%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET576+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 : n017.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 15:25:21 EDT 2023 % Result : Theorem 3.49s 1.24s % Output : Proof 4.46s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : SET576+3 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n017.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Sat Aug 26 11:44:10 EDT 2023 % 0.13/0.33 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.61/0.94 Prover 4: Preprocessing ... % 1.61/0.94 Prover 1: Preprocessing ... % 2.15/0.98 Prover 0: Preprocessing ... % 2.15/0.98 Prover 2: Preprocessing ... % 2.15/0.99 Prover 6: Preprocessing ... % 2.15/0.99 Prover 5: Preprocessing ... % 2.15/0.99 Prover 3: Preprocessing ... % 2.43/1.08 Prover 2: Proving ... % 2.43/1.10 Prover 5: Proving ... % 3.03/1.12 Prover 1: Constructing countermodel ... % 3.03/1.13 Prover 6: Proving ... % 3.03/1.13 Prover 3: Constructing countermodel ... % 3.03/1.19 Prover 0: Proving ... % 3.03/1.19 Prover 4: Constructing countermodel ... % 3.49/1.24 Prover 3: proved (615ms) % 3.49/1.24 % 3.49/1.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.49/1.24 % 3.49/1.24 Prover 5: stopped % 3.49/1.24 Prover 6: stopped % 3.49/1.25 Prover 2: stopped % 3.49/1.26 Prover 0: stopped % 3.49/1.26 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.49/1.26 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.49/1.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.49/1.26 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.49/1.26 Prover 7: Preprocessing ... % 3.49/1.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.02/1.28 Prover 10: Preprocessing ... % 4.02/1.29 Prover 13: Preprocessing ... % 4.02/1.30 Prover 10: Warning: ignoring some quantifiers % 4.02/1.30 Prover 8: Preprocessing ... % 4.16/1.30 Prover 11: Preprocessing ... % 4.16/1.30 Prover 7: Warning: ignoring some quantifiers % 4.16/1.30 Prover 10: Constructing countermodel ... % 4.16/1.31 Prover 7: Constructing countermodel ... % 4.16/1.31 Prover 13: Warning: ignoring some quantifiers % 4.16/1.32 Prover 13: Constructing countermodel ... % 4.16/1.34 Prover 10: gave up % 4.16/1.34 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 4.16/1.34 Prover 1: Found proof (size 18) % 4.16/1.34 Prover 1: proved (722ms) % 4.16/1.34 Prover 13: gave up % 4.16/1.34 Prover 4: stopped % 4.16/1.34 Prover 7: stopped % 4.16/1.35 Prover 8: Warning: ignoring some quantifiers % 4.16/1.35 Prover 16: Preprocessing ... % 4.16/1.35 Prover 8: Constructing countermodel ... % 4.16/1.36 Prover 8: stopped % 4.16/1.36 Prover 16: Warning: ignoring some quantifiers % 4.16/1.37 Prover 16: Constructing countermodel ... % 4.16/1.37 Prover 16: stopped % 4.16/1.38 Prover 11: Constructing countermodel ... % 4.46/1.39 Prover 11: stopped % 4.46/1.39 % 4.46/1.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.46/1.39 % 4.46/1.39 % SZS output start Proof for theBenchmark % 4.46/1.39 Assumptions after simplification: % 4.46/1.39 --------------------------------- % 4.46/1.39 % 4.46/1.39 (disjoint_defn) % 4.46/1.43 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) = % 4.46/1.43 v2) | ~ $i(v1) | ~ $i(v0) | intersect(v0, v1) = 0) & ! [v0: $i] : ! % 4.46/1.43 [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : % 4.46/1.43 ( ~ (v2 = 0) & intersect(v0, v1) = v2)) % 4.46/1.43 % 4.46/1.43 (intersect_defn) % 4.46/1.43 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0, v1) = % 4.46/1.43 v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (member(v3, v0) = 0) | ~ % 4.46/1.43 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4))) & ! [v0: % 4.46/1.43 $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 4.46/1.43 [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2))) % 4.46/1.43 % 4.46/1.43 (prove_th17) % 4.46/1.43 ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & disjoint(v0, v1) = % 4.46/1.43 v2 & $i(v1) & $i(v0) & ! [v3: $i] : ( ~ (member(v3, v0) = 0) | ~ $i(v3) | % 4.46/1.43 ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4))) % 4.46/1.43 % 4.46/1.43 (function-axioms) % 4.46/1.44 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 4.46/1.44 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0)) % 4.46/1.44 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 4.46/1.44 [v3: $i] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) = % 4.46/1.44 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 4.46/1.44 $i] : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 4.46/1.44 = v0)) % 4.46/1.44 % 4.46/1.44 Further assumptions not needed in the proof: % 4.46/1.44 -------------------------------------------- % 4.46/1.44 symmetry_of_intersect % 4.46/1.44 % 4.46/1.44 Those formulas are unsatisfiable: % 4.46/1.44 --------------------------------- % 4.46/1.44 % 4.46/1.44 Begin of proof % 4.46/1.44 | % 4.46/1.44 | ALPHA: (intersect_defn) implies: % 4.46/1.44 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | % 4.46/1.44 | ~ $i(v0) | ? [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & % 4.46/1.44 | $i(v2))) % 4.46/1.44 | % 4.46/1.44 | ALPHA: (disjoint_defn) implies: % 4.46/1.44 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, % 4.46/1.44 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | intersect(v0, v1) = 0) % 4.46/1.44 | % 4.46/1.44 | ALPHA: (function-axioms) implies: % 4.46/1.45 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.46/1.45 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 4.46/1.45 | = v0)) % 4.46/1.45 | % 4.46/1.45 | DELTA: instantiating (prove_th17) with fresh symbols all_6_0, all_6_1, all_6_2 % 4.46/1.45 | gives: % 4.46/1.45 | (4) ~ (all_6_0 = 0) & disjoint(all_6_2, all_6_1) = all_6_0 & $i(all_6_1) & % 4.46/1.45 | $i(all_6_2) & ! [v0: $i] : ( ~ (member(v0, all_6_2) = 0) | ~ $i(v0) | % 4.46/1.45 | ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_6_1) = v1)) % 4.46/1.45 | % 4.46/1.45 | ALPHA: (4) implies: % 4.46/1.45 | (5) ~ (all_6_0 = 0) % 4.46/1.45 | (6) $i(all_6_2) % 4.46/1.45 | (7) $i(all_6_1) % 4.46/1.45 | (8) disjoint(all_6_2, all_6_1) = all_6_0 % 4.46/1.45 | (9) ! [v0: $i] : ( ~ (member(v0, all_6_2) = 0) | ~ $i(v0) | ? [v1: int] % 4.46/1.45 | : ( ~ (v1 = 0) & member(v0, all_6_1) = v1)) % 4.46/1.45 | % 4.46/1.45 | GROUND_INST: instantiating (2) with all_6_2, all_6_1, all_6_0, simplifying % 4.46/1.45 | with (6), (7), (8) gives: % 4.46/1.45 | (10) all_6_0 = 0 | intersect(all_6_2, all_6_1) = 0 % 4.46/1.45 | % 4.46/1.45 | BETA: splitting (10) gives: % 4.46/1.45 | % 4.46/1.45 | Case 1: % 4.46/1.45 | | % 4.46/1.45 | | (11) intersect(all_6_2, all_6_1) = 0 % 4.46/1.45 | | % 4.46/1.45 | | GROUND_INST: instantiating (1) with all_6_2, all_6_1, simplifying with (6), % 4.46/1.45 | | (7), (11) gives: % 4.46/1.45 | | (12) ? [v0: $i] : (member(v0, all_6_1) = 0 & member(v0, all_6_2) = 0 & % 4.46/1.45 | | $i(v0)) % 4.46/1.46 | | % 4.46/1.46 | | DELTA: instantiating (12) with fresh symbol all_22_0 gives: % 4.46/1.46 | | (13) member(all_22_0, all_6_1) = 0 & member(all_22_0, all_6_2) = 0 & % 4.46/1.46 | | $i(all_22_0) % 4.46/1.46 | | % 4.46/1.46 | | ALPHA: (13) implies: % 4.46/1.46 | | (14) $i(all_22_0) % 4.46/1.46 | | (15) member(all_22_0, all_6_2) = 0 % 4.46/1.46 | | (16) member(all_22_0, all_6_1) = 0 % 4.46/1.46 | | % 4.46/1.46 | | GROUND_INST: instantiating (9) with all_22_0, simplifying with (14), (15) % 4.46/1.46 | | gives: % 4.46/1.46 | | (17) ? [v0: int] : ( ~ (v0 = 0) & member(all_22_0, all_6_1) = v0) % 4.46/1.46 | | % 4.46/1.46 | | DELTA: instantiating (17) with fresh symbol all_29_0 gives: % 4.46/1.46 | | (18) ~ (all_29_0 = 0) & member(all_22_0, all_6_1) = all_29_0 % 4.46/1.46 | | % 4.46/1.46 | | ALPHA: (18) implies: % 4.46/1.46 | | (19) ~ (all_29_0 = 0) % 4.46/1.46 | | (20) member(all_22_0, all_6_1) = all_29_0 % 4.46/1.46 | | % 4.46/1.46 | | GROUND_INST: instantiating (3) with 0, all_29_0, all_6_1, all_22_0, % 4.46/1.46 | | simplifying with (16), (20) gives: % 4.46/1.46 | | (21) all_29_0 = 0 % 4.46/1.46 | | % 4.46/1.46 | | REDUCE: (19), (21) imply: % 4.46/1.46 | | (22) $false % 4.46/1.46 | | % 4.46/1.46 | | CLOSE: (22) is inconsistent. % 4.46/1.46 | | % 4.46/1.46 | Case 2: % 4.46/1.46 | | % 4.46/1.46 | | (23) all_6_0 = 0 % 4.46/1.46 | | % 4.46/1.46 | | REDUCE: (5), (23) imply: % 4.46/1.46 | | (24) $false % 4.46/1.46 | | % 4.46/1.46 | | CLOSE: (24) is inconsistent. % 4.46/1.46 | | % 4.46/1.46 | End of split % 4.46/1.46 | % 4.46/1.46 End of proof % 4.46/1.46 % SZS output end Proof for theBenchmark % 4.46/1.46 % 4.46/1.46 867ms %------------------------------------------------------------------------------