%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET625+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 : n012.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 4.24s 1.24s % Output : Proof 4.24s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET625+3 : TPTP v8.1.2. Released v2.2.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.34 % Computer : n012.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 11:56:25 EDT 2023 % 0.14/0.34 % CPUTime : % 0.20/0.60 ________ _____ % 0.20/0.60 ___ __ \_________(_)________________________________ % 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.60 % 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.60 (2023-06-19) % 0.20/0.60 % 0.20/0.60 (c) Philipp Rümmer, 2009-2023 % 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.60 Amanda Stjerna. % 0.20/0.60 Free software under BSD-3-Clause. % 0.20/0.60 % 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.60 % 0.20/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 1.79/0.93 Prover 1: Preprocessing ... % 1.79/0.93 Prover 4: Preprocessing ... % 2.09/0.98 Prover 6: Preprocessing ... % 2.09/0.98 Prover 5: Preprocessing ... % 2.09/0.98 Prover 2: Preprocessing ... % 2.09/0.98 Prover 3: Preprocessing ... % 2.09/0.98 Prover 0: Preprocessing ... % 2.88/1.07 Prover 5: Proving ... % 2.88/1.08 Prover 2: Proving ... % 2.88/1.11 Prover 6: Proving ... % 2.88/1.11 Prover 1: Constructing countermodel ... % 2.88/1.11 Prover 3: Constructing countermodel ... % 2.88/1.14 Prover 4: Constructing countermodel ... % 2.88/1.15 Prover 0: Proving ... % 3.89/1.24 Prover 3: proved (617ms) % 4.22/1.24 % 4.24/1.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.24/1.24 % 4.24/1.24 Prover 0: proved (625ms) % 4.24/1.24 % 4.24/1.24 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.24/1.24 % 4.24/1.25 Prover 5: stopped % 4.24/1.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.24/1.25 Prover 6: stopped % 4.24/1.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.24/1.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.24/1.25 Prover 2: proved (635ms) % 4.24/1.25 % 4.24/1.25 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.24/1.25 % 4.24/1.26 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.24/1.26 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.24/1.27 Prover 8: Preprocessing ... % 4.24/1.27 Prover 7: Preprocessing ... % 4.24/1.27 Prover 11: Preprocessing ... % 4.24/1.28 Prover 10: Preprocessing ... % 4.24/1.29 Prover 13: Preprocessing ... % 4.24/1.29 Prover 7: Warning: ignoring some quantifiers % 4.24/1.29 Prover 7: Constructing countermodel ... % 4.24/1.29 Prover 4: Found proof (size 19) % 4.24/1.29 Prover 4: proved (670ms) % 4.24/1.29 Prover 11: stopped % 4.24/1.29 Prover 10: Warning: ignoring some quantifiers % 4.24/1.30 Prover 1: stopped % 4.24/1.30 Prover 10: Constructing countermodel ... % 4.24/1.30 Prover 10: stopped % 4.24/1.30 Prover 7: stopped % 4.24/1.30 Prover 13: Warning: ignoring some quantifiers % 4.24/1.31 Prover 13: Constructing countermodel ... % 4.24/1.31 Prover 13: stopped % 4.24/1.32 Prover 8: Warning: ignoring some quantifiers % 4.24/1.32 Prover 8: Constructing countermodel ... % 4.24/1.33 Prover 8: stopped % 4.24/1.33 % 4.24/1.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.24/1.33 % 4.24/1.33 % SZS output start Proof for theBenchmark % 4.24/1.33 Assumptions after simplification: % 4.24/1.33 --------------------------------- % 4.24/1.33 % 4.24/1.33 (intersect_defn) % 4.24/1.36 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ % 4.24/1.36 (intersect(v0, v1) = v2) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v1) | % 4.24/1.36 ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v0) = v4)) & ! [v0: % 4.24/1.36 $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ (intersect(v0, % 4.24/1.36 v1) = v2) | ~ (member(v3, v0) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) % 4.24/1.36 | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4)) & ! [v0: $i] : ! % 4.24/1.36 [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : % 4.24/1.36 (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2))) % 4.24/1.36 % 4.24/1.36 (prove_th101) % 4.24/1.37 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & % 4.24/1.37 subset(v1, v2) = 0 & intersect(v0, v2) = v3 & intersect(v0, v1) = 0 & $i(v2) % 4.24/1.37 & $i(v1) & $i(v0)) % 4.24/1.37 % 4.24/1.37 (subset_defn) % 4.24/1.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 4.24/1.37 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ % 4.24/1.37 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] : % 4.24/1.37 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) | % 4.24/1.37 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 & % 4.24/1.37 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 4.24/1.37 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | % 4.24/1.37 ~ $i(v0) | member(v2, v1) = 0) % 4.24/1.37 % 4.24/1.37 (function-axioms) % 4.24/1.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 4.24/1.37 [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & % 4.24/1.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: % 4.24/1.37 $i] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) = v0)) % 4.24/1.37 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 4.24/1.37 [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 4.24/1.37 % 4.24/1.37 Further assumptions not needed in the proof: % 4.24/1.37 -------------------------------------------- % 4.24/1.37 reflexivity_of_subset, symmetry_of_intersect % 4.24/1.37 % 4.24/1.37 Those formulas are unsatisfiable: % 4.24/1.37 --------------------------------- % 4.24/1.37 % 4.24/1.37 Begin of proof % 4.24/1.37 | % 4.24/1.38 | ALPHA: (intersect_defn) implies: % 4.24/1.38 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | % 4.24/1.38 | ~ $i(v0) | ? [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & % 4.24/1.38 | $i(v2))) % 4.24/1.38 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ % 4.24/1.38 | (intersect(v0, v1) = v2) | ~ (member(v3, v0) = 0) | ~ $i(v3) | ~ % 4.24/1.38 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = % 4.24/1.38 | v4)) % 4.24/1.38 | % 4.24/1.38 | ALPHA: (subset_defn) implies: % 4.24/1.38 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~ % 4.24/1.38 | (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | member(v2, % 4.24/1.38 | v1) = 0) % 4.24/1.38 | % 4.24/1.38 | ALPHA: (function-axioms) implies: % 4.24/1.38 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 4.24/1.38 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 4.24/1.38 | = v0)) % 4.24/1.38 | % 4.24/1.38 | DELTA: instantiating (prove_th101) with fresh symbols all_7_0, all_7_1, % 4.24/1.38 | all_7_2, all_7_3 gives: % 4.24/1.38 | (5) ~ (all_7_0 = 0) & subset(all_7_2, all_7_1) = 0 & intersect(all_7_3, % 4.24/1.38 | all_7_1) = all_7_0 & intersect(all_7_3, all_7_2) = 0 & $i(all_7_1) & % 4.24/1.38 | $i(all_7_2) & $i(all_7_3) % 4.24/1.38 | % 4.24/1.38 | ALPHA: (5) implies: % 4.24/1.39 | (6) ~ (all_7_0 = 0) % 4.24/1.39 | (7) $i(all_7_3) % 4.24/1.39 | (8) $i(all_7_2) % 4.24/1.39 | (9) $i(all_7_1) % 4.24/1.39 | (10) intersect(all_7_3, all_7_2) = 0 % 4.24/1.39 | (11) intersect(all_7_3, all_7_1) = all_7_0 % 4.24/1.39 | (12) subset(all_7_2, all_7_1) = 0 % 4.24/1.39 | % 4.24/1.39 | GROUND_INST: instantiating (1) with all_7_3, all_7_2, simplifying with (7), % 4.24/1.39 | (8), (10) gives: % 4.24/1.39 | (13) ? [v0: $i] : (member(v0, all_7_2) = 0 & member(v0, all_7_3) = 0 & % 4.24/1.39 | $i(v0)) % 4.24/1.39 | % 4.24/1.39 | DELTA: instantiating (13) with fresh symbol all_15_0 gives: % 4.24/1.39 | (14) member(all_15_0, all_7_2) = 0 & member(all_15_0, all_7_3) = 0 & % 4.24/1.39 | $i(all_15_0) % 4.24/1.39 | % 4.24/1.39 | ALPHA: (14) implies: % 4.24/1.39 | (15) $i(all_15_0) % 4.24/1.39 | (16) member(all_15_0, all_7_3) = 0 % 4.24/1.39 | (17) member(all_15_0, all_7_2) = 0 % 4.24/1.39 | % 4.24/1.39 | GROUND_INST: instantiating (2) with all_7_3, all_7_1, all_7_0, all_15_0, % 4.24/1.39 | simplifying with (7), (9), (11), (15), (16) gives: % 4.24/1.39 | (18) all_7_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_15_0, all_7_1) % 4.24/1.39 | = v0) % 4.24/1.39 | % 4.24/1.39 | GROUND_INST: instantiating (3) with all_7_2, all_7_1, all_15_0, simplifying % 4.24/1.39 | with (8), (9), (12), (15), (17) gives: % 4.24/1.39 | (19) member(all_15_0, all_7_1) = 0 % 4.24/1.39 | % 4.24/1.39 | BETA: splitting (18) gives: % 4.24/1.39 | % 4.24/1.39 | Case 1: % 4.24/1.39 | | % 4.24/1.39 | | (20) all_7_0 = 0 % 4.24/1.39 | | % 4.24/1.39 | | REDUCE: (6), (20) imply: % 4.24/1.39 | | (21) $false % 4.24/1.39 | | % 4.24/1.39 | | CLOSE: (21) is inconsistent. % 4.24/1.39 | | % 4.24/1.39 | Case 2: % 4.24/1.39 | | % 4.24/1.40 | | (22) ? [v0: int] : ( ~ (v0 = 0) & member(all_15_0, all_7_1) = v0) % 4.24/1.40 | | % 4.24/1.40 | | DELTA: instantiating (22) with fresh symbol all_35_0 gives: % 4.24/1.40 | | (23) ~ (all_35_0 = 0) & member(all_15_0, all_7_1) = all_35_0 % 4.24/1.40 | | % 4.24/1.40 | | ALPHA: (23) implies: % 4.24/1.40 | | (24) ~ (all_35_0 = 0) % 4.24/1.40 | | (25) member(all_15_0, all_7_1) = all_35_0 % 4.24/1.40 | | % 4.24/1.40 | | GROUND_INST: instantiating (4) with 0, all_35_0, all_7_1, all_15_0, % 4.24/1.40 | | simplifying with (19), (25) gives: % 4.24/1.40 | | (26) all_35_0 = 0 % 4.24/1.40 | | % 4.24/1.40 | | REDUCE: (24), (26) imply: % 4.24/1.40 | | (27) $false % 4.24/1.40 | | % 4.24/1.40 | | CLOSE: (27) is inconsistent. % 4.24/1.40 | | % 4.24/1.40 | End of split % 4.24/1.40 | % 4.24/1.40 End of proof % 4.24/1.40 % SZS output end Proof for theBenchmark % 4.24/1.40 % 4.24/1.40 798ms %------------------------------------------------------------------------------