%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET978+1 : TPTP v8.1.2. Released v3.2.0. % 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 15:27:16 EDT 2023 % Result : Theorem 3.88s 1.31s % Output : Proof 5.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SET978+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.15/0.34 % Computer : n028.cluster.edu % 0.15/0.34 % Model : x86_64 x86_64 % 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.34 % Memory : 8042.1875MB % 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.34 % CPULimit : 300 % 0.15/0.34 % WCLimit : 300 % 0.15/0.34 % DateTime : Sat Aug 26 08:29:37 EDT 2023 % 0.15/0.34 % CPUTime : % 0.20/0.59 ________ _____ % 0.20/0.59 ___ __ \_________(_)________________________________ % 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.59 % 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.59 (2023-06-19) % 0.20/0.59 % 0.20/0.59 (c) Philipp Rümmer, 2009-2023 % 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.59 Amanda Stjerna. % 0.20/0.59 Free software under BSD-3-Clause. % 0.20/0.59 % 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.59 % 0.20/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.60 Running up to 7 provers in parallel. % 0.20/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.02/0.95 Prover 1: Preprocessing ... % 2.02/0.95 Prover 4: Preprocessing ... % 2.02/0.99 Prover 6: Preprocessing ... % 2.02/0.99 Prover 0: Preprocessing ... % 2.02/0.99 Prover 5: Preprocessing ... % 2.02/0.99 Prover 2: Preprocessing ... % 2.02/0.99 Prover 3: Preprocessing ... % 3.21/1.12 Prover 1: Constructing countermodel ... % 3.21/1.13 Prover 5: Proving ... % 3.21/1.13 Prover 2: Proving ... % 3.21/1.13 Prover 3: Constructing countermodel ... % 3.21/1.13 Prover 4: Constructing countermodel ... % 3.21/1.13 Prover 0: Proving ... % 3.21/1.13 Prover 6: Constructing countermodel ... % 3.88/1.30 Prover 5: proved (691ms) % 3.88/1.31 % 3.88/1.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 3.88/1.31 % 3.88/1.31 Prover 3: stopped % 3.88/1.31 Prover 0: stopped % 3.88/1.31 Prover 2: stopped % 3.88/1.32 Prover 6: stopped % 3.88/1.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 3.88/1.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 3.88/1.32 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 3.88/1.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 3.88/1.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 3.88/1.34 Prover 7: Preprocessing ... % 3.88/1.34 Prover 8: Preprocessing ... % 4.76/1.34 Prover 13: Preprocessing ... % 4.76/1.35 Prover 11: Preprocessing ... % 4.76/1.35 Prover 10: Preprocessing ... % 4.76/1.37 Prover 7: Constructing countermodel ... % 4.76/1.38 Prover 4: Found proof (size 30) % 4.76/1.38 Prover 4: proved (772ms) % 4.76/1.38 Prover 1: stopped % 4.76/1.39 Prover 7: stopped % 4.76/1.40 Prover 13: Warning: ignoring some quantifiers % 4.76/1.40 Prover 8: Warning: ignoring some quantifiers % 4.76/1.40 Prover 10: Constructing countermodel ... % 4.76/1.40 Prover 13: Constructing countermodel ... % 4.76/1.40 Prover 8: Constructing countermodel ... % 4.76/1.40 Prover 11: Constructing countermodel ... % 4.76/1.40 Prover 10: stopped % 4.76/1.41 Prover 13: stopped % 4.76/1.41 Prover 8: stopped % 4.76/1.41 Prover 11: stopped % 4.76/1.41 % 4.76/1.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 4.76/1.41 % 4.76/1.41 % SZS output start Proof for theBenchmark % 4.76/1.42 Assumptions after simplification: % 4.76/1.42 --------------------------------- % 4.76/1.42 % 4.76/1.42 (t127_zfmisc_1) % 5.47/1.44 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: % 5.47/1.44 $i] : ! [v6: int] : (v6 = 0 | ~ (cartesian_product2(v1, v3) = v5) | ~ % 5.47/1.44 (cartesian_product2(v0, v2) = v4) | ~ (disjoint(v4, v5) = v6) | ~ $i(v3) | % 5.47/1.44 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: int] : ? [v8: int] : ( ~ (v8 = % 5.47/1.44 0) & ~ (v7 = 0) & disjoint(v2, v3) = v8 & disjoint(v0, v1) = v7)) % 5.47/1.44 % 5.47/1.45 (t131_zfmisc_1) % 5.47/1.45 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5: % 5.47/1.45 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: any] : ? [v9: $i] : ? [v10: $i] % 5.47/1.45 : ? [v11: any] : ( ~ (v1 = v0) & singleton(v1) = v6 & singleton(v0) = v4 & % 5.47/1.45 cartesian_product2(v6, v3) = v7 & cartesian_product2(v4, v2) = v5 & % 5.47/1.45 cartesian_product2(v3, v6) = v10 & cartesian_product2(v2, v4) = v9 & % 5.47/1.45 disjoint(v9, v10) = v11 & disjoint(v5, v7) = v8 & $i(v10) & $i(v9) & $i(v7) % 5.47/1.45 & $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v11 = % 5.47/1.45 0) | ~ (v8 = 0))) % 5.47/1.45 % 5.47/1.45 (t17_zfmisc_1) % 5.47/1.45 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 % 5.47/1.45 | v1 = v0 | ~ (singleton(v1) = v3) | ~ (singleton(v0) = v2) | ~ % 5.47/1.45 (disjoint(v2, v3) = v4) | ~ $i(v1) | ~ $i(v0)) % 5.47/1.45 % 5.47/1.45 Further assumptions not needed in the proof: % 5.47/1.45 -------------------------------------------- % 5.47/1.45 rc1_xboole_0, rc2_xboole_0, symmetry_r1_xboole_0 % 5.47/1.45 % 5.47/1.45 Those formulas are unsatisfiable: % 5.47/1.45 --------------------------------- % 5.47/1.45 % 5.47/1.45 Begin of proof % 5.47/1.45 | % 5.47/1.45 | DELTA: instantiating (t131_zfmisc_1) with fresh symbols all_10_0, all_10_1, % 5.47/1.45 | all_10_2, all_10_3, all_10_4, all_10_5, all_10_6, all_10_7, all_10_8, % 5.47/1.45 | all_10_9, all_10_10, all_10_11 gives: % 5.47/1.46 | (1) ~ (all_10_10 = all_10_11) & singleton(all_10_10) = all_10_5 & % 5.47/1.46 | singleton(all_10_11) = all_10_7 & cartesian_product2(all_10_5, % 5.47/1.46 | all_10_8) = all_10_4 & cartesian_product2(all_10_7, all_10_9) = % 5.47/1.46 | all_10_6 & cartesian_product2(all_10_8, all_10_5) = all_10_1 & % 5.47/1.46 | cartesian_product2(all_10_9, all_10_7) = all_10_2 & disjoint(all_10_2, % 5.47/1.46 | all_10_1) = all_10_0 & disjoint(all_10_6, all_10_4) = all_10_3 & % 5.47/1.46 | $i(all_10_1) & $i(all_10_2) & $i(all_10_4) & $i(all_10_5) & % 5.47/1.46 | $i(all_10_6) & $i(all_10_7) & $i(all_10_8) & $i(all_10_9) & % 5.47/1.46 | $i(all_10_10) & $i(all_10_11) & ( ~ (all_10_0 = 0) | ~ (all_10_3 = 0)) % 5.47/1.46 | % 5.47/1.46 | ALPHA: (1) implies: % 5.47/1.46 | (2) ~ (all_10_10 = all_10_11) % 5.47/1.46 | (3) $i(all_10_11) % 5.47/1.46 | (4) $i(all_10_10) % 5.47/1.46 | (5) $i(all_10_9) % 5.47/1.46 | (6) $i(all_10_8) % 5.47/1.46 | (7) $i(all_10_7) % 5.47/1.46 | (8) $i(all_10_5) % 5.47/1.46 | (9) disjoint(all_10_6, all_10_4) = all_10_3 % 5.47/1.46 | (10) disjoint(all_10_2, all_10_1) = all_10_0 % 5.47/1.46 | (11) cartesian_product2(all_10_9, all_10_7) = all_10_2 % 5.47/1.46 | (12) cartesian_product2(all_10_8, all_10_5) = all_10_1 % 5.47/1.46 | (13) cartesian_product2(all_10_7, all_10_9) = all_10_6 % 5.47/1.46 | (14) cartesian_product2(all_10_5, all_10_8) = all_10_4 % 5.47/1.46 | (15) singleton(all_10_11) = all_10_7 % 5.47/1.46 | (16) singleton(all_10_10) = all_10_5 % 5.47/1.46 | (17) ~ (all_10_0 = 0) | ~ (all_10_3 = 0) % 5.47/1.46 | % 5.47/1.47 | GROUND_INST: instantiating (t127_zfmisc_1) with all_10_9, all_10_8, all_10_7, % 5.47/1.47 | all_10_5, all_10_2, all_10_1, all_10_0, simplifying with (5), % 5.47/1.47 | (6), (7), (8), (10), (11), (12) gives: % 5.47/1.47 | (18) all_10_0 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 5.47/1.47 | 0) & disjoint(all_10_7, all_10_5) = v1 & disjoint(all_10_9, % 5.47/1.47 | all_10_8) = v0) % 5.47/1.47 | % 5.47/1.47 | GROUND_INST: instantiating (t127_zfmisc_1) with all_10_7, all_10_5, all_10_9, % 5.47/1.47 | all_10_8, all_10_6, all_10_4, all_10_3, simplifying with (5), % 5.47/1.47 | (6), (7), (8), (9), (13), (14) gives: % 5.47/1.47 | (19) all_10_3 = 0 | ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = % 5.47/1.47 | 0) & disjoint(all_10_7, all_10_5) = v0 & disjoint(all_10_9, % 5.47/1.47 | all_10_8) = v1) % 5.47/1.47 | % 5.47/1.47 | BETA: splitting (17) gives: % 5.47/1.47 | % 5.47/1.47 | Case 1: % 5.47/1.47 | | % 5.47/1.47 | | (20) ~ (all_10_0 = 0) % 5.47/1.47 | | % 5.47/1.47 | | BETA: splitting (18) gives: % 5.47/1.47 | | % 5.47/1.47 | | Case 1: % 5.47/1.47 | | | % 5.47/1.47 | | | (21) all_10_0 = 0 % 5.47/1.47 | | | % 5.47/1.47 | | | REDUCE: (20), (21) imply: % 5.47/1.47 | | | (22) $false % 5.47/1.47 | | | % 5.47/1.47 | | | CLOSE: (22) is inconsistent. % 5.47/1.47 | | | % 5.47/1.47 | | Case 2: % 5.47/1.47 | | | % 5.47/1.47 | | | (23) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 5.47/1.47 | | | disjoint(all_10_7, all_10_5) = v1 & disjoint(all_10_9, all_10_8) % 5.47/1.47 | | | = v0) % 5.47/1.47 | | | % 5.47/1.47 | | | DELTA: instantiating (23) with fresh symbols all_28_0, all_28_1 gives: % 5.47/1.47 | | | (24) ~ (all_28_0 = 0) & ~ (all_28_1 = 0) & disjoint(all_10_7, % 5.47/1.47 | | | all_10_5) = all_28_0 & disjoint(all_10_9, all_10_8) = all_28_1 % 5.47/1.47 | | | % 5.47/1.47 | | | ALPHA: (24) implies: % 5.47/1.47 | | | (25) ~ (all_28_0 = 0) % 5.47/1.47 | | | (26) disjoint(all_10_7, all_10_5) = all_28_0 % 5.47/1.47 | | | % 5.47/1.47 | | | GROUND_INST: instantiating (t17_zfmisc_1) with all_10_11, all_10_10, % 5.47/1.47 | | | all_10_7, all_10_5, all_28_0, simplifying with (3), (4), % 5.47/1.47 | | | (15), (16), (26) gives: % 5.47/1.47 | | | (27) all_28_0 = 0 | all_10_10 = all_10_11 % 5.47/1.47 | | | % 5.47/1.47 | | | BETA: splitting (27) gives: % 5.47/1.47 | | | % 5.47/1.47 | | | Case 1: % 5.47/1.47 | | | | % 5.47/1.47 | | | | (28) all_28_0 = 0 % 5.47/1.47 | | | | % 5.47/1.47 | | | | REDUCE: (25), (28) imply: % 5.47/1.47 | | | | (29) $false % 5.47/1.47 | | | | % 5.47/1.47 | | | | CLOSE: (29) is inconsistent. % 5.47/1.47 | | | | % 5.47/1.47 | | | Case 2: % 5.47/1.47 | | | | % 5.47/1.48 | | | | (30) all_10_10 = all_10_11 % 5.47/1.48 | | | | % 5.47/1.48 | | | | REDUCE: (2), (30) imply: % 5.47/1.48 | | | | (31) $false % 5.47/1.48 | | | | % 5.47/1.48 | | | | CLOSE: (31) is inconsistent. % 5.47/1.48 | | | | % 5.47/1.48 | | | End of split % 5.47/1.48 | | | % 5.47/1.48 | | End of split % 5.47/1.48 | | % 5.47/1.48 | Case 2: % 5.47/1.48 | | % 5.47/1.48 | | (32) ~ (all_10_3 = 0) % 5.47/1.48 | | % 5.47/1.48 | | BETA: splitting (19) gives: % 5.47/1.48 | | % 5.47/1.48 | | Case 1: % 5.47/1.48 | | | % 5.47/1.48 | | | (33) all_10_3 = 0 % 5.47/1.48 | | | % 5.47/1.48 | | | REDUCE: (32), (33) imply: % 5.47/1.48 | | | (34) $false % 5.47/1.48 | | | % 5.47/1.48 | | | CLOSE: (34) is inconsistent. % 5.47/1.48 | | | % 5.47/1.48 | | Case 2: % 5.47/1.48 | | | % 5.47/1.48 | | | (35) ? [v0: int] : ? [v1: int] : ( ~ (v1 = 0) & ~ (v0 = 0) & % 5.47/1.48 | | | disjoint(all_10_7, all_10_5) = v0 & disjoint(all_10_9, all_10_8) % 5.47/1.48 | | | = v1) % 5.47/1.48 | | | % 5.47/1.48 | | | DELTA: instantiating (35) with fresh symbols all_28_0, all_28_1 gives: % 5.47/1.48 | | | (36) ~ (all_28_0 = 0) & ~ (all_28_1 = 0) & disjoint(all_10_7, % 5.47/1.48 | | | all_10_5) = all_28_1 & disjoint(all_10_9, all_10_8) = all_28_0 % 5.47/1.48 | | | % 5.47/1.48 | | | ALPHA: (36) implies: % 5.47/1.48 | | | (37) ~ (all_28_1 = 0) % 5.47/1.48 | | | (38) disjoint(all_10_7, all_10_5) = all_28_1 % 5.47/1.48 | | | % 5.47/1.48 | | | GROUND_INST: instantiating (t17_zfmisc_1) with all_10_11, all_10_10, % 5.47/1.48 | | | all_10_7, all_10_5, all_28_1, simplifying with (3), (4), % 5.47/1.48 | | | (15), (16), (38) gives: % 5.47/1.48 | | | (39) all_28_1 = 0 | all_10_10 = all_10_11 % 5.47/1.48 | | | % 5.47/1.48 | | | BETA: splitting (39) gives: % 5.47/1.48 | | | % 5.47/1.48 | | | Case 1: % 5.47/1.48 | | | | % 5.47/1.48 | | | | (40) all_28_1 = 0 % 5.47/1.48 | | | | % 5.47/1.48 | | | | REDUCE: (37), (40) imply: % 5.47/1.48 | | | | (41) $false % 5.47/1.48 | | | | % 5.47/1.48 | | | | CLOSE: (41) is inconsistent. % 5.47/1.48 | | | | % 5.47/1.48 | | | Case 2: % 5.47/1.48 | | | | % 5.47/1.48 | | | | (42) all_10_10 = all_10_11 % 5.47/1.48 | | | | % 5.47/1.48 | | | | REDUCE: (2), (42) imply: % 5.47/1.48 | | | | (43) $false % 5.47/1.48 | | | | % 5.47/1.48 | | | | CLOSE: (43) is inconsistent. % 5.47/1.48 | | | | % 5.47/1.48 | | | End of split % 5.47/1.48 | | | % 5.47/1.48 | | End of split % 5.47/1.48 | | % 5.47/1.48 | End of split % 5.47/1.48 | % 5.47/1.48 End of proof % 5.47/1.48 % SZS output end Proof for theBenchmark % 5.47/1.48 % 5.47/1.48 890ms %------------------------------------------------------------------------------