%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU160+2 : TPTP v8.1.2. Released v3.3.0. % 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 17:42:54 EDT 2023 % Result : Theorem 12.30s 2.41s % Output : Proof 14.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU160+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.34 % Computer : n012.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 : Wed Aug 23 13:50:57 EDT 2023 % 0.12/0.34 % 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 ... % 0.20/0.61 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 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 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 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 % 3.16/1.16 Prover 1: Preprocessing ... % 3.16/1.16 Prover 4: Preprocessing ... % 3.65/1.20 Prover 3: Preprocessing ... % 3.65/1.20 Prover 0: Preprocessing ... % 3.65/1.20 Prover 6: Preprocessing ... % 3.65/1.20 Prover 5: Preprocessing ... % 3.65/1.20 Prover 2: Preprocessing ... % 9.12/2.00 Prover 1: Warning: ignoring some quantifiers % 9.68/2.05 Prover 5: Proving ... % 9.68/2.09 Prover 1: Constructing countermodel ... % 9.68/2.09 Prover 4: Warning: ignoring some quantifiers % 9.68/2.11 Prover 3: Warning: ignoring some quantifiers % 9.68/2.14 Prover 6: Proving ... % 9.68/2.14 Prover 3: Constructing countermodel ... % 9.68/2.18 Prover 2: Proving ... % 10.32/2.23 Prover 4: Constructing countermodel ... % 11.76/2.37 Prover 0: Proving ... % 12.30/2.41 Prover 3: proved (1792ms) % 12.30/2.41 % 12.30/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 12.30/2.41 % 12.30/2.41 Prover 6: stopped % 12.30/2.41 Prover 5: stopped % 12.30/2.42 Prover 0: stopped % 12.30/2.42 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 12.30/2.42 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 12.30/2.42 Prover 2: stopped % 12.30/2.44 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 12.30/2.44 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 12.30/2.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 12.79/2.52 Prover 8: Preprocessing ... % 12.79/2.52 Prover 7: Preprocessing ... % 12.79/2.54 Prover 10: Preprocessing ... % 12.79/2.55 Prover 1: Found proof (size 27) % 12.79/2.55 Prover 13: Preprocessing ... % 12.79/2.55 Prover 1: proved (1940ms) % 12.79/2.55 Prover 4: stopped % 12.79/2.56 Prover 11: Preprocessing ... % 13.43/2.58 Prover 10: stopped % 13.64/2.59 Prover 7: stopped % 13.90/2.63 Prover 11: stopped % 13.96/2.64 Prover 13: stopped % 13.96/2.71 Prover 8: Warning: ignoring some quantifiers % 13.96/2.74 Prover 8: Constructing countermodel ... % 13.96/2.75 Prover 8: stopped % 13.96/2.75 % 13.96/2.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 13.96/2.75 % 13.96/2.76 % SZS output start Proof for theBenchmark % 13.96/2.76 Assumptions after simplification: % 13.96/2.76 --------------------------------- % 13.96/2.76 % 13.96/2.76 (l4_zfmisc_1) % 13.96/2.79 $i(empty_set) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = % 13.96/2.79 0 | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = v3) | ~ $i(v1) | ~ % 13.96/2.79 $i(v0) | ( ~ (v2 = v0) & ~ (v0 = empty_set))) & ! [v0: $i] : ! [v1: $i] : % 13.96/2.79 ! [v2: $i] : (v2 = v0 | v0 = empty_set | ~ (singleton(v1) = v2) | ~ % 13.96/2.79 (subset(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0)) % 13.96/2.79 % 13.96/2.79 (t39_zfmisc_1) % 13.96/2.79 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : % 13.96/2.79 (singleton(v1) = v2 & subset(v0, v2) = v3 & $i(v2) & $i(v1) & $i(v0) & ((v3 = % 13.96/2.79 0 & ~ (v2 = v0) & ~ (v0 = empty_set)) | ( ~ (v3 = 0) & (v2 = v0 | v0 = % 13.96/2.79 empty_set)))) % 13.96/2.79 % 13.96/2.79 Further assumptions not needed in the proof: % 13.96/2.79 -------------------------------------------- % 13.96/2.79 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_tarski, % 13.96/2.79 commutativity_k2_xboole_0, commutativity_k3_xboole_0, d10_xboole_0, d1_tarski, % 13.96/2.79 d1_xboole_0, d1_zfmisc_1, d2_tarski, d2_xboole_0, d2_zfmisc_1, d3_tarski, % 13.96/2.79 d3_xboole_0, d4_tarski, d4_xboole_0, d5_tarski, d7_xboole_0, d8_xboole_0, % 13.96/2.79 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k2_xboole_0, % 13.96/2.80 dt_k2_zfmisc_1, dt_k3_tarski, dt_k3_xboole_0, dt_k4_tarski, dt_k4_xboole_0, % 13.96/2.80 fc1_xboole_0, fc1_zfmisc_1, fc2_xboole_0, fc3_xboole_0, idempotence_k2_xboole_0, % 13.96/2.80 idempotence_k3_xboole_0, irreflexivity_r2_xboole_0, l1_zfmisc_1, l23_zfmisc_1, % 13.96/2.80 l25_zfmisc_1, l28_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_zfmisc_1, % 13.96/2.80 l50_zfmisc_1, l55_zfmisc_1, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, % 13.96/2.80 symmetry_r1_xboole_0, t10_zfmisc_1, t12_xboole_1, t17_xboole_1, t19_xboole_1, % 13.96/2.80 t1_boole, t1_xboole_1, t1_zfmisc_1, t26_xboole_1, t28_xboole_1, t2_boole, % 13.96/2.80 t2_tarski, t2_xboole_1, t33_xboole_1, t33_zfmisc_1, t36_xboole_1, t37_xboole_1, % 13.96/2.80 t37_zfmisc_1, t38_zfmisc_1, t39_xboole_1, t3_boole, t3_xboole_0, t3_xboole_1, % 13.96/2.80 t40_xboole_1, t45_xboole_1, t48_xboole_1, t4_boole, t4_xboole_0, t60_xboole_1, % 13.96/2.80 t63_xboole_1, t69_enumset1, t6_boole, t6_zfmisc_1, t7_boole, t7_xboole_1, % 13.96/2.80 t83_xboole_1, t8_boole, t8_xboole_1, t8_zfmisc_1, t9_zfmisc_1 % 13.96/2.80 % 13.96/2.80 Those formulas are unsatisfiable: % 13.96/2.80 --------------------------------- % 13.96/2.80 % 13.96/2.80 Begin of proof % 13.96/2.80 | % 13.96/2.80 | ALPHA: (l4_zfmisc_1) implies: % 13.96/2.80 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v0 | v0 = empty_set | % 13.96/2.80 | ~ (singleton(v1) = v2) | ~ (subset(v0, v2) = 0) | ~ $i(v1) | ~ % 13.96/2.80 | $i(v0)) % 13.96/2.80 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 13.96/2.80 | (singleton(v1) = v2) | ~ (subset(v0, v2) = v3) | ~ $i(v1) | ~ % 13.96/2.80 | $i(v0) | ( ~ (v2 = v0) & ~ (v0 = empty_set))) % 13.96/2.80 | % 13.96/2.80 | ALPHA: (t39_zfmisc_1) implies: % 13.96/2.80 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : (singleton(v1) % 13.96/2.80 | = v2 & subset(v0, v2) = v3 & $i(v2) & $i(v1) & $i(v0) & ((v3 = 0 & ~ % 13.96/2.80 | (v2 = v0) & ~ (v0 = empty_set)) | ( ~ (v3 = 0) & (v2 = v0 | v0 = % 13.96/2.80 | empty_set)))) % 13.96/2.80 | % 13.96/2.80 | DELTA: instantiating (3) with fresh symbols all_94_0, all_94_1, all_94_2, % 13.96/2.80 | all_94_3 gives: % 13.96/2.80 | (4) singleton(all_94_2) = all_94_1 & subset(all_94_3, all_94_1) = all_94_0 % 13.96/2.80 | & $i(all_94_1) & $i(all_94_2) & $i(all_94_3) & ((all_94_0 = 0 & ~ % 13.96/2.80 | (all_94_1 = all_94_3) & ~ (all_94_3 = empty_set)) | ( ~ (all_94_0 % 13.96/2.80 | = 0) & (all_94_1 = all_94_3 | all_94_3 = empty_set))) % 13.96/2.80 | % 13.96/2.81 | ALPHA: (4) implies: % 14.56/2.81 | (5) $i(all_94_3) % 14.56/2.81 | (6) $i(all_94_2) % 14.56/2.81 | (7) subset(all_94_3, all_94_1) = all_94_0 % 14.56/2.81 | (8) singleton(all_94_2) = all_94_1 % 14.56/2.81 | (9) (all_94_0 = 0 & ~ (all_94_1 = all_94_3) & ~ (all_94_3 = empty_set)) | % 14.56/2.81 | ( ~ (all_94_0 = 0) & (all_94_1 = all_94_3 | all_94_3 = empty_set)) % 14.56/2.81 | % 14.56/2.81 | GROUND_INST: instantiating (2) with all_94_3, all_94_2, all_94_1, all_94_0, % 14.56/2.81 | simplifying with (5), (6), (7), (8) gives: % 14.56/2.81 | (10) all_94_0 = 0 | ( ~ (all_94_1 = all_94_3) & ~ (all_94_3 = empty_set)) % 14.56/2.81 | % 14.56/2.81 | BETA: splitting (9) gives: % 14.56/2.81 | % 14.56/2.81 | Case 1: % 14.56/2.81 | | % 14.56/2.81 | | (11) all_94_0 = 0 & ~ (all_94_1 = all_94_3) & ~ (all_94_3 = empty_set) % 14.56/2.81 | | % 14.56/2.81 | | ALPHA: (11) implies: % 14.56/2.81 | | (12) all_94_0 = 0 % 14.56/2.81 | | (13) ~ (all_94_3 = empty_set) % 14.56/2.81 | | (14) ~ (all_94_1 = all_94_3) % 14.56/2.81 | | % 14.56/2.81 | | REDUCE: (7), (12) imply: % 14.56/2.81 | | (15) subset(all_94_3, all_94_1) = 0 % 14.56/2.81 | | % 14.56/2.81 | | GROUND_INST: instantiating (1) with all_94_3, all_94_2, all_94_1, % 14.56/2.81 | | simplifying with (5), (6), (8), (15) gives: % 14.56/2.81 | | (16) all_94_1 = all_94_3 | all_94_3 = empty_set % 14.56/2.81 | | % 14.56/2.81 | | REF_CLOSE: (13), (14), (16) are inconsistent by sub-proof #1. % 14.56/2.81 | | % 14.56/2.81 | Case 2: % 14.56/2.81 | | % 14.56/2.81 | | (17) ~ (all_94_0 = 0) & (all_94_1 = all_94_3 | all_94_3 = empty_set) % 14.56/2.81 | | % 14.56/2.81 | | ALPHA: (17) implies: % 14.56/2.81 | | (18) ~ (all_94_0 = 0) % 14.56/2.81 | | (19) all_94_1 = all_94_3 | all_94_3 = empty_set % 14.56/2.81 | | % 14.56/2.81 | | BETA: splitting (10) gives: % 14.56/2.81 | | % 14.56/2.81 | | Case 1: % 14.56/2.81 | | | % 14.56/2.81 | | | (20) all_94_0 = 0 % 14.56/2.81 | | | % 14.56/2.81 | | | REDUCE: (18), (20) imply: % 14.56/2.81 | | | (21) $false % 14.56/2.81 | | | % 14.56/2.81 | | | CLOSE: (21) is inconsistent. % 14.56/2.81 | | | % 14.56/2.81 | | Case 2: % 14.56/2.81 | | | % 14.56/2.81 | | | (22) ~ (all_94_1 = all_94_3) & ~ (all_94_3 = empty_set) % 14.56/2.81 | | | % 14.56/2.81 | | | ALPHA: (22) implies: % 14.56/2.81 | | | (23) ~ (all_94_3 = empty_set) % 14.56/2.81 | | | (24) ~ (all_94_1 = all_94_3) % 14.56/2.81 | | | % 14.56/2.81 | | | REF_CLOSE: (19), (23), (24) are inconsistent by sub-proof #1. % 14.56/2.81 | | | % 14.56/2.81 | | End of split % 14.56/2.81 | | % 14.56/2.81 | End of split % 14.56/2.81 | % 14.56/2.81 End of proof % 14.56/2.81 % 14.56/2.81 Sub-proof #1 shows that the following formulas are inconsistent: % 14.56/2.81 ---------------------------------------------------------------- % 14.56/2.82 (1) all_94_1 = all_94_3 | all_94_3 = empty_set % 14.56/2.82 (2) ~ (all_94_3 = empty_set) % 14.56/2.82 (3) ~ (all_94_1 = all_94_3) % 14.56/2.82 % 14.56/2.82 Begin of proof % 14.56/2.82 | % 14.56/2.82 | BETA: splitting (1) gives: % 14.56/2.82 | % 14.56/2.82 | Case 1: % 14.56/2.82 | | % 14.56/2.82 | | (4) all_94_3 = empty_set % 14.56/2.82 | | % 14.56/2.82 | | REDUCE: (2), (4) imply: % 14.56/2.82 | | (5) $false % 14.56/2.82 | | % 14.56/2.82 | | CLOSE: (5) is inconsistent. % 14.56/2.82 | | % 14.56/2.82 | Case 2: % 14.56/2.82 | | % 14.56/2.82 | | (6) all_94_1 = all_94_3 % 14.56/2.82 | | % 14.56/2.82 | | REDUCE: (3), (6) imply: % 14.56/2.82 | | (7) $false % 14.56/2.82 | | % 14.56/2.82 | | CLOSE: (7) is inconsistent. % 14.56/2.82 | | % 14.56/2.82 | End of split % 14.56/2.82 | % 14.56/2.82 End of proof % 14.56/2.82 % SZS output end Proof for theBenchmark % 14.56/2.82 % 14.56/2.82 2222ms %------------------------------------------------------------------------------