%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SYO523_1 : TPTP v8.1.2. Released v5.0.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n027.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 : Fri Sep 1 04:53:09 EDT 2023 % Result : Theorem 3.48s 1.29s % Output : Proof 4.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.13/0.14 % Problem : SYO523_1 : TPTP v8.1.2. Released v5.0.0. % 0.13/0.15 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.36 % Computer : n027.cluster.edu % 0.14/0.36 % Model : x86_64 x86_64 % 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.36 % Memory : 8042.1875MB % 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.21/0.36 % CPULimit : 300 % 0.21/0.36 % WCLimit : 300 % 0.21/0.36 % DateTime : Sat Aug 26 07:48:49 EDT 2023 % 0.21/0.36 % CPUTime : % 0.21/0.62 ________ _____ % 0.21/0.62 ___ __ \_________(_)________________________________ % 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.21/0.62 % 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.21/0.62 (2023-06-19) % 0.21/0.62 % 0.21/0.62 (c) Philipp Rümmer, 2009-2023 % 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.21/0.62 Amanda Stjerna. % 0.21/0.62 Free software under BSD-3-Clause. % 0.21/0.62 % 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.21/0.62 % 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.21/0.63 Running up to 7 provers in parallel. % 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.07/1.02 Prover 1: Preprocessing ... % 2.07/1.02 Prover 4: Preprocessing ... % 2.07/1.07 Prover 3: Preprocessing ... % 2.07/1.07 Prover 2: Preprocessing ... % 2.07/1.07 Prover 6: Preprocessing ... % 2.07/1.07 Prover 0: Preprocessing ... % 2.48/1.08 Prover 5: Preprocessing ... % 2.48/1.15 Prover 3: Constructing countermodel ... % 2.48/1.15 Prover 1: Constructing countermodel ... % 2.48/1.15 Prover 4: Constructing countermodel ... % 2.48/1.16 Prover 0: Proving ... % 2.48/1.16 Prover 6: Proving ... % 3.03/1.16 Prover 2: Proving ... % 3.03/1.17 Prover 5: Proving ... % 3.48/1.29 Prover 3: proved (649ms) % 3.48/1.29 % 3.48/1.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.48/1.29 % 3.48/1.29 Prover 6: stopped % 3.48/1.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.94/1.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.94/1.31 Prover 5: proved (659ms) % 3.94/1.31 Prover 2: proved (666ms) % 3.94/1.31 % 3.94/1.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.94/1.31 % 3.94/1.31 % 3.94/1.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.94/1.31 % 3.94/1.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.94/1.31 Prover 0: proved (669ms) % 3.94/1.31 % 3.94/1.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 3.94/1.31 % 3.94/1.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.94/1.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.94/1.32 Prover 8: Preprocessing ... % 3.94/1.32 Prover 7: Preprocessing ... % 3.94/1.32 Prover 10: Preprocessing ... % 3.94/1.33 Prover 1: Found proof (size 29) % 3.94/1.33 Prover 1: proved (687ms) % 3.94/1.33 Prover 4: Found proof (size 29) % 3.94/1.33 Prover 4: proved (690ms) % 3.94/1.33 Prover 13: Preprocessing ... % 3.94/1.34 Prover 8: Warning: ignoring some quantifiers % 3.94/1.34 Prover 7: Constructing countermodel ... % 3.94/1.34 Prover 8: Constructing countermodel ... % 3.94/1.34 Prover 7: stopped % 3.94/1.34 Prover 8: stopped % 3.94/1.35 Prover 11: Preprocessing ... % 3.94/1.35 Prover 10: Constructing countermodel ... % 3.94/1.35 Prover 10: stopped % 3.94/1.36 Prover 13: Warning: ignoring some quantifiers % 3.94/1.37 Prover 13: Constructing countermodel ... % 3.94/1.37 Prover 13: stopped % 3.94/1.37 Prover 11: Constructing countermodel ... % 3.94/1.37 Prover 11: stopped % 4.35/1.37 % 4.35/1.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 4.35/1.37 % 4.35/1.38 % SZS output start Proof for theBenchmark % 4.35/1.38 Assumptions after simplification: % 4.35/1.38 --------------------------------- % 4.35/1.38 % 4.35/1.38 (injective_f_pigeonhole) % 4.35/1.41 ? [v0: int] : ? [v1: int] : ? [v2: int] : ($lesseq(v2, 8) & $lesseq(7, v2) % 4.35/1.41 & $lesseq(v1, 8) & $lesseq(7, v1) & $lesseq(v0, 8) & $lesseq(7, v0) & f(5) = % 4.35/1.41 v2 & f(4) = v1 & f(3) = v0 & ! [v3: int] : ! [v4: int] : ! [v5: int] : % 4.35/1.41 (v4 = v3 | ~ (f(v4) = v5) | ~ (f(v3) = v5))) % 4.35/1.41 % 4.35/1.41 Those formulas are unsatisfiable: % 4.35/1.41 --------------------------------- % 4.35/1.41 % 4.35/1.41 Begin of proof % 4.35/1.41 | % 4.35/1.41 | DELTA: instantiating (injective_f_pigeonhole) with fresh symbols all_3_0, % 4.35/1.41 | all_3_1, all_3_2 gives: % 4.35/1.41 | (1) $lesseq(all_3_0, 8) & $lesseq(7, all_3_0) & $lesseq(all_3_1, 8) & % 4.35/1.41 | $lesseq(7, all_3_1) & $lesseq(all_3_2, 8) & $lesseq(7, all_3_2) & f(5) % 4.35/1.41 | = all_3_0 & f(4) = all_3_1 & f(3) = all_3_2 & ! [v0: int] : ! [v1: % 4.35/1.41 | int] : ! [v2: int] : (v1 = v0 | ~ (f(v1) = v2) | ~ (f(v0) = v2)) % 4.35/1.41 | % 4.35/1.41 | ALPHA: (1) implies: % 4.35/1.42 | (2) $lesseq(7, all_3_2) % 4.35/1.42 | (3) $lesseq(all_3_2, 8) % 4.35/1.42 | (4) $lesseq(7, all_3_1) % 4.35/1.42 | (5) $lesseq(all_3_1, 8) % 4.35/1.42 | (6) $lesseq(7, all_3_0) % 4.35/1.42 | (7) $lesseq(all_3_0, 8) % 4.35/1.42 | (8) f(3) = all_3_2 % 4.35/1.42 | (9) f(4) = all_3_1 % 4.35/1.42 | (10) f(5) = all_3_0 % 4.35/1.42 | (11) ! [v0: int] : ! [v1: int] : ! [v2: int] : (v1 = v0 | ~ (f(v1) = % 4.35/1.42 | v2) | ~ (f(v0) = v2)) % 4.35/1.42 | % 4.35/1.42 | GROUND_INST: instantiating (11) with 3, 4, all_3_2, simplifying with (8) % 4.35/1.42 | gives: % 4.35/1.42 | (12) ~ (f(4) = all_3_2) % 4.35/1.42 | % 4.35/1.42 | GROUND_INST: instantiating (11) with 4, 5, all_3_1, simplifying with (9) % 4.35/1.42 | gives: % 4.35/1.42 | (13) ~ (f(5) = all_3_1) % 4.35/1.42 | % 4.35/1.42 | GROUND_INST: instantiating (11) with 3, 5, all_3_2, simplifying with (8) % 4.35/1.42 | gives: % 4.35/1.42 | (14) ~ (f(5) = all_3_2) % 4.35/1.42 | % 4.35/1.42 | PRED_UNIFY: (9), (12) imply: % 4.35/1.42 | (15) ~ (all_3_1 = all_3_2) % 4.35/1.42 | % 4.35/1.42 | PRED_UNIFY: (10), (14) imply: % 4.35/1.42 | (16) ~ (all_3_0 = all_3_2) % 4.35/1.42 | % 4.35/1.42 | PRED_UNIFY: (10), (13) imply: % 4.35/1.42 | (17) ~ (all_3_0 = all_3_1) % 4.35/1.42 | % 4.35/1.42 | SPLIT-EQ: splitting (15) gives: % 4.35/1.42 | % 4.35/1.42 | Case 1: % 4.35/1.42 | | % 4.35/1.43 | | (18) $lesseq(1, $difference(all_3_2, all_3_1)) % 4.35/1.43 | | % 4.35/1.43 | | COMBINE_INEQS: (4), (18) imply: % 4.35/1.43 | | (19) $lesseq(8, all_3_2) % 4.35/1.43 | | % 4.35/1.43 | | ANTI_SYMM: (3), (19) imply: % 4.35/1.43 | | (20) all_3_2 = 8 % 4.35/1.43 | | % 4.35/1.43 | | COMBINE_INEQS: (3), (18) imply: % 4.35/1.43 | | (21) $lesseq(all_3_1, 7) % 4.35/1.43 | | % 4.35/1.43 | | ANTI_SYMM: (4), (21) imply: % 4.35/1.43 | | (22) all_3_1 = 7 % 4.35/1.43 | | % 4.35/1.43 | | REDUCE: (17), (22) imply: % 4.35/1.43 | | (23) ~ (all_3_0 = 7) % 4.35/1.43 | | % 4.35/1.43 | | REDUCE: (16), (20) imply: % 4.35/1.43 | | (24) ~ (all_3_0 = 8) % 4.35/1.43 | | % 4.35/1.43 | | REF_CLOSE: (6), (7), (23), (24) are inconsistent by sub-proof #1. % 4.35/1.43 | | % 4.35/1.43 | Case 2: % 4.35/1.43 | | % 4.35/1.43 | | (25) $lesseq(1, $difference(all_3_1, all_3_2)) % 4.35/1.43 | | % 4.35/1.43 | | COMBINE_INEQS: (5), (25) imply: % 4.35/1.43 | | (26) $lesseq(all_3_2, 7) % 4.35/1.43 | | % 4.35/1.43 | | ANTI_SYMM: (2), (26) imply: % 4.35/1.43 | | (27) all_3_2 = 7 % 4.35/1.43 | | % 4.35/1.43 | | COMBINE_INEQS: (2), (25) imply: % 4.35/1.43 | | (28) $lesseq(8, all_3_1) % 4.35/1.43 | | % 4.35/1.43 | | ANTI_SYMM: (5), (28) imply: % 4.35/1.43 | | (29) all_3_1 = 8 % 4.35/1.43 | | % 4.35/1.43 | | REDUCE: (17), (29) imply: % 4.35/1.43 | | (30) ~ (all_3_0 = 8) % 4.35/1.43 | | % 4.35/1.43 | | REDUCE: (16), (27) imply: % 4.35/1.43 | | (31) ~ (all_3_0 = 7) % 4.35/1.43 | | % 4.35/1.43 | | REF_CLOSE: (6), (7), (30), (31) are inconsistent by sub-proof #1. % 4.35/1.43 | | % 4.35/1.43 | End of split % 4.35/1.43 | % 4.35/1.43 End of proof % 4.35/1.43 % 4.35/1.43 Sub-proof #1 shows that the following formulas are inconsistent: % 4.35/1.43 ---------------------------------------------------------------- % 4.35/1.43 (1) $lesseq(all_3_0, 8) % 4.35/1.43 (2) ~ (all_3_0 = 8) % 4.35/1.43 (3) ~ (all_3_0 = 7) % 4.35/1.43 (4) $lesseq(7, all_3_0) % 4.35/1.43 % 4.35/1.43 Begin of proof % 4.35/1.43 | % 4.35/1.43 | STRENGTHEN: (1), (2) imply: % 4.35/1.43 | (5) $lesseq(all_3_0, 7) % 4.35/1.43 | % 4.35/1.43 | STRENGTHEN: (3), (5) imply: % 4.35/1.44 | (6) $lesseq(all_3_0, 6) % 4.35/1.44 | % 4.35/1.44 | COMBINE_INEQS: (4), (6) imply: % 4.35/1.44 | (7) $false % 4.35/1.44 | % 4.35/1.44 | CLOSE: (7) is inconsistent. % 4.35/1.44 | % 4.35/1.44 End of proof % 4.35/1.44 % SZS output end Proof for theBenchmark % 4.35/1.44 % 4.35/1.44 815ms %------------------------------------------------------------------------------