%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM383+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 : n003.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 11:47:32 EDT 2023 % Result : Theorem 8.05s 1.77s % Output : Proof 10.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM383+1 : TPTP v8.1.2. Released v3.2.0. % 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n003.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Aug 25 14:19:08 EDT 2023 % 0.13/0.34 % CPUTime : % 0.20/0.63 ________ _____ % 0.20/0.63 ___ __ \_________(_)________________________________ % 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.20/0.63 % 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.20/0.63 (2023-06-19) % 0.20/0.63 % 0.20/0.63 (c) Philipp Rümmer, 2009-2023 % 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.20/0.63 Amanda Stjerna. % 0.20/0.63 Free software under BSD-3-Clause. % 0.20/0.63 % 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.20/0.63 % 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.20/0.65 Running up to 7 provers in parallel. % 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.19/1.04 Prover 4: Preprocessing ... % 2.19/1.05 Prover 1: Preprocessing ... % 2.90/1.08 Prover 5: Preprocessing ... % 2.90/1.08 Prover 0: Preprocessing ... % 2.90/1.08 Prover 3: Preprocessing ... % 2.90/1.08 Prover 6: Preprocessing ... % 2.90/1.08 Prover 2: Preprocessing ... % 4.40/1.32 Prover 2: Proving ... % 4.40/1.32 Prover 5: Proving ... % 4.40/1.39 Prover 1: Warning: ignoring some quantifiers % 4.40/1.39 Prover 6: Proving ... % 4.40/1.41 Prover 1: Constructing countermodel ... % 4.40/1.42 Prover 3: Warning: ignoring some quantifiers % 4.40/1.43 Prover 3: Constructing countermodel ... % 4.40/1.44 Prover 0: Proving ... % 4.40/1.45 Prover 4: Warning: ignoring some quantifiers % 5.77/1.48 Prover 4: Constructing countermodel ... % 6.83/1.63 Prover 3: gave up % 6.83/1.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 7.37/1.68 Prover 7: Preprocessing ... % 7.37/1.69 Prover 1: gave up % 7.37/1.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 7.37/1.73 Prover 7: Warning: ignoring some quantifiers % 7.37/1.74 Prover 7: Constructing countermodel ... % 7.37/1.75 Prover 8: Preprocessing ... % 7.37/1.77 Prover 5: proved (1112ms) % 7.37/1.77 % 8.05/1.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.05/1.77 % 8.05/1.77 Prover 0: stopped % 8.05/1.77 Prover 6: stopped % 8.05/1.78 Prover 2: proved (1118ms) % 8.05/1.78 % 8.05/1.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 8.05/1.78 % 8.20/1.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.20/1.80 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.20/1.80 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.20/1.80 Prover 10: Preprocessing ... % 8.20/1.80 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 8.42/1.82 Prover 11: Preprocessing ... % 8.42/1.82 Prover 13: Preprocessing ... % 8.48/1.83 Prover 16: Preprocessing ... % 8.48/1.84 Prover 8: Warning: ignoring some quantifiers % 8.48/1.84 Prover 8: Constructing countermodel ... % 8.48/1.85 Prover 10: Warning: ignoring some quantifiers % 8.48/1.86 Prover 10: Constructing countermodel ... % 8.48/1.87 Prover 7: gave up % 8.48/1.87 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 8.48/1.87 Prover 13: Warning: ignoring some quantifiers % 8.48/1.88 Prover 13: Constructing countermodel ... % 8.48/1.89 Prover 16: Warning: ignoring some quantifiers % 8.48/1.90 Prover 16: Constructing countermodel ... % 8.48/1.90 Prover 19: Preprocessing ... % 9.11/1.94 Prover 10: gave up % 9.11/1.96 Prover 11: Warning: ignoring some quantifiers % 9.11/1.97 Prover 11: Constructing countermodel ... % 9.11/2.00 Prover 19: Warning: ignoring some quantifiers % 9.11/2.01 Prover 19: Constructing countermodel ... % 9.11/2.04 Prover 8: gave up % 10.22/2.10 Prover 13: Found proof (size 16) % 10.22/2.10 Prover 13: proved (312ms) % 10.22/2.10 Prover 11: stopped % 10.22/2.10 Prover 19: stopped % 10.22/2.10 Prover 16: stopped % 10.22/2.10 Prover 4: stopped % 10.22/2.10 % 10.22/2.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 10.22/2.10 % 10.22/2.10 % SZS output start Proof for theBenchmark % 10.22/2.10 Assumptions after simplification: % 10.22/2.10 --------------------------------- % 10.22/2.10 % 10.22/2.10 (antisymmetry_r2_hidden) % 10.22/2.11 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ in(v1, v0) | ~ in(v0, % 10.22/2.11 v1)) % 10.22/2.11 % 10.22/2.11 (t2_subset) % 10.22/2.11 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ element(v0, v1) | % 10.22/2.11 empty(v1) | in(v0, v1)) % 10.22/2.11 % 10.22/2.11 (t3_subset) % 10.22/2.13 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ $i(v1) % 10.22/2.13 | ~ $i(v0) | ~ subset(v0, v1) | element(v0, v2)) & ! [v0: $i] : ! [v1: % 10.22/2.13 $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 10.22/2.13 element(v0, v2) | subset(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | % 10.22/2.13 ~ $i(v0) | ~ subset(v0, v1) | ? [v2: $i] : (powerset(v1) = v2 & $i(v2) & % 10.22/2.13 element(v0, v2))) & ? [v0: $i] : ? [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 10.22/2.13 subset(v0, v1) | ? [v2: $i] : (powerset(v1) = v2 & $i(v2) & ~ element(v0, % 10.22/2.13 v2))) % 10.22/2.13 % 10.22/2.13 (t4_subset) % 10.22/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) = % 10.22/2.14 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ element(v1, v3) | ~ in(v0, % 10.22/2.14 v1) | element(v0, v2)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 10.22/2.14 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v1, v2) | element(v1, v0) | ? [v3: % 10.22/2.14 $i] : (powerset(v0) = v3 & $i(v3) & ~ element(v2, v3))) % 10.22/2.14 % 10.22/2.14 (t5_subset) % 10.22/2.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) = % 10.22/2.14 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ element(v1, v3) | ~ % 10.22/2.14 empty(v2) | ~ in(v0, v1)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 10.22/2.14 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ empty(v2) | ~ in(v0, v1) | ? [v3: $i] % 10.22/2.14 : (powerset(v2) = v3 & $i(v3) & ~ element(v1, v3))) % 10.22/2.14 % 10.22/2.14 (t7_ordinal1) % 10.22/2.14 ? [v0: $i] : ? [v1: $i] : ($i(v1) & $i(v0) & subset(v1, v0) & in(v0, v1)) % 10.22/2.14 % 10.22/2.14 Further assumptions not needed in the proof: % 10.22/2.14 -------------------------------------------- % 10.22/2.14 cc1_funct_1, cc1_relat_1, cc2_funct_1, existence_m1_subset_1, fc12_relat_1, % 10.22/2.14 fc1_xboole_0, fc4_relat_1, rc1_funct_1, rc1_relat_1, rc1_xboole_0, rc2_funct_1, % 10.22/2.14 rc2_relat_1, rc2_xboole_0, rc3_funct_1, rc3_relat_1, rc4_funct_1, rc5_funct_1, % 10.22/2.14 reflexivity_r1_tarski, t1_subset, t6_boole, t7_boole, t8_boole % 10.22/2.14 % 10.22/2.14 Those formulas are unsatisfiable: % 10.22/2.14 --------------------------------- % 10.22/2.14 % 10.22/2.14 Begin of proof % 10.22/2.14 | % 10.22/2.14 | ALPHA: (t3_subset) implies: % 10.22/2.14 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1) % 10.22/2.14 | | ? [v2: $i] : (powerset(v1) = v2 & $i(v2) & element(v0, v2))) % 10.22/2.14 | % 10.22/2.14 | ALPHA: (t4_subset) implies: % 10.22/2.15 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.22/2.15 | (powerset(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 10.22/2.15 | element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 10.22/2.15 | % 10.22/2.15 | ALPHA: (t5_subset) implies: % 10.22/2.15 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 10.22/2.15 | (powerset(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 10.22/2.15 | element(v1, v3) | ~ empty(v2) | ~ in(v0, v1)) % 10.22/2.15 | % 10.22/2.15 | DELTA: instantiating (t7_ordinal1) with fresh symbols all_34_0, all_34_1 % 10.22/2.15 | gives: % 10.22/2.15 | (4) $i(all_34_0) & $i(all_34_1) & subset(all_34_0, all_34_1) & in(all_34_1, % 10.22/2.15 | all_34_0) % 10.22/2.15 | % 10.22/2.15 | ALPHA: (4) implies: % 10.22/2.15 | (5) in(all_34_1, all_34_0) % 10.22/2.15 | (6) subset(all_34_0, all_34_1) % 10.22/2.15 | (7) $i(all_34_1) % 10.22/2.15 | (8) $i(all_34_0) % 10.22/2.15 | % 10.22/2.15 | GROUND_INST: instantiating (1) with all_34_0, all_34_1, simplifying with (6), % 10.22/2.15 | (7), (8) gives: % 10.22/2.15 | (9) ? [v0: $i] : (powerset(all_34_1) = v0 & $i(v0) & element(all_34_0, % 10.22/2.15 | v0)) % 10.22/2.15 | % 10.22/2.15 | DELTA: instantiating (9) with fresh symbol all_49_0 gives: % 10.22/2.15 | (10) powerset(all_34_1) = all_49_0 & $i(all_49_0) & element(all_34_0, % 10.22/2.15 | all_49_0) % 10.22/2.15 | % 10.22/2.15 | ALPHA: (10) implies: % 10.22/2.15 | (11) element(all_34_0, all_49_0) % 10.22/2.15 | (12) powerset(all_34_1) = all_49_0 % 10.22/2.15 | % 10.22/2.15 | GROUND_INST: instantiating (2) with all_34_1, all_34_0, all_34_1, all_49_0, % 10.22/2.15 | simplifying with (5), (7), (8), (11), (12) gives: % 10.22/2.15 | (13) element(all_34_1, all_34_1) % 10.22/2.15 | % 10.22/2.15 | GROUND_INST: instantiating (t2_subset) with all_34_1, all_34_1, simplifying % 10.22/2.15 | with (7), (13) gives: % 10.22/2.15 | (14) empty(all_34_1) | in(all_34_1, all_34_1) % 10.22/2.15 | % 10.22/2.15 | BETA: splitting (14) gives: % 10.22/2.15 | % 10.22/2.15 | Case 1: % 10.22/2.15 | | % 10.22/2.15 | | (15) empty(all_34_1) % 10.22/2.15 | | % 10.22/2.15 | | GROUND_INST: instantiating (3) with all_34_1, all_34_0, all_34_1, all_49_0, % 10.22/2.15 | | simplifying with (5), (7), (8), (11), (12), (15) gives: % 10.22/2.15 | | (16) $false % 10.22/2.15 | | % 10.22/2.15 | | CLOSE: (16) is inconsistent. % 10.22/2.15 | | % 10.22/2.15 | Case 2: % 10.22/2.15 | | % 10.22/2.16 | | (17) in(all_34_1, all_34_1) % 10.22/2.16 | | % 10.22/2.16 | | GROUND_INST: instantiating (antisymmetry_r2_hidden) with all_34_1, all_34_1, % 10.22/2.16 | | simplifying with (7), (17) gives: % 10.22/2.16 | | (18) $false % 10.22/2.16 | | % 10.22/2.16 | | CLOSE: (18) is inconsistent. % 10.22/2.16 | | % 10.22/2.16 | End of split % 10.22/2.16 | % 10.22/2.16 End of proof % 10.22/2.16 % SZS output end Proof for theBenchmark % 10.22/2.16 % 10.22/2.16 1522ms %------------------------------------------------------------------------------