%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET626+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 : n028.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 3.85s 1.43s % Output : Proof 5.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET626+3 : TPTP v8.1.2. Released v2.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n028.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 16:29:22 EDT 2023 % 0.12/0.34 % 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/sandbox/benchmark/theBenchmark.p ... % 0.20/0.61 Running up to 7 provers in parallel. % 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.60/1.00 Prover 4: Preprocessing ... % 1.60/1.00 Prover 1: Preprocessing ... % 2.16/1.04 Prover 6: Preprocessing ... % 2.16/1.04 Prover 3: Preprocessing ... % 2.16/1.04 Prover 2: Preprocessing ... % 2.16/1.04 Prover 5: Preprocessing ... % 2.16/1.04 Prover 0: Preprocessing ... % 3.41/1.24 Prover 1: Warning: ignoring some quantifiers % 3.41/1.24 Prover 5: Proving ... % 3.41/1.25 Prover 6: Proving ... % 3.41/1.25 Prover 1: Constructing countermodel ... % 3.41/1.25 Prover 3: Warning: ignoring some quantifiers % 3.41/1.26 Prover 2: Proving ... % 3.41/1.26 Prover 3: Constructing countermodel ... % 3.41/1.26 Prover 4: Warning: ignoring some quantifiers % 3.41/1.27 Prover 0: Proving ... % 3.41/1.28 Prover 4: Constructing countermodel ... % 3.85/1.41 Prover 3: proved (777ms) % 3.85/1.41 % 3.85/1.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.85/1.43 % 3.85/1.43 Prover 2: stopped % 3.85/1.43 Prover 0: stopped % 4.94/1.44 Prover 6: stopped % 4.94/1.44 Prover 5: stopped % 4.94/1.45 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 4.94/1.45 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 4.94/1.45 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 4.94/1.45 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 4.94/1.45 Prover 7: Preprocessing ... % 4.94/1.46 Prover 4: Found proof (size 23) % 4.94/1.46 Prover 10: Preprocessing ... % 4.94/1.46 Prover 4: proved (823ms) % 4.94/1.46 Prover 1: Found proof (size 22) % 4.94/1.46 Prover 1: proved (832ms) % 4.94/1.46 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 4.94/1.46 Prover 8: Preprocessing ... % 4.94/1.46 Prover 7: stopped % 4.94/1.47 Prover 11: Preprocessing ... % 4.94/1.47 Prover 13: Preprocessing ... % 4.94/1.48 Prover 10: stopped % 4.94/1.49 Prover 13: stopped % 4.94/1.50 Prover 11: stopped % 5.49/1.54 Prover 8: Warning: ignoring some quantifiers % 5.49/1.55 Prover 8: Constructing countermodel ... % 5.49/1.55 Prover 8: stopped % 5.49/1.55 % 5.49/1.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 5.49/1.55 % 5.49/1.56 % SZS output start Proof for theBenchmark % 5.49/1.56 Assumptions after simplification: % 5.49/1.56 --------------------------------- % 5.49/1.56 % 5.49/1.56 (commutativity_of_intersection) % 5.75/1.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = v2) | ~ % 5.75/1.60 $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) & ! [v0: $i] : % 5.75/1.60 ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v0, v1) = v2) | ~ $i(v1) | ~ % 5.75/1.60 $i(v0) | (intersection(v1, v0) = v2 & $i(v2))) % 5.75/1.60 % 5.75/1.60 (intersect_defn) % 5.75/1.60 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ % 5.75/1.60 (intersect(v0, v1) = v2) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v1) | % 5.75/1.60 ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v0) = v4)) & ! [v0: % 5.75/1.60 $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ (intersect(v0, % 5.75/1.60 v1) = v2) | ~ (member(v3, v0) = 0) | ~ $i(v3) | ~ $i(v1) | ~ $i(v0) % 5.75/1.60 | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4)) & ! [v0: $i] : ! % 5.75/1.60 [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : % 5.75/1.60 (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2))) % 5.75/1.60 % 5.75/1.60 (intersection_defn) % 5.75/1.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 5.75/1.61 | ~ (intersection(v0, v1) = v3) | ~ (member(v2, v3) = v4) | ~ $i(v2) | ~ % 5.75/1.61 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v2, v1) = v6 & % 5.75/1.61 member(v2, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : ! % 5.75/1.61 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v0, v1) = v3) | ~ % 5.75/1.61 (member(v2, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = % 5.75/1.61 0 & member(v2, v0) = 0)) % 5.75/1.61 % 5.75/1.61 (prove_th102) % 5.75/1.61 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4 % 5.75/1.61 = 0) & intersect(v0, v3) = 0 & intersect(v0, v1) = v4 & intersection(v1, % 5.75/1.61 v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 5.75/1.61 % 5.75/1.61 (function-axioms) % 5.75/1.61 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 5.75/1.61 [v3: $i] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) = % 5.75/1.61 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | % 5.75/1.61 ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) = v0)) & ! [v0: % 5.75/1.61 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] % 5.75/1.61 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) % 5.75/1.61 % 5.75/1.61 Further assumptions not needed in the proof: % 5.75/1.61 -------------------------------------------- % 5.75/1.61 equal_member_defn, symmetry_of_intersect % 5.75/1.61 % 5.75/1.61 Those formulas are unsatisfiable: % 5.75/1.61 --------------------------------- % 5.75/1.61 % 5.75/1.61 Begin of proof % 5.75/1.61 | % 5.75/1.62 | ALPHA: (intersection_defn) implies: % 5.75/1.62 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 5.75/1.62 | (intersection(v0, v1) = v3) | ~ (member(v2, v3) = 0) | ~ $i(v2) | % 5.75/1.62 | ~ $i(v1) | ~ $i(v0) | (member(v2, v1) = 0 & member(v2, v0) = 0)) % 5.75/1.62 | % 5.75/1.62 | ALPHA: (intersect_defn) implies: % 5.75/1.62 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | % 5.75/1.62 | ~ $i(v0) | ? [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & % 5.75/1.62 | $i(v2))) % 5.75/1.62 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : ! [v3: $i] : (v2 = 0 | ~ % 5.75/1.62 | (intersect(v0, v1) = v2) | ~ (member(v3, v0) = 0) | ~ $i(v3) | ~ % 5.75/1.62 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = % 5.75/1.62 | v4)) % 5.75/1.62 | % 5.75/1.62 | ALPHA: (commutativity_of_intersection) implies: % 5.75/1.62 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (intersection(v1, v0) = % 5.75/1.62 | v2) | ~ $i(v1) | ~ $i(v0) | (intersection(v0, v1) = v2 & $i(v2))) % 5.75/1.62 | % 5.75/1.62 | ALPHA: (function-axioms) implies: % 5.75/1.62 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 5.75/1.62 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 5.75/1.62 | = v0)) % 5.75/1.62 | % 5.75/1.62 | DELTA: instantiating (prove_th102) with fresh symbols all_7_0, all_7_1, % 5.75/1.62 | all_7_2, all_7_3, all_7_4 gives: % 5.75/1.63 | (6) ~ (all_7_0 = 0) & intersect(all_7_4, all_7_1) = 0 & intersect(all_7_4, % 5.75/1.63 | all_7_3) = all_7_0 & intersection(all_7_3, all_7_2) = all_7_1 & % 5.75/1.63 | $i(all_7_1) & $i(all_7_2) & $i(all_7_3) & $i(all_7_4) % 5.75/1.63 | % 5.75/1.63 | ALPHA: (6) implies: % 5.75/1.63 | (7) ~ (all_7_0 = 0) % 5.75/1.63 | (8) $i(all_7_4) % 5.75/1.63 | (9) $i(all_7_3) % 5.75/1.63 | (10) $i(all_7_2) % 5.75/1.63 | (11) intersection(all_7_3, all_7_2) = all_7_1 % 5.75/1.63 | (12) intersect(all_7_4, all_7_3) = all_7_0 % 5.75/1.63 | (13) intersect(all_7_4, all_7_1) = 0 % 5.75/1.63 | % 5.75/1.63 | GROUND_INST: instantiating (4) with all_7_2, all_7_3, all_7_1, simplifying % 5.75/1.63 | with (9), (10), (11) gives: % 5.75/1.63 | (14) intersection(all_7_2, all_7_3) = all_7_1 & $i(all_7_1) % 5.75/1.63 | % 5.75/1.63 | ALPHA: (14) implies: % 5.75/1.63 | (15) $i(all_7_1) % 5.75/1.63 | (16) intersection(all_7_2, all_7_3) = all_7_1 % 5.75/1.63 | % 5.75/1.63 | GROUND_INST: instantiating (2) with all_7_4, all_7_1, simplifying with (8), % 5.75/1.63 | (13), (15) gives: % 5.75/1.63 | (17) ? [v0: $i] : (member(v0, all_7_1) = 0 & member(v0, all_7_4) = 0 & % 5.75/1.63 | $i(v0)) % 5.75/1.63 | % 5.75/1.63 | DELTA: instantiating (17) with fresh symbol all_16_0 gives: % 5.75/1.63 | (18) member(all_16_0, all_7_1) = 0 & member(all_16_0, all_7_4) = 0 & % 5.75/1.63 | $i(all_16_0) % 5.75/1.63 | % 5.75/1.63 | ALPHA: (18) implies: % 5.75/1.63 | (19) $i(all_16_0) % 5.75/1.63 | (20) member(all_16_0, all_7_4) = 0 % 5.75/1.63 | (21) member(all_16_0, all_7_1) = 0 % 5.75/1.63 | % 5.75/1.63 | GROUND_INST: instantiating (3) with all_7_4, all_7_3, all_7_0, all_16_0, % 5.75/1.64 | simplifying with (8), (9), (12), (19), (20) gives: % 5.75/1.64 | (22) all_7_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_16_0, all_7_3) % 5.75/1.64 | = v0) % 5.75/1.64 | % 5.75/1.64 | GROUND_INST: instantiating (1) with all_7_2, all_7_3, all_16_0, all_7_1, % 5.75/1.64 | simplifying with (9), (10), (16), (19), (21) gives: % 5.75/1.64 | (23) member(all_16_0, all_7_2) = 0 & member(all_16_0, all_7_3) = 0 % 5.75/1.64 | % 5.75/1.64 | ALPHA: (23) implies: % 5.75/1.64 | (24) member(all_16_0, all_7_3) = 0 % 5.75/1.64 | % 5.75/1.64 | BETA: splitting (22) gives: % 5.75/1.64 | % 5.75/1.64 | Case 1: % 5.75/1.64 | | % 5.75/1.64 | | (25) all_7_0 = 0 % 5.75/1.64 | | % 5.75/1.64 | | REDUCE: (7), (25) imply: % 5.75/1.64 | | (26) $false % 5.75/1.64 | | % 5.75/1.64 | | CLOSE: (26) is inconsistent. % 5.75/1.64 | | % 5.75/1.64 | Case 2: % 5.75/1.64 | | % 5.75/1.64 | | (27) ? [v0: int] : ( ~ (v0 = 0) & member(all_16_0, all_7_3) = v0) % 5.75/1.64 | | % 5.75/1.64 | | DELTA: instantiating (27) with fresh symbol all_36_0 gives: % 5.75/1.64 | | (28) ~ (all_36_0 = 0) & member(all_16_0, all_7_3) = all_36_0 % 5.75/1.64 | | % 5.75/1.64 | | ALPHA: (28) implies: % 5.75/1.64 | | (29) ~ (all_36_0 = 0) % 5.75/1.64 | | (30) member(all_16_0, all_7_3) = all_36_0 % 5.75/1.64 | | % 5.75/1.64 | | GROUND_INST: instantiating (5) with 0, all_36_0, all_7_3, all_16_0, % 5.75/1.64 | | simplifying with (24), (30) gives: % 5.75/1.64 | | (31) all_36_0 = 0 % 5.75/1.64 | | % 5.75/1.64 | | REDUCE: (29), (31) imply: % 5.75/1.64 | | (32) $false % 5.75/1.64 | | % 5.75/1.64 | | CLOSE: (32) is inconsistent. % 5.75/1.64 | | % 5.75/1.64 | End of split % 5.75/1.64 | % 5.75/1.64 End of proof % 5.75/1.64 % SZS output end Proof for theBenchmark % 5.75/1.64 % 5.75/1.64 1040ms %------------------------------------------------------------------------------