%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM388+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 : n007.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 1.83s % Output : Proof 11.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : NUM388+1 : TPTP v8.1.2. Released v3.2.0. % 0.06/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.34 % Computer : n007.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 15:31:11 EDT 2023 % 0.13/0.34 % CPUTime : % 0.19/0.59 ________ _____ % 0.19/0.59 ___ __ \_________(_)________________________________ % 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.19/0.59 % 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.19/0.59 (2023-06-19) % 0.19/0.60 % 0.19/0.60 (c) Philipp Rümmer, 2009-2023 % 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.60 Amanda Stjerna. % 0.19/0.60 Free software under BSD-3-Clause. % 0.19/0.60 % 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.60 % 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 2.81/1.04 Prover 4: Preprocessing ... % 2.81/1.04 Prover 1: Preprocessing ... % 2.81/1.08 Prover 0: Preprocessing ... % 2.81/1.08 Prover 3: Preprocessing ... % 2.81/1.09 Prover 6: Preprocessing ... % 2.81/1.09 Prover 2: Preprocessing ... % 2.81/1.09 Prover 5: Preprocessing ... % 4.72/1.37 Prover 2: Proving ... % 4.72/1.38 Prover 5: Proving ... % 5.40/1.48 Prover 6: Proving ... % 5.94/1.49 Prover 1: Warning: ignoring some quantifiers % 5.94/1.51 Prover 4: Warning: ignoring some quantifiers % 5.94/1.52 Prover 1: Constructing countermodel ... % 5.94/1.52 Prover 3: Warning: ignoring some quantifiers % 5.94/1.52 Prover 4: Constructing countermodel ... % 5.94/1.53 Prover 3: Constructing countermodel ... % 6.58/1.58 Prover 0: Proving ... % 8.15/1.82 Prover 2: proved (1207ms) % 8.15/1.83 % 8.15/1.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 8.15/1.83 % 8.15/1.83 Prover 6: stopped % 8.15/1.83 Prover 0: stopped % 8.15/1.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 8.15/1.83 Prover 5: stopped % 8.15/1.84 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 8.15/1.84 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 8.15/1.84 Prover 3: stopped % 8.15/1.84 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 8.15/1.84 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 8.69/1.90 Prover 10: Preprocessing ... % 8.69/1.91 Prover 8: Preprocessing ... % 8.69/1.92 Prover 13: Preprocessing ... % 8.69/1.92 Prover 7: Preprocessing ... % 8.69/1.93 Prover 11: Preprocessing ... % 8.93/1.98 Prover 10: Warning: ignoring some quantifiers % 8.93/1.98 Prover 10: Constructing countermodel ... % 9.63/2.01 Prover 13: Warning: ignoring some quantifiers % 9.63/2.02 Prover 1: gave up % 9.69/2.02 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 9.69/2.03 Prover 13: Constructing countermodel ... % 9.69/2.04 Prover 7: Warning: ignoring some quantifiers % 9.69/2.04 Prover 7: Constructing countermodel ... % 9.69/2.06 Prover 16: Preprocessing ... % 9.69/2.10 Prover 8: Warning: ignoring some quantifiers % 10.35/2.11 Prover 8: Constructing countermodel ... % 10.35/2.12 Prover 10: gave up % 10.35/2.12 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085 % 10.35/2.14 Prover 16: Warning: ignoring some quantifiers % 10.35/2.14 Prover 19: Preprocessing ... % 10.35/2.15 Prover 16: Constructing countermodel ... % 10.94/2.19 Prover 11: Warning: ignoring some quantifiers % 10.94/2.20 Prover 11: Constructing countermodel ... % 10.94/2.27 Prover 8: gave up % 11.74/2.29 Prover 19: Warning: ignoring some quantifiers % 11.74/2.30 Prover 19: Constructing countermodel ... % 11.93/2.32 Prover 13: Found proof (size 15) % 11.93/2.32 Prover 13: proved (479ms) % 11.93/2.32 Prover 16: stopped % 11.93/2.32 Prover 19: stopped % 11.93/2.32 Prover 4: stopped % 11.93/2.32 Prover 11: stopped % 11.93/2.32 Prover 7: stopped % 11.93/2.32 % 11.93/2.32 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.93/2.32 % 11.98/2.32 % SZS output start Proof for theBenchmark % 11.98/2.33 Assumptions after simplification: % 11.98/2.33 --------------------------------- % 11.98/2.33 % 11.98/2.33 (cc1_ordinal1) % 11.98/2.33 ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) | epsilon_connected(v0)) & ! [v0: % 11.98/2.33 $i] : ( ~ $i(v0) | ~ ordinal(v0) | epsilon_transitive(v0)) % 11.98/2.33 % 11.98/2.33 (d2_ordinal1) % 11.98/2.33 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ epsilon_transitive(v0) % 11.98/2.33 | ~ in(v1, v0) | subset(v1, v0)) & ? [v0: $i] : ( ~ $i(v0) | % 11.98/2.33 epsilon_transitive(v0) | ? [v1: $i] : ($i(v1) & in(v1, v0) & ~ subset(v1, % 11.98/2.33 v0))) % 11.98/2.33 % 11.98/2.33 (t19_ordinal1) % 11.98/2.33 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ($i(v2) & $i(v1) & $i(v0) & % 11.98/2.33 epsilon_transitive(v2) & ordinal(v1) & ordinal(v0) & in(v2, v0) & in(v0, v1) % 11.98/2.33 & ~ in(v2, v1)) % 11.98/2.33 % 11.98/2.33 (t2_subset) % 11.98/2.34 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ element(v0, v1) | % 11.98/2.34 empty(v1) | in(v0, v1)) % 11.98/2.34 % 11.98/2.34 (t3_subset) % 11.98/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ $i(v1) % 11.98/2.36 | ~ $i(v0) | ~ element(v0, v2) | subset(v0, v1)) & ! [v0: $i] : ! [v1: % 11.98/2.36 $i] : ! [v2: $i] : ( ~ (powerset(v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 11.98/2.36 subset(v0, v1) | element(v0, v2)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | % 11.98/2.36 ~ $i(v0) | ~ subset(v0, v1) | ? [v2: $i] : (powerset(v1) = v2 & $i(v2) & % 11.98/2.36 element(v0, v2))) & ? [v0: $i] : ? [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | % 11.98/2.36 subset(v0, v1) | ? [v2: $i] : (powerset(v1) = v2 & $i(v2) & ~ element(v0, % 11.98/2.36 v2))) % 11.98/2.36 % 11.98/2.36 (t4_subset) % 11.98/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (powerset(v2) = % 11.98/2.36 v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ element(v1, v3) | ~ in(v0, % 11.98/2.36 v1) | element(v0, v2)) & ? [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 11.98/2.36 $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ in(v1, v2) | element(v1, v0) | ? [v3: % 11.98/2.36 $i] : (powerset(v0) = v3 & $i(v3) & ~ element(v2, v3))) % 11.98/2.36 % 11.98/2.36 (t7_boole) % 11.98/2.36 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ empty(v1) | ~ in(v0, % 11.98/2.36 v1)) % 11.98/2.36 % 11.98/2.36 Further assumptions not needed in the proof: % 11.98/2.36 -------------------------------------------- % 11.98/2.36 antisymmetry_r2_hidden, cc1_funct_1, cc1_relat_1, cc2_funct_1, cc2_ordinal1, % 11.98/2.36 existence_m1_subset_1, fc12_relat_1, fc1_xboole_0, fc4_relat_1, rc1_funct_1, % 11.98/2.36 rc1_ordinal1, rc1_relat_1, rc1_xboole_0, rc2_funct_1, rc2_relat_1, rc2_xboole_0, % 11.98/2.36 rc3_funct_1, rc3_relat_1, rc4_funct_1, rc5_funct_1, reflexivity_r1_tarski, % 11.98/2.36 t1_subset, t5_subset, t6_boole, t8_boole % 11.98/2.36 % 11.98/2.36 Those formulas are unsatisfiable: % 11.98/2.36 --------------------------------- % 11.98/2.36 % 11.98/2.36 Begin of proof % 11.98/2.36 | % 11.98/2.36 | ALPHA: (cc1_ordinal1) implies: % 11.98/2.37 | (1) ! [v0: $i] : ( ~ $i(v0) | ~ ordinal(v0) | epsilon_transitive(v0)) % 11.98/2.37 | % 11.98/2.37 | ALPHA: (d2_ordinal1) implies: % 11.98/2.37 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 11.98/2.37 | epsilon_transitive(v0) | ~ in(v1, v0) | subset(v1, v0)) % 11.98/2.37 | % 11.98/2.37 | ALPHA: (t3_subset) implies: % 11.98/2.37 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ subset(v0, v1) % 11.98/2.37 | | ? [v2: $i] : (powerset(v1) = v2 & $i(v2) & element(v0, v2))) % 11.98/2.37 | % 11.98/2.37 | ALPHA: (t4_subset) implies: % 11.98/2.37 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ % 11.98/2.37 | (powerset(v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ~ % 11.98/2.37 | element(v1, v3) | ~ in(v0, v1) | element(v0, v2)) % 11.98/2.37 | % 11.98/2.37 | DELTA: instantiating (t19_ordinal1) with fresh symbols all_47_0, all_47_1, % 11.98/2.37 | all_47_2 gives: % 11.98/2.37 | (5) $i(all_47_0) & $i(all_47_1) & $i(all_47_2) & % 11.98/2.37 | epsilon_transitive(all_47_0) & ordinal(all_47_1) & ordinal(all_47_2) & % 11.98/2.37 | in(all_47_0, all_47_2) & in(all_47_2, all_47_1) & ~ in(all_47_0, % 11.98/2.37 | all_47_1) % 11.98/2.37 | % 11.98/2.37 | ALPHA: (5) implies: % 11.98/2.37 | (6) ~ in(all_47_0, all_47_1) % 11.98/2.37 | (7) in(all_47_2, all_47_1) % 11.98/2.37 | (8) in(all_47_0, all_47_2) % 11.98/2.37 | (9) ordinal(all_47_1) % 11.98/2.37 | (10) $i(all_47_2) % 11.98/2.37 | (11) $i(all_47_1) % 11.98/2.37 | (12) $i(all_47_0) % 11.98/2.37 | % 11.98/2.37 | GROUND_INST: instantiating (1) with all_47_1, simplifying with (9), (11) % 11.98/2.37 | gives: % 11.98/2.37 | (13) epsilon_transitive(all_47_1) % 11.98/2.37 | % 11.98/2.37 | GROUND_INST: instantiating (2) with all_47_1, all_47_2, simplifying with (7), % 11.98/2.37 | (10), (11), (13) gives: % 11.98/2.37 | (14) subset(all_47_2, all_47_1) % 11.98/2.38 | % 11.98/2.38 | GROUND_INST: instantiating (3) with all_47_2, all_47_1, simplifying with (10), % 11.98/2.38 | (11), (14) gives: % 11.98/2.38 | (15) ? [v0: $i] : (powerset(all_47_1) = v0 & $i(v0) & element(all_47_2, % 11.98/2.38 | v0)) % 11.98/2.38 | % 11.98/2.38 | DELTA: instantiating (15) with fresh symbol all_88_0 gives: % 11.98/2.38 | (16) powerset(all_47_1) = all_88_0 & $i(all_88_0) & element(all_47_2, % 11.98/2.38 | all_88_0) % 11.98/2.38 | % 11.98/2.38 | ALPHA: (16) implies: % 11.98/2.38 | (17) element(all_47_2, all_88_0) % 11.98/2.38 | (18) powerset(all_47_1) = all_88_0 % 11.98/2.38 | % 11.98/2.38 | GROUND_INST: instantiating (4) with all_47_0, all_47_2, all_47_1, all_88_0, % 11.98/2.38 | simplifying with (8), (10), (11), (12), (17), (18) gives: % 11.98/2.38 | (19) element(all_47_0, all_47_1) % 11.98/2.38 | % 11.98/2.38 | GROUND_INST: instantiating (t2_subset) with all_47_0, all_47_1, simplifying % 11.98/2.38 | with (6), (11), (12), (19) gives: % 11.98/2.38 | (20) empty(all_47_1) % 11.98/2.38 | % 11.98/2.38 | GROUND_INST: instantiating (t7_boole) with all_47_2, all_47_1, simplifying % 11.98/2.38 | with (7), (10), (11), (20) gives: % 11.98/2.38 | (21) $false % 11.98/2.38 | % 11.98/2.38 | CLOSE: (21) is inconsistent. % 11.98/2.38 | % 11.98/2.38 End of proof % 11.98/2.38 % SZS output end Proof for theBenchmark % 11.98/2.38 % 11.98/2.38 1784ms %------------------------------------------------------------------------------