetry_of_intersect % 11.14/2.43 % 11.14/2.43 Those formulas are unsatisfiable: % 11.14/2.43 --------------------------------- % 11.14/2.43 % 11.14/2.43 Begin of proof % 11.14/2.44 | % 11.14/2.44 | ALPHA: (symmetric_difference_defn) implies: % 11.14/2.44 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (difference(v1, v0) = v2) % 11.14/2.44 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 11.14/2.44 | (symmetric_difference(v0, v1) = v3 & difference(v0, v1) = v4 & % 11.14/2.44 | union(v4, v2) = v3 & $i(v4) & $i(v3))) % 11.14/2.44 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v0, % 11.14/2.44 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : % 11.14/2.44 | (difference(v1, v0) = v4 & difference(v0, v1) = v3 & union(v3, v4) = % 11.14/2.44 | v2 & $i(v4) & $i(v3) & $i(v2))) % 11.14/2.44 | % 11.14/2.44 | ALPHA: (intersect_with_union) implies: % 11.14/2.44 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 11.14/2.44 | (intersect(v0, v3) = 0) | ~ (union(v1, v2) = v3) | ~ $i(v2) | ~ % 11.14/2.44 | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (intersect(v0, v2) % 11.14/2.44 | = v5 & intersect(v0, v1) = v4 & (v5 = 0 | v4 = 0))) % 11.14/2.44 | % 11.14/2.44 | ALPHA: (intersection_and_union_disjoint) implies: % 11.14/2.45 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (difference(v0, v1) = v2) % 11.14/2.45 | | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (intersection(v0, v1) = v3 & % 11.14/2.45 | disjoint(v3, v2) = 0 & $i(v3))) % 11.14/2.45 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = % 11.14/2.45 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (disjoint(v2, v3) = 0 & % 11.14/2.45 | difference(v0, v1) = v3 & $i(v3))) % 11.14/2.45 | % 11.14/2.45 | ALPHA: (disjoint_defn) implies: % 11.14/2.45 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ % 11.14/2.45 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & intersect(v0, v1) = v2)) % 11.14/2.45 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, % 11.14/2.45 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | intersect(v0, v1) = 0) % 11.14/2.45 | % 11.14/2.45 | ALPHA: (commutativity_of_intersection) implies: % 11.14/2.45 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = % 11.14/2.45 | v2) | ~ $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) % 11.14/2.45 | % 11.14/2.45 | ALPHA: (commutativity_of_symmetric_difference) implies: % 11.14/2.45 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (symmetric_difference(v1, % 11.14/2.45 | v0) = v2) | ~ $i(v1) | ~ $i(v0) | (symmetric_difference(v0, v1) % 11.14/2.45 | = v2 & $i(v2))) % 11.14/2.45 | % 11.14/2.45 | ALPHA: (function-axioms) implies: % 11.14/2.45 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.14/2.45 | (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) % 11.14/2.46 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] % 11.14/2.46 | : ! [v3: $i] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ % 11.14/2.46 | (intersect(v3, v2) = v0)) % 11.14/2.46 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ % 11.14/2.46 | (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) % 11.14/2.46 | % 11.14/2.46 | DELTA: instantiating (prove_intersection_and_symmetric_difference_disjoint) % 11.14/2.46 | with fresh symbols all_13_0, all_13_1, all_13_2, all_13_3, all_13_4 % 11.14/2.46 | gives: % 11.14/2.46 | (13) ~ (all_13_0 = 0) & intersection(all_13_4, all_13_3) = all_13_2 & % 11.14/2.46 | disjoint(all_13_2, all_13_1) = all_13_0 & % 11.29/2.46 | symmetric_difference(all_13_4, all_13_3) = all_13_1 & $i(all_13_1) & % 11.29/2.46 | $i(all_13_2) & $i(all_13_3) & $i(all_13_4) % 11.29/2.46 | % 11.29/2.46 | ALPHA: (13) implies: % 11.29/2.46 | (14) ~ (all_13_0 = 0) % 11.29/2.46 | (15) $i(all_13_4) % 11.29/2.46 | (16) $i(all_13_3) % 11.29/2.46 | (17) $i(all_13_2) % 11.29/2.46 | (18) symmetric_difference(all_13_4, all_13_3) = all_13_1 % 11.29/2.46 | (19) disjoint(all_13_2, all_13_1) = all_13_0 % 11.29/2.46 | (20) intersection(all_13_4, all_13_3) = all_13_2 % 11.29/2.46 | % 11.29/2.46 | GROUND_INST: instantiating (9) with all_13_3, all_13_4, all_13_1, simplifying % 11.29/2.46 | with (15), (16), (18) gives: % 11.29/2.46 | (21) symmetric_difference(all_13_3, all_13_4) = all_13_1 & $i(all_13_1) % 11.29/2.46 | % 11.29/2.46 | ALPHA: (21) implies: % 11.29/2.46 | (22) $i(all_13_1) % 11.29/2.46 | (23) symmetric_difference(all_13_3, all_13_4) = all_13_1 % 11.29/2.46 | % 11.29/2.46 | GROUND_INST: instantiating (2) with all_13_4, all_13_3, all_13_1, simplifying % 11.29/2.46 | with (15), (16), (18) gives: % 11.29/2.46 | (24) ? [v0: $i] : ? [v1: $i] : (difference(all_13_3, all_13_4) = v1 & % 11.29/2.47 | difference(all_13_4, all_13_3) = v0 & union(v0, v1) = all_13_1 & % 11.29/2.47 | $i(v1) & $i(v0) & $i(all_13_1)) % 11.29/2.47 | % 11.29/2.47 | GROUND_INST: instantiating (7) with all_13_2, all_13_1, all_13_0, simplifying % 11.29/2.47 | with (17), (19), (22) gives: % 11.29/2.47 | (25) all_13_0 = 0 | intersect(all_13_2, all_13_1) = 0 % 11.29/2.47 | % 11.29/2.47 | GROUND_INST: instantiating (8) with all_13_3, all_13_4, all_13_2, simplifying % 11.29/2.47 | with (15), (16), (20) gives: % 11.29/2.47 | (26) intersection(all_13_3, all_13_4) = all_13_2 & $i(all_13_2) % 11.29/2.47 | % 11.29/2.47 | ALPHA: (26) implies: % 11.29/2.47 | (27) intersection(all_13_3, all_13_4) = all_13_2 % 11.29/2.47 | % 11.29/2.47 | GROUND_INST: instantiating (5) with all_13_4, all_13_3, all_13_2, simplifying % 11.29/2.47 | with (15), (16), (20) gives: % 11.29/2.47 | (28) ? [v0: $i] : (disjoint(all_13_2, v0) = 0 & difference(all_13_4, % 11.29/2.47 | all_13_3) = v0 & $i(v0)) % 11.29/2.47 | % 11.29/2.47 | DELTA: instantiating (28) with fresh symbol all_22_0 gives: % 11.29/2.47 | (29) disjoint(all_13_2, all_22_0) = 0 & difference(all_13_4, all_13_3) = % 11.29/2.47 | all_22_0 & $i(all_22_0) % 11.29/2.47 | % 11.29/2.47 | ALPHA: (29) implies: % 11.29/2.47 | (30) difference(all_13_4, all_13_3) = all_22_0 % 11.29/2.47 | (31) disjoint(all_13_2, all_22_0) = 0 % 11.29/2.47 | % 11.29/2.47 | DELTA: instantiating (24) with fresh symbols all_24_0, all_24_1 gives: % 11.29/2.47 | (32) difference(all_13_3, all_13_4) = all_24_0 & difference(all_13_4, % 11.29/2.47 | all_13_3) = all_24_1 & union(all_24_1, all_24_0) = all_13_1 & % 11.29/2.47 | $i(all_24_0) & $i(all_24_1) & $i(all_13_1) % 11.29/2.47 | % 11.29/2.47 | ALPHA: (32) implies: % 11.29/2.47 | (33) $i(all_24_1) % 11.29/2.47 | (34) $i(all_24_0) % 11.29/2.47 | (35) union(all_24_1, all_24_0) = all_13_1 % 11.29/2.47 | (36) difference(all_13_4, all_13_3) = all_24_1 % 11.29/2.47 | (37) difference(all_13_3, all_13_4) = all_24_0 % 11.29/2.47 | % 11.29/2.47 | BETA: splitting (25) gives: % 11.29/2.47 | % 11.29/2.47 | Case 1: % 11.29/2.47 | | % 11.29/2.47 | | (38) intersect(all_13_2, all_13_1) = 0 % 11.29/2.48 | | % 11.29/2.48 | | GROUND_INST: instantiating (10) with all_22_0, all_24_1, all_13_3, all_13_4, % 11.29/2.48 | | simplifying with (30), (36) gives: % 11.29/2.48 | | (39) all_24_1 = all_22_0 % 11.29/2.48 | | % 11.29/2.48 | | REDUCE: (35), (39) imply: % 11.29/2.48 | | (40) union(all_22_0, all_24_0) = all_13_1 % 11.29/2.48 | | % 11.29/2.48 | | REDUCE: (33), (39) imply: % 11.29/2.48 | | (41) $i(all_22_0) % 11.29/2.48 | | % 11.29/2.48 | | GROUND_INST: instantiating (1) with all_13_3, all_13_4, all_22_0, % 11.29/2.48 | | simplifying with (15), (16), (30) gives: % 11.29/2.48 | | (42) ? [v0: $i] : ? [v1: $i] : (symmetric_difference(all_13_3, % 11.29/2.48 | | all_13_4) = v0 & difference(all_13_3, all_13_4) = v1 & union(v1, % 11.29/2.48 | | all_22_0) = v0 & $i(v1) & $i(v0)) % 11.29/2.48 | | % 11.29/2.48 | | GROUND_INST: instantiating (4) with all_13_3, all_13_4, all_24_0, % 11.29/2.48 | | simplifying with (15), (16), (37) gives: % 11.29/2.48 | | (43) ? [v0: $i] : (intersection(all_13_3, all_13_4) = v0 & disjoint(v0, % 11.29/2.48 | | all_24_0) = 0 & $i(v0)) % 11.29/2.48 | | % 11.29/2.48 | | GROUND_INST: instantiating (2) with all_13_3, all_13_4, all_13_1, % 11.29/2.48 | | simplifying with (15), (16), (23) gives: % 11.29/2.48 | | (44) ? [v0: $i] : ? [v1: $i] : (difference(all_13_3, all_13_4) = v0 & % 11.29/2.48 | | difference(all_13_4, all_13_3) = v1 & union(v0, v1) = all_13_1 & % 11.29/2.48 | | $i(v1) & $i(v0) & $i(all_13_1)) % 11.29/2.48 | | % 11.29/2.48 | | GROUND_INST: instantiating (3) with all_13_2, all_22_0, all_24_0, all_13_1, % 11.29/2.48 | | simplifying with (17), (34), (38), (40), (41) gives: % 11.29/2.48 | | (45) ? [v0: any] : ? [v1: any] : (intersect(all_13_2, all_24_0) = v1 & % 11.29/2.48 | | intersect(all_13_2, all_22_0) = v0 & (v1 = 0 | v0 = 0)) % 11.29/2.48 | | % 11.29/2.48 | | GROUND_INST: instantiating (6) with all_13_2, all_22_0, simplifying with % 11.29/2.48 | | (17), (31), (41) gives: % 11.29/2.49 | | (46) ? [v0: int] : ( ~ (v0 = 0) & intersect(all_13_2, all_22_0) = v0) % 11.29/2.49 | | % 11.29/2.49 | | GROUND_INST: instantiating (5) with all_13_3, all_13_4, all_13_2, % 11.29/2.49 | | simplifying with (15), (16), (27) gives: % 11.29/2.49 | | (47) ? [v0: $i] : (disjoint(all_13_2, v0) = 0 & difference(all_13_3, % 11.29/2.49 | | all_13_4) = v0 & $i(v0)) % 11.29/2.49 | | % 11.29/2.49 | | DELTA: instantiating (46) with fresh symbol all_40_0 gives: % 11.29/2.49 | | (48) ~ (all_40_0 = 0) & intersect(all_13_2, all_22_0) = all_40_0 % 11.29/2.49 | | % 11.29/2.49 | | ALPHA: (48) implies: % 11.29/2.49 | | (49) ~ (all_40_0 = 0) % 11.29/2.49 | | (50) intersect(all_13_2, all_22_0) = all_40_0 % 11.29/2.49 | | % 11.29/2.49 | | DELTA: instantiating (47) with fresh symbol all_42_0 gives: % 11.29/2.49 | | (51) disjoint(all_13_2, all_42_0) = 0 & difference(all_13_3, all_13_4) = % 11.29/2.49 | | all_42_0 & $i(all_42_0) % 11.29/2.49 | | % 11.29/2.49 | | ALPHA: (51) implies: % 11.29/2.49 | | (52) $i(all_42_0) % 11.29/2.49 | | (53) difference(all_13_3, all_13_4) = all_42_0 % 11.29/2.49 | | (54) disjoint(all_13_2, all_42_0) = 0 % 11.29/2.49 | | % 11.29/2.49 | | DELTA: instantiating (43) with fresh symbol all_46_0 gives: % 11.29/2.49 | | (55) intersection(all_13_3, all_13_4) = all_46_0 & disjoint(all_46_0, % 11.29/2.49 | | all_24_0) = 0 & $i(all_46_0) % 11.29/2.49 | | % 11.29/2.49 | | ALPHA: (55) implies: % 11.29/2.49 | | (56) $i(all_46_0) % 11.29/2.49 | | (57) intersection(all_13_3, all_13_4) = all_46_0 % 11.29/2.49 | | % 11.29/2.49 | | DELTA: instantiating (45) with fresh symbols all_48_0, all_48_1 gives: % 11.29/2.49 | | (58) intersect(all_13_2, all_24_0) = all_48_0 & intersect(all_13_2, % 11.29/2.49 | | all_22_0) = all_48_1 & (all_48_0 = 0 | all_48_1 = 0) % 11.29/2.49 | | % 11.29/2.49 | | ALPHA: (58) implies: % 11.29/2.49 | | (59) intersect(all_13_2, all_22_0) = all_48_1 % 11.29/2.49 | | (60) intersect(all_13_2, all_24_0) = all_48_0 % 11.29/2.49 | | (61) all_48_0 = 0 | all_48_1 = 0 % 11.29/2.49 | | % 11.29/2.49 | | DELTA: instantiating (42) with fresh symbols all_52_0, all_52_1 gives: % 11.29/2.49 | | (62) symmetric_difference(all_13_3, all_13_4) = all_52_1 & % 11.29/2.49 | | difference(all_13_3, all_13_4) = all_52_0 & union(all_52_0, % 11.29/2.49 | | all_22_0) = all_52_1 & $i(all_52_0) & $i(all_52_1) % 11.29/2.49 | | % 11.29/2.49 | | ALPHA: (62) implies: % 11.29/2.49 | | (63) difference(all_13_3, all_13_4) = all_52_0 % 11.29/2.49 | | % 11.29/2.49 | | DELTA: instantiating (44) with fresh symbols all_54_0, all_54_1 gives: % 11.29/2.50 | | (64) difference(all_13_3, all_13_4) = all_54_1 & difference(all_13_4, % 11.29/2.50 | | all_13_3) = all_54_0 & union(all_54_1, all_54_0) = all_13_1 & % 11.29/2.50 | | $i(all_54_0) & $i(all_54_1) & $i(all_13_1) % 11.29/2.50 | | % 11.29/2.50 | | ALPHA: (64) implies: % 11.29/2.50 | | (65) difference(all_13_3, all_13_4) = all_54_1 % 11.29/2.50 | | % 11.29/2.50 | | GROUND_INST: instantiating (10) with all_24_0, all_54_1, all_13_4, all_13_3, % 11.29/2.50 | | simplifying with (37), (65) gives: % 11.29/2.50 | | (66) all_54_1 = all_24_0 % 11.29/2.50 | | % 11.29/2.50 | | GROUND_INST: instantiating (10) with all_52_0, all_54_1, all_13_4, all_13_3, % 11.29/2.50 | | simplifying with (63), (65) gives: % 11.29/2.50 | | (67) all_54_1 = all_52_0 % 11.29/2.50 | | % 11.29/2.50 | | GROUND_INST: instantiating (10) with all_42_0, all_54_1, all_13_4, all_13_3, % 11.29/2.50 | | simplifying with (53), (65) gives: % 11.29/2.50 | | (68) all_54_1 = all_42_0 % 11.29/2.50 | | % 11.29/2.50 | | GROUND_INST: instantiating (11) with all_40_0, all_48_1, all_22_0, all_13_2, % 11.29/2.50 | | simplifying with (50), (59) gives: % 11.29/2.50 | | (69) all_48_1 = all_40_0 % 11.29/2.50 | | % 11.29/2.50 | | GROUND_INST: instantiating (12) with all_13_2, all_46_0, all_13_4, all_13_3, % 11.29/2.50 | | simplifying with (27), (57) gives: % 11.29/2.50 | | (70) all_46_0 = all_13_2 % 11.29/2.50 | | % 11.29/2.50 | | COMBINE_EQS: (66), (67) imply: % 11.29/2.50 | | (71) all_52_0 = all_24_0 % 11.29/2.50 | | % 11.29/2.50 | | COMBINE_EQS: (67), (68) imply: % 11.29/2.50 | | (72) all_52_0 = all_42_0 % 11.29/2.50 | | % 11.29/2.50 | | COMBINE_EQS: (71), (72) imply: % 11.29/2.50 | | (73) all_42_0 = all_24_0 % 11.29/2.50 | | % 11.29/2.50 | | REDUCE: (54), (73) imply: % 11.29/2.50 | | (74) disjoint(all_13_2, all_24_0) = 0 % 11.29/2.50 | | % 11.29/2.50 | | BETA: splitting (61) gives: % 11.29/2.50 | | % 11.29/2.50 | | Case 1: % 11.29/2.50 | | | % 11.29/2.50 | | | (75) all_48_0 = 0 % 11.29/2.50 | | | % 11.29/2.50 | | | REDUCE: (60), (75) imply: % 11.29/2.50 | | | (76) intersect(all_13_2, all_24_0) = 0 % 11.29/2.50 | | | % 11.29/2.50 | | | GROUND_INST: instantiating (6) with all_13_2, all_24_0, simplifying with % 11.29/2.50 | | | (17), (34), (74) gives: % 11.29/2.50 | | | (77) ? [v0: int] : ( ~ (v0 = 0) & intersect(all_13_2, all_24_0) = v0) % 11.29/2.50 | | | % 11.29/2.50 | | | DELTA: instantiating (77) with fresh symbol all_70_0 gives: % 11.29/2.50 | | | (78) ~ (all_70_0 = 0) & intersect(all_13_2, all_24_0) = all_70_0 % 11.29/2.50 | | | % 11.29/2.50 | | | ALPHA: (78) implies: % 11.29/2.51 | | | (79) ~ (all_70_0 = 0) % 11.29/2.51 | | | (80) intersect(all_13_2, all_24_0) = all_70_0 % 11.29/2.51 | | | % 11.29/2.51 | | | GROUND_INST: instantiating (11) with 0, all_70_0, all_24_0, all_13_2, % 11.29/2.51 | | | simplifying with (76), (80) gives: % 11.29/2.51 | | | (81) all_70_0 = 0 % 11.29/2.51 | | | % 11.29/2.51 | | | REDUCE: (79), (81) imply: % 11.29/2.51 | | | (82) $false % 11.29/2.51 | | | % 11.29/2.51 | | | CLOSE: (82) is inconsistent. % 11.29/2.51 | | | % 11.29/2.51 | | Case 2: % 11.29/2.51 | | | % 11.29/2.51 | | | (83) all_48_1 = 0 % 11.29/2.51 | | | % 11.29/2.51 | | | COMBINE_EQS: (69), (83) imply: % 11.29/2.51 | | | (84) all_40_0 = 0 % 11.29/2.51 | | | % 11.29/2.51 | | | REDUCE: (49), (84) imply: % 11.29/2.51 | | | (85) $false % 11.29/2.51 | | | % 11.29/2.51 | | | CLOSE: (85) is inconsistent. % 11.29/2.51 | | | % 11.29/2.51 | | End of split % 11.29/2.51 | | % 11.29/2.51 | Case 2: % 11.29/2.51 | | % 11.29/2.51 | | (86) all_13_0 = 0 % 11.29/2.51 | | % 11.29/2.51 | | REDUCE: (14), (86) imply: % 11.29/2.51 | | (87) $false % 11.29/2.51 | | % 11.29/2.51 | | CLOSE: (87) is inconsistent. % 11.29/2.51 | | % 11.29/2.51 | End of split % 11.29/2.51 | % 11.29/2.51 End of proof % 11.29/2.51 % SZS output end Proof for theBenchmark % 11.29/2.51 % 11.29/2.51 1913ms %------------------------------------------------------------------------------