%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SEU151+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 : n025.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 17:42:49 EDT 2023 % Result : Theorem 18.25s 3.43s % Output : Proof 23.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SEU151+2 : TPTP v8.1.2. Released v3.3.0. % 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.11/0.32 % Computer : n025.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 300 % 0.11/0.32 % DateTime : Wed Aug 23 17:15:50 EDT 2023 % 0.11/0.32 % CPUTime : % 0.17/0.60 ________ _____ % 0.17/0.60 ___ __ \_________(_)________________________________ % 0.17/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.17/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.17/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.17/0.60 % 0.17/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.17/0.60 (2023-06-19) % 0.17/0.60 % 0.17/0.60 (c) Philipp Rümmer, 2009-2023 % 0.17/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.17/0.60 Amanda Stjerna. % 0.17/0.60 Free software under BSD-3-Clause. % 0.17/0.60 % 0.17/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.17/0.60 % 0.17/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.17/0.62 Running up to 7 provers in parallel. % 0.17/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.17/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.17/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.17/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.17/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.17/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.17/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.48/1.31 Prover 4: Preprocessing ... % 3.48/1.31 Prover 1: Preprocessing ... % 3.85/1.36 Prover 2: Preprocessing ... % 3.85/1.36 Prover 5: Preprocessing ... % 3.85/1.36 Prover 0: Preprocessing ... % 3.85/1.36 Prover 6: Preprocessing ... % 3.85/1.36 Prover 3: Preprocessing ... % 11.21/2.43 Prover 5: Proving ... % 11.29/2.51 Prover 1: Warning: ignoring some quantifiers % 12.17/2.58 Prover 3: Warning: ignoring some quantifiers % 12.17/2.60 Prover 6: Proving ... % 12.17/2.62 Prover 3: Constructing countermodel ... % 12.17/2.63 Prover 4: Warning: ignoring some quantifiers % 12.17/2.64 Prover 1: Constructing countermodel ... % 13.30/2.74 Prover 4: Constructing countermodel ... % 13.37/2.81 Prover 0: Proving ... % 13.37/2.83 Prover 2: Proving ... % 16.13/3.14 Prover 3: gave up % 16.13/3.15 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 17.34/3.29 Prover 7: Preprocessing ... % 18.25/3.42 Prover 2: proved (2796ms) % 18.25/3.43 % 18.25/3.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 18.25/3.43 % 18.25/3.43 Prover 5: stopped % 18.25/3.43 Prover 6: stopped % 18.25/3.43 Prover 0: stopped % 18.25/3.46 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 18.25/3.46 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 18.25/3.46 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 18.25/3.48 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 19.22/3.58 Prover 10: Preprocessing ... % 19.22/3.60 Prover 11: Preprocessing ... % 19.22/3.60 Prover 8: Preprocessing ... % 19.22/3.61 Prover 13: Preprocessing ... % 19.22/3.69 Prover 7: Warning: ignoring some quantifiers % 19.22/3.76 Prover 7: Constructing countermodel ... % 19.22/3.78 Prover 10: Warning: ignoring some quantifiers % 19.22/3.79 Prover 1: gave up % 19.22/3.81 Prover 10: Constructing countermodel ... % 19.22/3.81 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 19.22/3.83 Prover 8: Warning: ignoring some quantifiers % 19.65/3.84 Prover 13: Warning: ignoring some quantifiers % 19.65/3.86 Prover 8: Constructing countermodel ... % 21.62/3.89 Prover 13: Constructing countermodel ... % 21.95/3.94 Prover 16: Preprocessing ... % 21.95/3.99 Prover 10: Found proof (size 28) % 21.95/3.99 Prover 10: proved (556ms) % 21.95/3.99 Prover 7: stopped % 21.95/3.99 Prover 4: stopped % 21.95/3.99 Prover 13: stopped % 21.95/3.99 Prover 8: stopped % 22.54/4.02 Prover 16: stopped % 22.54/4.04 Prover 11: Warning: ignoring some quantifiers % 22.87/4.08 Prover 11: Constructing countermodel ... % 22.87/4.12 Prover 11: stopped % 22.87/4.12 % 22.87/4.12 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 22.87/4.12 % 22.87/4.13 % SZS output start Proof for theBenchmark % 22.87/4.14 Assumptions after simplification: % 22.87/4.14 --------------------------------- % 22.87/4.14 % 22.87/4.14 (commutativity_k2_tarski) % 23.29/4.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | % 23.29/4.18 ~ $i(v1) | ~ $i(v0) | (unordered_pair(v1, v0) = v2 & $i(v2))) % 23.29/4.18 % 23.29/4.18 (d2_tarski) % 23.39/4.19 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = v0 | % 23.39/4.19 ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ % 23.39/4.19 $i(v0) | ~ in(v3, v2)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: % 23.39/4.19 $i] : (v3 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | % 23.39/4.19 ~ $i(v0) | ? [v4: $i] : ($i(v4) & (v4 = v2 | v4 = v1 | in(v4, v0)) & ( ~ % 23.39/4.19 in(v4, v0) | ( ~ (v4 = v2) & ~ (v4 = v1))))) & ! [v0: $i] : ! [v1: % 23.39/4.19 $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ % 23.39/4.19 $i(v1) | ~ $i(v0) | in(v1, v2)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : % 23.39/4.19 ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0, % 23.39/4.19 v2)) % 23.39/4.19 % 23.39/4.19 (t10_zfmisc_1) % 23.39/4.19 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ( ~ (v3 % 23.39/4.19 = v0) & ~ (v2 = v0) & unordered_pair(v2, v3) = v4 & unordered_pair(v0, % 23.39/4.19 v1) = v4 & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0)) % 23.39/4.19 % 23.39/4.19 Further assumptions not needed in the proof: % 23.39/4.19 -------------------------------------------- % 23.39/4.19 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_xboole_0, % 23.39/4.19 commutativity_k3_xboole_0, d10_xboole_0, d1_tarski, d1_xboole_0, d1_zfmisc_1, % 23.39/4.19 d2_xboole_0, d3_tarski, d3_xboole_0, d4_xboole_0, d7_xboole_0, d8_xboole_0, % 23.39/4.19 dt_k1_tarski, dt_k1_xboole_0, dt_k1_zfmisc_1, dt_k2_tarski, dt_k2_xboole_0, % 23.39/4.19 dt_k3_xboole_0, dt_k4_xboole_0, fc1_xboole_0, fc2_xboole_0, fc3_xboole_0, % 23.39/4.19 idempotence_k2_xboole_0, idempotence_k3_xboole_0, irreflexivity_r2_xboole_0, % 23.39/4.19 l1_zfmisc_1, l2_zfmisc_1, l32_xboole_1, l3_zfmisc_1, l4_zfmisc_1, rc1_xboole_0, % 23.39/4.19 rc2_xboole_0, reflexivity_r1_tarski, symmetry_r1_xboole_0, t12_xboole_1, % 23.39/4.19 t17_xboole_1, t19_xboole_1, t1_boole, t1_xboole_1, t1_zfmisc_1, t26_xboole_1, % 23.39/4.19 t28_xboole_1, t2_boole, t2_tarski, t2_xboole_1, t33_xboole_1, t36_xboole_1, % 23.39/4.20 t37_xboole_1, t39_xboole_1, t3_boole, t3_xboole_0, t3_xboole_1, t40_xboole_1, % 23.39/4.20 t45_xboole_1, t48_xboole_1, t4_boole, t4_xboole_0, t60_xboole_1, t63_xboole_1, % 23.39/4.20 t69_enumset1, t6_boole, t6_zfmisc_1, t7_boole, t7_xboole_1, t83_xboole_1, % 23.39/4.20 t8_boole, t8_xboole_1, t8_zfmisc_1, t9_zfmisc_1 % 23.39/4.20 % 23.39/4.20 Those formulas are unsatisfiable: % 23.39/4.20 --------------------------------- % 23.39/4.20 % 23.39/4.20 Begin of proof % 23.39/4.20 | % 23.39/4.20 | ALPHA: (d2_tarski) implies: % 23.39/4.20 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 23.39/4.20 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v0, v2)) % 23.39/4.20 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = % 23.39/4.20 | v2) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | in(v1, v2)) % 23.39/4.20 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v3 = v1 | v3 = % 23.39/4.20 | v0 | ~ (unordered_pair(v0, v1) = v2) | ~ $i(v3) | ~ $i(v2) | ~ % 23.39/4.20 | $i(v1) | ~ $i(v0) | ~ in(v3, v2)) % 23.39/4.20 | % 23.39/4.20 | DELTA: instantiating (t10_zfmisc_1) with fresh symbols all_78_0, all_78_1, % 23.39/4.20 | all_78_2, all_78_3, all_78_4 gives: % 23.39/4.20 | (4) ~ (all_78_1 = all_78_4) & ~ (all_78_2 = all_78_4) & % 23.39/4.20 | unordered_pair(all_78_2, all_78_1) = all_78_0 & % 23.39/4.21 | unordered_pair(all_78_4, all_78_3) = all_78_0 & $i(all_78_0) & % 23.39/4.21 | $i(all_78_1) & $i(all_78_2) & $i(all_78_3) & $i(all_78_4) % 23.39/4.21 | % 23.39/4.21 | ALPHA: (4) implies: % 23.39/4.21 | (5) ~ (all_78_2 = all_78_4) % 23.39/4.21 | (6) ~ (all_78_1 = all_78_4) % 23.39/4.21 | (7) $i(all_78_4) % 23.39/4.21 | (8) $i(all_78_3) % 23.39/4.21 | (9) $i(all_78_2) % 23.39/4.21 | (10) $i(all_78_1) % 23.39/4.21 | (11) $i(all_78_0) % 23.39/4.21 | (12) unordered_pair(all_78_4, all_78_3) = all_78_0 % 23.39/4.21 | (13) unordered_pair(all_78_2, all_78_1) = all_78_0 % 23.39/4.21 | % 23.39/4.21 | GROUND_INST: instantiating (1) with all_78_4, all_78_3, all_78_0, simplifying % 23.39/4.21 | with (7), (8), (11), (12) gives: % 23.39/4.21 | (14) in(all_78_4, all_78_0) % 23.39/4.21 | % 23.39/4.21 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_78_4, all_78_3, % 23.39/4.21 | all_78_0, simplifying with (7), (8), (12) gives: % 23.39/4.21 | (15) unordered_pair(all_78_3, all_78_4) = all_78_0 & $i(all_78_0) % 23.39/4.21 | % 23.39/4.21 | ALPHA: (15) implies: % 23.39/4.21 | (16) unordered_pair(all_78_3, all_78_4) = all_78_0 % 23.39/4.21 | % 23.39/4.21 | GROUND_INST: instantiating (2) with all_78_2, all_78_1, all_78_0, simplifying % 23.39/4.21 | with (9), (10), (11), (13) gives: % 23.39/4.21 | (17) in(all_78_1, all_78_0) % 23.39/4.21 | % 23.39/4.21 | GROUND_INST: instantiating (1) with all_78_2, all_78_1, all_78_0, simplifying % 23.39/4.21 | with (9), (10), (11), (13) gives: % 23.39/4.21 | (18) in(all_78_2, all_78_0) % 23.39/4.21 | % 23.39/4.21 | GROUND_INST: instantiating (commutativity_k2_tarski) with all_78_2, all_78_1, % 23.39/4.21 | all_78_0, simplifying with (9), (10), (13) gives: % 23.39/4.21 | (19) unordered_pair(all_78_1, all_78_2) = all_78_0 & $i(all_78_0) % 23.39/4.21 | % 23.39/4.21 | ALPHA: (19) implies: % 23.39/4.21 | (20) unordered_pair(all_78_1, all_78_2) = all_78_0 % 23.39/4.21 | % 23.39/4.22 | GROUND_INST: instantiating (3) with all_78_3, all_78_4, all_78_0, all_78_1, % 23.39/4.22 | simplifying with (7), (8), (10), (11), (16), (17) gives: % 23.39/4.22 | (21) all_78_1 = all_78_3 | all_78_1 = all_78_4 % 23.39/4.22 | % 23.39/4.22 | GROUND_INST: instantiating (3) with all_78_3, all_78_4, all_78_0, all_78_2, % 23.39/4.22 | simplifying with (7), (8), (9), (11), (16), (18) gives: % 23.39/4.22 | (22) all_78_2 = all_78_3 | all_78_2 = all_78_4 % 23.39/4.22 | % 23.39/4.22 | GROUND_INST: instantiating (3) with all_78_1, all_78_2, all_78_0, all_78_4, % 23.39/4.22 | simplifying with (7), (9), (10), (11), (14), (20) gives: % 23.39/4.22 | (23) all_78_1 = all_78_4 | all_78_2 = all_78_4 % 23.39/4.22 | % 23.39/4.22 | BETA: splitting (21) gives: % 23.56/4.22 | % 23.56/4.22 | Case 1: % 23.56/4.22 | | % 23.56/4.22 | | (24) all_78_1 = all_78_3 % 23.56/4.22 | | % 23.56/4.22 | | BETA: splitting (22) gives: % 23.56/4.22 | | % 23.56/4.22 | | Case 1: % 23.56/4.22 | | | % 23.56/4.22 | | | (25) all_78_2 = all_78_3 % 23.56/4.22 | | | % 23.56/4.22 | | | REDUCE: (5), (25) imply: % 23.56/4.22 | | | (26) ~ (all_78_3 = all_78_4) % 23.56/4.22 | | | % 23.56/4.22 | | | BETA: splitting (23) gives: % 23.56/4.22 | | | % 23.56/4.22 | | | Case 1: % 23.56/4.22 | | | | % 23.56/4.22 | | | | (27) all_78_1 = all_78_4 % 23.56/4.22 | | | | % 23.56/4.22 | | | | COMBINE_EQS: (24), (27) imply: % 23.56/4.22 | | | | (28) all_78_3 = all_78_4 % 23.56/4.22 | | | | % 23.56/4.22 | | | | REDUCE: (26), (28) imply: % 23.56/4.22 | | | | (29) $false % 23.56/4.22 | | | | % 23.56/4.22 | | | | CLOSE: (29) is inconsistent. % 23.56/4.22 | | | | % 23.56/4.22 | | | Case 2: % 23.56/4.22 | | | | % 23.56/4.22 | | | | (30) all_78_2 = all_78_4 % 23.56/4.22 | | | | % 23.56/4.22 | | | | COMBINE_EQS: (25), (30) imply: % 23.56/4.22 | | | | (31) all_78_3 = all_78_4 % 23.56/4.22 | | | | % 23.56/4.22 | | | | SIMP: (31) implies: % 23.56/4.22 | | | | (32) all_78_3 = all_78_4 % 23.56/4.22 | | | | % 23.56/4.22 | | | | REDUCE: (26), (32) imply: % 23.56/4.23 | | | | (33) $false % 23.56/4.23 | | | | % 23.56/4.23 | | | | CLOSE: (33) is inconsistent. % 23.56/4.23 | | | | % 23.56/4.23 | | | End of split % 23.56/4.23 | | | % 23.56/4.23 | | Case 2: % 23.56/4.23 | | | % 23.56/4.23 | | | (34) all_78_2 = all_78_4 % 23.56/4.23 | | | % 23.56/4.23 | | | REDUCE: (5), (34) imply: % 23.56/4.23 | | | (35) $false % 23.56/4.23 | | | % 23.56/4.23 | | | CLOSE: (35) is inconsistent. % 23.56/4.23 | | | % 23.56/4.23 | | End of split % 23.56/4.23 | | % 23.56/4.23 | Case 2: % 23.56/4.23 | | % 23.56/4.23 | | (36) all_78_1 = all_78_4 % 23.56/4.23 | | % 23.56/4.23 | | REDUCE: (6), (36) imply: % 23.56/4.23 | | (37) $false % 23.56/4.23 | | % 23.56/4.23 | | CLOSE: (37) is inconsistent. % 23.56/4.23 | | % 23.56/4.23 | End of split % 23.56/4.23 | % 23.56/4.23 End of proof % 23.56/4.23 % SZS output end Proof for theBenchmark % 23.56/4.23 % 23.56/4.23 3625ms %------------------------------------------------------------------------------