%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET627+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 : n009.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 15:25:43 EDT 2023 % Result : Theorem 3.92s 1.24s % Output : Proof 5.23s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET627+3 : TPTP v8.1.2. Released v2.2.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Sat Aug 26 12:37:20 EDT 2023 % 0.13/0.34 % 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. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.86/0.93 Prover 1: Preprocessing ... % 1.86/0.93 Prover 4: Preprocessing ... % 2.28/0.98 Prover 6: Preprocessing ... % 2.28/0.98 Prover 0: Preprocessing ... % 2.28/0.98 Prover 2: Preprocessing ... % 2.28/0.98 Prover 5: Preprocessing ... % 2.28/0.98 Prover 3: Preprocessing ... % 3.17/1.12 Prover 2: Proving ... % 3.17/1.12 Prover 5: Proving ... % 3.17/1.12 Prover 6: Proving ... % 3.43/1.14 Prover 3: Constructing countermodel ... % 3.43/1.14 Prover 1: Constructing countermodel ... % 3.43/1.15 Prover 4: Constructing countermodel ... % 3.43/1.17 Prover 0: Proving ... % 3.92/1.24 Prover 3: proved (620ms) % 3.92/1.24 % 3.92/1.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.92/1.24 % 3.92/1.24 Prover 0: stopped % 3.92/1.24 Prover 5: stopped % 3.92/1.24 Prover 2: stopped % 3.92/1.24 Prover 6: stopped % 3.92/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.92/1.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.92/1.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.92/1.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.92/1.26 Prover 7: Preprocessing ... % 3.92/1.26 Prover 8: Preprocessing ... % 4.37/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.37/1.27 Prover 11: Preprocessing ... % 4.37/1.28 Prover 13: Preprocessing ... % 4.37/1.28 Prover 10: Preprocessing ... % 4.37/1.28 Prover 7: Warning: ignoring some quantifiers % 4.37/1.29 Prover 7: Constructing countermodel ... % 4.37/1.31 Prover 13: Warning: ignoring some quantifiers % 4.37/1.31 Prover 10: Warning: ignoring some quantifiers % 4.37/1.32 Prover 13: Constructing countermodel ... % 4.37/1.32 Prover 10: Constructing countermodel ... % 4.37/1.32 Prover 4: Found proof (size 15) % 4.37/1.32 Prover 4: proved (708ms) % 4.37/1.33 Prover 1: Found proof (size 15) % 4.37/1.33 Prover 1: proved (709ms) % 4.37/1.33 Prover 10: stopped % 4.37/1.33 Prover 13: stopped % 4.37/1.33 Prover 7: stopped % 4.37/1.33 Prover 8: Warning: ignoring some quantifiers % 4.37/1.34 Prover 8: Constructing countermodel ... % 4.37/1.35 Prover 8: stopped % 4.37/1.35 Prover 11: Constructing countermodel ... % 4.37/1.36 Prover 11: stopped % 4.37/1.36 % 4.37/1.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.37/1.36 % 4.37/1.36 % SZS output start Proof for theBenchmark % 4.37/1.36 Assumptions after simplification: % 4.37/1.36 --------------------------------- % 4.37/1.36 % 4.37/1.36 (disjoint_defn) % 5.07/1.40 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) = % 5.07/1.40 v2) | ~ $i(v1) | ~ $i(v0) | intersect(v0, v1) = 0) & ! [v0: $i] : ! % 5.07/1.40 [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0, v1) = v2) | ~ $i(v1) | % 5.07/1.40 ~ $i(v0) | disjoint(v0, v1) = 0) & ! [v0: $i] : ! [v1: $i] : ( ~ % 5.07/1.40 (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) % 5.07/1.40 & intersect(v0, v1) = v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ % 5.07/1.40 (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = % 5.07/1.40 0) & disjoint(v0, v1) = v2)) % 5.07/1.40 % 5.07/1.40 (empty_set_defn) % 5.07/1.40 $i(empty_set) & ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0)) % 5.07/1.40 % 5.07/1.40 (intersect_defn) % 5.07/1.40 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ % 5.07/1.40 (intersect(v0, v1) = v2) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v1) | % 5.07/1.40 ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v0) = v4)) & ! [v0: % 5.07/1.40 $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ (intersect(v0, % 5.07/1.40 v1) = v2) | ~ (member(v3, v0) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) % 5.07/1.40 | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4)) & ! [v0: $i] : ! % 5.07/1.40 [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : % 5.07/1.40 (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2))) % 5.07/1.40 % 5.07/1.41 (prove_th104) % 5.23/1.41 $i(empty_set) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & disjoint(v0, % 5.23/1.41 empty_set) = v1 & $i(v0)) % 5.23/1.41 % 5.23/1.41 Further assumptions not needed in the proof: % 5.23/1.41 -------------------------------------------- % 5.23/1.41 empty_defn, symmetry_of_intersect % 5.23/1.41 % 5.23/1.41 Those formulas are unsatisfiable: % 5.23/1.41 --------------------------------- % 5.23/1.41 % 5.23/1.41 Begin of proof % 5.23/1.41 | % 5.23/1.41 | ALPHA: (empty_set_defn) implies: % 5.23/1.41 | (1) ! [v0: $i] : ( ~ (member(v0, empty_set) = 0) | ~ $i(v0)) % 5.23/1.41 | % 5.23/1.41 | ALPHA: (intersect_defn) implies: % 5.23/1.41 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | % 5.23/1.41 | ~ $i(v0) | ? [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & % 5.23/1.41 | $i(v2))) % 5.23/1.41 | % 5.23/1.41 | ALPHA: (disjoint_defn) implies: % 5.23/1.41 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, % 5.23/1.41 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | intersect(v0, v1) = 0) % 5.23/1.41 | % 5.23/1.41 | ALPHA: (prove_th104) implies: % 5.23/1.41 | (4) $i(empty_set) % 5.23/1.41 | (5) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & disjoint(v0, empty_set) = % 5.23/1.42 | v1 & $i(v0)) % 5.23/1.42 | % 5.23/1.42 | DELTA: instantiating (5) with fresh symbols all_9_0, all_9_1 gives: % 5.23/1.42 | (6) ~ (all_9_0 = 0) & disjoint(all_9_1, empty_set) = all_9_0 & $i(all_9_1) % 5.23/1.42 | % 5.23/1.42 | ALPHA: (6) implies: % 5.23/1.42 | (7) ~ (all_9_0 = 0) % 5.23/1.42 | (8) $i(all_9_1) % 5.23/1.42 | (9) disjoint(all_9_1, empty_set) = all_9_0 % 5.23/1.42 | % 5.23/1.42 | GROUND_INST: instantiating (3) with all_9_1, empty_set, all_9_0, simplifying % 5.23/1.42 | with (4), (8), (9) gives: % 5.23/1.42 | (10) all_9_0 = 0 | intersect(all_9_1, empty_set) = 0 % 5.23/1.42 | % 5.23/1.42 | BETA: splitting (10) gives: % 5.23/1.42 | % 5.23/1.42 | Case 1: % 5.23/1.42 | | % 5.23/1.42 | | (11) intersect(all_9_1, empty_set) = 0 % 5.23/1.42 | | % 5.23/1.42 | | GROUND_INST: instantiating (2) with all_9_1, empty_set, simplifying with % 5.23/1.42 | | (4), (8), (11) gives: % 5.23/1.42 | | (12) ? [v0: $i] : (member(v0, all_9_1) = 0 & member(v0, empty_set) = 0 & % 5.23/1.42 | | $i(v0)) % 5.23/1.42 | | % 5.23/1.42 | | DELTA: instantiating (12) with fresh symbol all_24_0 gives: % 5.23/1.42 | | (13) member(all_24_0, all_9_1) = 0 & member(all_24_0, empty_set) = 0 & % 5.23/1.42 | | $i(all_24_0) % 5.23/1.42 | | % 5.23/1.42 | | ALPHA: (13) implies: % 5.23/1.42 | | (14) $i(all_24_0) % 5.23/1.42 | | (15) member(all_24_0, empty_set) = 0 % 5.23/1.42 | | % 5.23/1.42 | | GROUND_INST: instantiating (1) with all_24_0, simplifying with (14), (15) % 5.23/1.42 | | gives: % 5.23/1.42 | | (16) $false % 5.23/1.42 | | % 5.23/1.42 | | CLOSE: (16) is inconsistent. % 5.23/1.42 | | % 5.23/1.42 | Case 2: % 5.23/1.42 | | % 5.23/1.43 | | (17) all_9_0 = 0 % 5.23/1.43 | | % 5.23/1.43 | | REDUCE: (7), (17) imply: % 5.23/1.43 | | (18) $false % 5.23/1.43 | | % 5.23/1.43 | | CLOSE: (18) is inconsistent. % 5.23/1.43 | | % 5.23/1.43 | End of split % 5.23/1.43 | % 5.23/1.43 End of proof % 5.23/1.43 % SZS output end Proof for theBenchmark % 5.23/1.43 % 5.23/1.43 828ms %------------------------------------------------------------------------------