%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM390+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 : n022.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 11:47:33 EDT 2023 % Result : Theorem 8.15s 1.90s % Output : Proof 11.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.13 % Problem : NUM390+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.14/0.35 % Computer : n022.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Aug 25 11:47:25 EDT 2023 % 0.14/0.35 % 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/sandbox/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 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 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 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 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 % 2.31/1.07 Prover 1: Preprocessing ... % 2.31/1.07 Prover 4: Preprocessing ... % 3.06/1.11 Prover 3: Preprocessing ... % 3.06/1.11 Prover 5: Preprocessing ... % 3.06/1.12 Prover 2: Preprocessing ... % 3.06/1.12 Prover 0: Preprocessing ... % 3.06/1.12 Prover 6: Preprocessing ... % 5.00/1.44 Prover 5: Proving ... % 5.00/1.45 Prover 2: Proving ... % 5.93/1.56 Prover 1: Warning: ignoring some quantifiers % 5.93/1.58 Prover 1: Constructing countermodel ... % 5.93/1.59 Prover 6: Proving ... % 5.93/1.60 Prover 3: Warning: ignoring some quantifiers % 5.93/1.62 Prover 3: Constructing countermodel ... % 5.93/1.63 Prover 4: Warning: ignoring some quantifiers % 6.64/1.67 Prover 4: Constructing countermodel ... % 7.44/1.76 Prover 0: Proving ... % 8.15/1.90 Prover 2: proved (1254ms) % 8.15/1.90 % 8.15/1.90 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.15/1.90 % 8.15/1.91 Prover 5: stopped % 8.15/1.91 Prover 3: stopped % 8.15/1.91 Prover 6: stopped % 8.15/1.91 Prover 0: stopped % 8.15/1.91 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.15/1.91 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.15/1.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.15/1.92 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.15/1.92 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.87/1.99 Prover 11: Preprocessing ... % 9.19/2.00 Prover 7: Preprocessing ... % 9.19/2.01 Prover 1: gave up % 9.19/2.01 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.19/2.01 Prover 8: Preprocessing ... % 9.19/2.01 Prover 13: Preprocessing ... % 9.19/2.02 Prover 10: Preprocessing ... % 9.19/2.04 Prover 16: Preprocessing ... % 9.61/2.10 Prover 7: Warning: ignoring some quantifiers % 9.61/2.10 Prover 10: Warning: ignoring some quantifiers % 9.61/2.11 Prover 10: Constructing countermodel ... % 9.61/2.11 Prover 13: Warning: ignoring some quantifiers % 9.61/2.12 Prover 16: Warning: ignoring some quantifiers % 9.61/2.12 Prover 7: Constructing countermodel ... % 9.61/2.13 Prover 13: Constructing countermodel ... % 9.61/2.13 Prover 16: Constructing countermodel ... % 9.61/2.14 Prover 8: Warning: ignoring some quantifiers % 9.73/2.16 Prover 8: Constructing countermodel ... % 11.12/2.29 Prover 11: Warning: ignoring some quantifiers % 11.12/2.31 Prover 11: Constructing countermodel ... % 11.12/2.32 Prover 7: Found proof (size 17) % 11.12/2.32 Prover 7: proved (410ms) % 11.12/2.32 Prover 10: Found proof (size 24) % 11.12/2.32 Prover 10: proved (410ms) % 11.12/2.32 Prover 4: stopped % 11.12/2.32 Prover 16: stopped % 11.12/2.32 Prover 13: stopped % 11.12/2.32 Prover 8: stopped % 11.12/2.33 Prover 11: stopped % 11.12/2.33 % 11.12/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 11.12/2.33 % 11.12/2.33 % SZS output start Proof for theBenchmark % 11.12/2.33 Assumptions after simplification: % 11.12/2.33 --------------------------------- % 11.12/2.34 % 11.12/2.34 (cc1_ordinal1) % 11.12/2.34 ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) | epsilon_connected(v0)) & ! [v0: % 11.12/2.34 $i] : ( ~ $i(v0) | ~ ordinal(v0) | epsilon_transitive(v0)) % 11.12/2.34 % 11.12/2.34 (d2_ordinal1) % 11.12/2.34 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ epsilon_transitive(v0) % 11.12/2.34 | ~ in(v1, v0) | subset(v1, v0)) & ? [v0: $i] : ( ~ $i(v0) | % 11.12/2.34 epsilon_transitive(v0) | ? [v1: $i] : ($i(v1) & in(v1, v0) & ~ subset(v1, % 11.12/2.34 v0))) % 11.12/2.34 % 11.12/2.34 (d8_xboole_0) % 11.12/2.34 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ subset(v0, % 11.12/2.34 v1) | proper_subset(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ % 11.12/2.34 $i(v0) | ~ proper_subset(v0, v1) | subset(v0, v1)) & ! [v0: $i] : ( ~ % 11.71/2.34 $i(v0) | ~ proper_subset(v0, v0)) % 11.71/2.34 % 11.71/2.34 (t1_xboole_1) % 11.71/2.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 11.71/2.35 ~ subset(v1, v2) | ~ subset(v0, v1) | subset(v0, v2)) % 11.71/2.35 % 11.71/2.35 (t21_ordinal1) % 11.71/2.35 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ epsilon_transitive(v0) % 11.71/2.35 | ~ ordinal(v1) | ~ proper_subset(v0, v1) | in(v0, v1)) % 11.71/2.35 % 11.71/2.35 (t22_ordinal1) % 11.71/2.35 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & $i(v0) & % 11.71/2.35 subset(v0, v1) & epsilon_transitive(v0) & ordinal(v2) & ordinal(v1) & in(v1, % 11.71/2.35 v2) & ~ in(v0, v2)) % 11.71/2.35 % 11.71/2.35 (t7_ordinal1) % 11.71/2.35 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v1, v0) | ~ % 11.71/2.35 in(v0, v1)) % 11.71/2.35 % 11.71/2.35 Further assumptions not needed in the proof: % 11.71/2.35 -------------------------------------------- % 11.71/2.35 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, cc1_funct_1, cc1_relat_1, % 11.71/2.35 cc2_funct_1, cc2_ordinal1, existence_m1_subset_1, fc12_relat_1, fc1_xboole_0, % 11.71/2.35 fc4_relat_1, irreflexivity_r2_xboole_0, rc1_funct_1, rc1_ordinal1, rc1_relat_1, % 11.71/2.35 rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, % 11.71/2.35 rc4_funct_1, rc5_funct_1, reflexivity_r1_tarski, t1_subset, t2_subset, % 11.71/2.35 t3_subset, t4_subset, t5_subset, t6_boole, t7_boole, t8_boole % 11.71/2.35 % 11.71/2.35 Those formulas are unsatisfiable: % 11.71/2.35 --------------------------------- % 11.71/2.35 % 11.71/2.35 Begin of proof % 11.71/2.35 | % 11.71/2.35 | ALPHA: (cc1_ordinal1) implies: % 11.71/2.35 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) | epsilon_transitive(v0)) % 11.71/2.35 | % 11.71/2.35 | ALPHA: (d2_ordinal1) implies: % 11.71/2.35 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 11.71/2.35 | epsilon_transitive(v0) | ~ in(v1, v0) | subset(v1, v0)) % 11.71/2.35 | % 11.71/2.35 | ALPHA: (d8_xboole_0) implies: % 11.71/2.35 | (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ $i(v1) | ~ $i(v0) | ~ % 11.71/2.35 | subset(v0, v1) | proper_subset(v0, v1)) % 11.71/2.35 | % 11.71/2.35 | DELTA: instantiating (t22_ordinal1) with fresh symbols all_50_0, all_50_1, % 11.71/2.35 | all_50_2 gives: % 11.71/2.35 | (4) $i(all_50_0) & $i(all_50_1) & $i(all_50_2) & subset(all_50_2, all_50_1) % 11.71/2.35 | & epsilon_transitive(all_50_2) & ordinal(all_50_0) & ordinal(all_50_1) % 11.71/2.35 | & in(all_50_1, all_50_0) & ~ in(all_50_2, all_50_0) % 11.71/2.35 | % 11.71/2.35 | ALPHA: (4) implies: % 11.71/2.36 | (5) ~ in(all_50_2, all_50_0) % 11.71/2.36 | (6) in(all_50_1, all_50_0) % 11.71/2.36 | (7) ordinal(all_50_0) % 11.71/2.36 | (8) epsilon_transitive(all_50_2) % 11.71/2.36 | (9) subset(all_50_2, all_50_1) % 11.71/2.36 | (10) $i(all_50_2) % 11.71/2.36 | (11) $i(all_50_1) % 11.71/2.36 | (12) $i(all_50_0) % 11.71/2.36 | % 11.71/2.36 | GROUND_INST: instantiating (1) with all_50_0, simplifying with (7), (12) % 11.71/2.36 | gives: % 11.71/2.36 | (13) epsilon_transitive(all_50_0) % 11.71/2.36 | % 11.71/2.36 | GROUND_INST: instantiating (t7_ordinal1) with all_50_1, all_50_2, simplifying % 11.71/2.36 | with (9), (10), (11) gives: % 11.71/2.36 | (14) ~ in(all_50_1, all_50_2) % 11.71/2.36 | % 11.71/2.36 | PRED_UNIFY: (6), (14) imply: % 11.71/2.36 | (15) ~ (all_50_0 = all_50_2) % 11.71/2.36 | % 11.71/2.36 | GROUND_INST: instantiating (2) with all_50_0, all_50_1, simplifying with (6), % 11.71/2.36 | (11), (12), (13) gives: % 11.71/2.36 | (16) subset(all_50_1, all_50_0) % 11.71/2.36 | % 11.71/2.36 | GROUND_INST: instantiating (t1_xboole_1) with all_50_2, all_50_1, all_50_0, % 11.71/2.36 | simplifying with (9), (10), (11), (12), (16) gives: % 11.71/2.36 | (17) subset(all_50_2, all_50_0) % 11.71/2.36 | % 11.71/2.36 | GROUND_INST: instantiating (3) with all_50_2, all_50_0, simplifying with (10), % 11.71/2.36 | (12), (17) gives: % 11.71/2.36 | (18) all_50_0 = all_50_2 | proper_subset(all_50_2, all_50_0) % 11.71/2.36 | % 11.71/2.36 | BETA: splitting (18) gives: % 11.71/2.36 | % 11.71/2.36 | Case 1: % 11.71/2.36 | | % 11.71/2.36 | | (19) proper_subset(all_50_2, all_50_0) % 11.71/2.36 | | % 11.71/2.36 | | GROUND_INST: instantiating (t21_ordinal1) with all_50_2, all_50_0, % 11.71/2.36 | | simplifying with (5), (7), (8), (10), (12), (19) gives: % 11.71/2.36 | | (20) $false % 11.71/2.36 | | % 11.71/2.36 | | CLOSE: (20) is inconsistent. % 11.71/2.36 | | % 11.71/2.36 | Case 2: % 11.71/2.36 | | % 11.71/2.36 | | (21) all_50_0 = all_50_2 % 11.71/2.36 | | % 11.71/2.36 | | REDUCE: (15), (21) imply: % 11.71/2.36 | | (22) $false % 11.71/2.36 | | % 11.71/2.36 | | CLOSE: (22) is inconsistent. % 11.71/2.36 | | % 11.71/2.36 | End of split % 11.71/2.36 | % 11.71/2.36 End of proof % 11.71/2.36 % SZS output end Proof for theBenchmark % 11.71/2.36 % 11.71/2.36 1744ms %------------------------------------------------------------------------------