%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET575+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 : n005.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 3.39s 1.16s % Output : Proof 3.93s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SET575+3 : TPTP v8.1.2. Released v2.2.0. % 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.35 % Computer : n005.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Sat Aug 26 12:38:08 EDT 2023 % 0.13/0.35 % CPUTime : % 0.20/0.62 ________ _____ % 0.20/0.62 ___ __ \_________(_)________________________________ % 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.62 % 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.62 (2023-06-19) % 0.20/0.62 % 0.20/0.62 (c) Philipp Rümmer, 2009-2023 % 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.62 Amanda Stjerna. % 0.20/0.62 Free software under BSD-3-Clause. % 0.20/0.62 % 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.62 % 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.63 Running up to 7 provers in parallel. % 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 1.88/0.94 Prover 1: Preprocessing ... % 1.88/0.94 Prover 4: Preprocessing ... % 2.16/0.98 Prover 3: Preprocessing ... % 2.16/0.98 Prover 0: Preprocessing ... % 2.16/0.98 Prover 5: Preprocessing ... % 2.16/0.98 Prover 2: Preprocessing ... % 2.16/0.98 Prover 6: Preprocessing ... % 2.67/1.05 Prover 2: Constructing countermodel ... % 2.67/1.07 Prover 5: Proving ... % 2.83/1.08 Prover 6: Proving ... % 2.83/1.08 Prover 3: Constructing countermodel ... % 2.83/1.08 Prover 1: Constructing countermodel ... % 2.83/1.11 Prover 4: Constructing countermodel ... % 2.83/1.11 Prover 0: Proving ... % 3.39/1.16 Prover 2: proved (512ms) % 3.39/1.16 Prover 3: proved (511ms) % 3.39/1.16 % 3.39/1.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.39/1.16 % 3.39/1.16 % 3.39/1.16 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.39/1.16 % 3.39/1.16 Prover 5: stopped % 3.39/1.17 Prover 0: stopped % 3.39/1.17 Prover 6: stopped % 3.39/1.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.39/1.19 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.39/1.19 Prover 8: Preprocessing ... % 3.39/1.19 Prover 7: Preprocessing ... % 3.39/1.19 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.39/1.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.39/1.19 Prover 10: Preprocessing ... % 3.39/1.19 Prover 11: Preprocessing ... % 3.39/1.19 Prover 1: Found proof (size 13) % 3.39/1.19 Prover 1: proved (549ms) % 3.39/1.19 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.39/1.19 Prover 4: stopped % 3.39/1.20 Prover 10: Constructing countermodel ... % 3.39/1.20 Prover 10: stopped % 3.39/1.20 Prover 7: Constructing countermodel ... % 3.39/1.20 Prover 7: stopped % 3.39/1.20 Prover 13: Preprocessing ... % 3.39/1.20 Prover 11: stopped % 3.39/1.22 Prover 13: Constructing countermodel ... % 3.39/1.22 Prover 13: stopped % 3.93/1.23 Prover 8: Warning: ignoring some quantifiers % 3.93/1.23 Prover 8: Constructing countermodel ... % 3.93/1.23 Prover 8: stopped % 3.93/1.23 % 3.93/1.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.93/1.23 % 3.93/1.24 % SZS output start Proof for theBenchmark % 3.93/1.24 Assumptions after simplification: % 3.93/1.24 --------------------------------- % 3.93/1.24 % 3.93/1.24 (intersect_defn) % 3.93/1.28 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (intersect(v0, v1) = % 3.93/1.28 v2) | ~ $i(v1) | ~ $i(v0) | ! [v3: $i] : ( ~ (member(v3, v0) = 0) | ~ % 3.93/1.28 $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4))) & ! [v0: % 3.93/1.28 $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? % 3.93/1.28 [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2))) % 3.93/1.28 % 3.93/1.28 (prove_th15) % 3.93/1.28 ? [v0: $i] : ? [v1: $i] : (intersect(v0, v1) = 0 & $i(v1) & $i(v0) & ! [v2: % 3.93/1.28 $i] : ( ~ (member(v2, v0) = 0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & % 3.93/1.28 member(v2, v1) = v3))) % 3.93/1.28 % 3.93/1.28 (function-axioms) % 3.93/1.28 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! % 3.93/1.28 [v3: $i] : (v1 = v0 | ~ (intersect(v3, v2) = v1) | ~ (intersect(v3, v2) = % 3.93/1.28 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: % 3.93/1.28 $i] : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 3.93/1.29 = v0)) % 3.93/1.29 % 3.93/1.29 Further assumptions not needed in the proof: % 3.93/1.29 -------------------------------------------- % 3.93/1.29 symmetry_of_intersect % 3.93/1.29 % 3.93/1.29 Those formulas are unsatisfiable: % 3.93/1.29 --------------------------------- % 3.93/1.29 % 3.93/1.29 Begin of proof % 3.93/1.29 | % 3.93/1.29 | ALPHA: (intersect_defn) implies: % 3.93/1.29 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (intersect(v0, v1) = 0) | ~ $i(v1) | % 3.93/1.29 | ~ $i(v0) | ? [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & % 3.93/1.29 | $i(v2))) % 3.93/1.29 | % 3.93/1.29 | ALPHA: (function-axioms) implies: % 3.93/1.29 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : % 3.93/1.29 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) % 3.93/1.29 | = v0)) % 3.93/1.29 | % 3.93/1.29 | DELTA: instantiating (prove_th15) with fresh symbols all_5_0, all_5_1 gives: % 3.93/1.30 | (3) intersect(all_5_1, all_5_0) = 0 & $i(all_5_0) & $i(all_5_1) & ! [v0: % 3.93/1.30 | $i] : ( ~ (member(v0, all_5_1) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ % 3.93/1.30 | (v1 = 0) & member(v0, all_5_0) = v1)) % 3.93/1.30 | % 3.93/1.30 | ALPHA: (3) implies: % 3.93/1.30 | (4) $i(all_5_1) % 3.93/1.30 | (5) $i(all_5_0) % 3.93/1.30 | (6) intersect(all_5_1, all_5_0) = 0 % 3.93/1.30 | (7) ! [v0: $i] : ( ~ (member(v0, all_5_1) = 0) | ~ $i(v0) | ? [v1: int] % 3.93/1.30 | : ( ~ (v1 = 0) & member(v0, all_5_0) = v1)) % 3.93/1.30 | % 3.93/1.30 | GROUND_INST: instantiating (1) with all_5_1, all_5_0, simplifying with (4), % 3.93/1.30 | (5), (6) gives: % 3.93/1.30 | (8) ? [v0: $i] : (member(v0, all_5_0) = 0 & member(v0, all_5_1) = 0 & % 3.93/1.30 | $i(v0)) % 3.93/1.30 | % 3.93/1.30 | DELTA: instantiating (8) with fresh symbol all_14_0 gives: % 3.93/1.30 | (9) member(all_14_0, all_5_0) = 0 & member(all_14_0, all_5_1) = 0 & % 3.93/1.30 | $i(all_14_0) % 3.93/1.30 | % 3.93/1.30 | ALPHA: (9) implies: % 3.93/1.30 | (10) $i(all_14_0) % 3.93/1.30 | (11) member(all_14_0, all_5_1) = 0 % 3.93/1.30 | (12) member(all_14_0, all_5_0) = 0 % 3.93/1.30 | % 3.93/1.30 | GROUND_INST: instantiating (7) with all_14_0, simplifying with (10), (11) % 3.93/1.30 | gives: % 3.93/1.30 | (13) ? [v0: int] : ( ~ (v0 = 0) & member(all_14_0, all_5_0) = v0) % 3.93/1.30 | % 3.93/1.30 | DELTA: instantiating (13) with fresh symbol all_21_0 gives: % 3.93/1.31 | (14) ~ (all_21_0 = 0) & member(all_14_0, all_5_0) = all_21_0 % 3.93/1.31 | % 3.93/1.31 | ALPHA: (14) implies: % 3.93/1.31 | (15) ~ (all_21_0 = 0) % 3.93/1.31 | (16) member(all_14_0, all_5_0) = all_21_0 % 3.93/1.31 | % 3.93/1.31 | GROUND_INST: instantiating (2) with 0, all_21_0, all_5_0, all_14_0, % 3.93/1.31 | simplifying with (12), (16) gives: % 3.93/1.31 | (17) all_21_0 = 0 % 3.93/1.31 | % 3.93/1.31 | REDUCE: (15), (17) imply: % 3.93/1.31 | (18) $false % 3.93/1.31 | % 3.93/1.31 | CLOSE: (18) is inconsistent. % 3.93/1.31 | % 3.93/1.31 End of proof % 3.93/1.31 % SZS output end Proof for theBenchmark % 3.93/1.31 % 3.93/1.31 685ms %------------------------------------------------------------------------------