%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : NUM412+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 : n001.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 11:47:36 EDT 2023 % Result : Theorem 11.50s 2.33s % Output : Proof 13.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : NUM412+1 : TPTP v8.1.2. Released v3.2.0. % 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.13/0.33 % Computer : n001.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Fri Aug 25 14:02:43 EDT 2023 % 0.13/0.33 % 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) % 0.19/0.59 % 0.19/0.59 (c) Philipp Rümmer, 2009-2023 % 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.19/0.59 Amanda Stjerna. % 0.19/0.59 Free software under BSD-3-Clause. % 0.19/0.59 % 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.19/0.59 % 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.19/0.61 Running up to 7 provers in parallel. % 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 3.00/1.12 Prover 4: Preprocessing ... % 3.00/1.12 Prover 1: Preprocessing ... % 3.19/1.16 Prover 3: Preprocessing ... % 3.19/1.16 Prover 0: Preprocessing ... % 3.19/1.16 Prover 6: Preprocessing ... % 3.19/1.16 Prover 5: Preprocessing ... % 3.19/1.16 Prover 2: Preprocessing ... % 6.26/1.59 Prover 1: Warning: ignoring some quantifiers % 6.26/1.60 Prover 2: Proving ... % 6.26/1.60 Prover 5: Proving ... % 6.26/1.62 Prover 1: Constructing countermodel ... % 7.01/1.67 Prover 4: Warning: ignoring some quantifiers % 7.01/1.68 Prover 6: Proving ... % 7.01/1.68 Prover 3: Warning: ignoring some quantifiers % 7.01/1.70 Prover 4: Constructing countermodel ... % 7.01/1.70 Prover 3: Constructing countermodel ... % 7.01/1.73 Prover 0: Proving ... % 9.12/2.05 Prover 3: gave up % 9.12/2.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 9.12/2.11 Prover 7: Preprocessing ... % 10.68/2.23 Prover 7: Warning: ignoring some quantifiers % 11.16/2.26 Prover 7: Constructing countermodel ... % 11.50/2.31 Prover 1: gave up % 11.50/2.33 Prover 0: proved (1707ms) % 11.50/2.33 % 11.50/2.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 11.50/2.33 % 11.50/2.33 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 11.50/2.33 Prover 5: stopped % 11.50/2.33 Prover 2: stopped % 11.50/2.33 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 11.50/2.33 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 11.50/2.33 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 11.50/2.34 Prover 6: stopped % 11.78/2.35 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 11.78/2.41 Prover 8: Preprocessing ... % 11.78/2.43 Prover 10: Preprocessing ... % 11.78/2.43 Prover 11: Preprocessing ... % 12.50/2.44 Prover 16: Preprocessing ... % 12.50/2.44 Prover 13: Preprocessing ... % 12.95/2.50 Prover 7: Found proof (size 16) % 12.95/2.50 Prover 7: proved (435ms) % 12.95/2.50 Prover 4: stopped % 12.95/2.51 Prover 10: Warning: ignoring some quantifiers % 12.95/2.51 Prover 11: stopped % 12.95/2.52 Prover 10: Constructing countermodel ... % 12.95/2.52 Prover 16: Warning: ignoring some quantifiers % 12.95/2.52 Prover 13: Warning: ignoring some quantifiers % 12.95/2.52 Prover 10: stopped % 12.95/2.52 Prover 16: Constructing countermodel ... % 12.95/2.53 Prover 16: stopped % 12.95/2.53 Prover 13: Constructing countermodel ... % 12.95/2.54 Prover 13: stopped % 13.37/2.57 Prover 8: Warning: ignoring some quantifiers % 13.37/2.58 Prover 8: Constructing countermodel ... % 13.37/2.59 Prover 8: stopped % 13.37/2.59 % 13.37/2.59 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 13.37/2.59 % 13.37/2.59 % SZS output start Proof for theBenchmark % 13.37/2.59 Assumptions after simplification: % 13.37/2.59 --------------------------------- % 13.37/2.59 % 13.37/2.59 (d8_ordinal1) % 13.55/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ % 13.55/2.62 $i(v1) | ~ $i(v0) | ~ subset(v2, v0) | ~ transfinite_sequence(v1) | ~ % 13.55/2.62 relation(v1) | ~ function(v1) | transfinite_sequence_of(v1, v0)) & ! [v0: % 13.55/2.62 $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | ~ $i(v1) | % 13.55/2.62 ~ $i(v0) | ~ transfinite_sequence_of(v1, v0) | ~ transfinite_sequence(v1) % 13.55/2.62 | ~ relation(v1) | ~ function(v1) | subset(v2, v0)) % 13.55/2.62 % 13.55/2.62 (dt_k2_ordinal1) % 13.55/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (tseq_dom_restriction(v0, v1) = % 13.55/2.62 v2) | ~ $i(v1) | ~ $i(v0) | ~ transfinite_sequence(v0) | ~ % 13.55/2.62 relation(v0) | ~ ordinal(v1) | ~ function(v0) | ? [v3: $i] : % 13.55/2.62 (relation_rng(v0) = v3 & $i(v3) & transfinite_sequence_of(v2, v3))) % 13.55/2.62 % 13.55/2.62 (dt_m1_ordinal1) % 13.55/2.62 ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 13.55/2.62 transfinite_sequence_of(v1, v0) | transfinite_sequence(v1)) & ! [v0: $i] : % 13.55/2.62 ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ transfinite_sequence_of(v1, v0) | % 13.55/2.62 relation(v1)) & ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 13.55/2.62 transfinite_sequence_of(v1, v0) | function(v1)) % 13.55/2.62 % 13.55/2.62 (redefinition_k2_ordinal1) % 13.55/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_dom_restriction(v0, % 13.55/2.62 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ transfinite_sequence(v0) | ~ % 13.55/2.62 relation(v0) | ~ ordinal(v1) | ~ function(v0) | (tseq_dom_restriction(v0, % 13.55/2.62 v1) = v2 & $i(v2))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ % 13.55/2.62 (tseq_dom_restriction(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ % 13.55/2.62 transfinite_sequence(v0) | ~ relation(v0) | ~ ordinal(v1) | ~ % 13.55/2.62 function(v0) | (relation_dom_restriction(v0, v1) = v2 & $i(v2))) % 13.55/2.62 % 13.55/2.62 (t47_ordinal1) % 13.55/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | % 13.55/2.62 ~ subset(v0, v1) | ~ transfinite_sequence_of(v2, v0) | % 13.55/2.62 transfinite_sequence_of(v2, v1)) % 13.55/2.62 % 13.55/2.62 (t48_ordinal1) % 13.55/2.63 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : % 13.55/2.63 (tseq_dom_restriction(v1, v2) = v3 & $i(v3) & $i(v2) & $i(v1) & $i(v0) & % 13.55/2.63 transfinite_sequence_of(v1, v0) & ordinal(v2) & ~ % 13.55/2.63 transfinite_sequence_of(v3, v0)) % 13.55/2.63 % 13.55/2.63 Further assumptions not needed in the proof: % 13.55/2.63 -------------------------------------------- % 13.55/2.63 antisymmetry_r2_hidden, cc1_funct_1, cc1_ordinal1, cc1_relat_1, cc2_funct_1, % 13.55/2.63 cc2_ordinal1, cc3_ordinal1, dt_k7_relat_1, existence_m1_ordinal1, % 13.55/2.63 existence_m1_subset_1, fc12_relat_1, fc13_relat_1, fc1_xboole_0, fc2_ordinal1, % 13.55/2.63 fc4_funct_1, fc4_relat_1, fc6_funct_1, fc6_relat_1, fc8_relat_1, rc1_funct_1, % 13.55/2.63 rc1_ordinal1, rc1_relat_1, rc1_xboole_0, rc2_funct_1, rc2_ordinal1, rc2_relat_1, % 13.55/2.63 rc2_xboole_0, rc3_funct_1, rc3_ordinal1, rc3_relat_1, rc4_funct_1, rc4_ordinal1, % 13.55/2.63 rc5_funct_1, reflexivity_r1_tarski, t1_subset, t2_subset, t3_subset, t4_subset, % 13.55/2.63 t5_subset, t6_boole, t7_boole, t8_boole % 13.55/2.63 % 13.55/2.63 Those formulas are unsatisfiable: % 13.55/2.63 --------------------------------- % 13.55/2.63 % 13.55/2.63 Begin of proof % 13.55/2.63 | % 13.55/2.63 | ALPHA: (d8_ordinal1) implies: % 13.55/2.63 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (relation_rng(v1) = v2) | % 13.55/2.63 | ~ $i(v1) | ~ $i(v0) | ~ transfinite_sequence_of(v1, v0) | ~ % 13.55/2.63 | transfinite_sequence(v1) | ~ relation(v1) | ~ function(v1) | % 13.55/2.63 | subset(v2, v0)) % 13.55/2.63 | % 13.55/2.63 | ALPHA: (dt_m1_ordinal1) implies: % 13.55/2.63 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 13.55/2.63 | transfinite_sequence_of(v1, v0) | function(v1)) % 13.55/2.63 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 13.55/2.63 | transfinite_sequence_of(v1, v0) | relation(v1)) % 13.55/2.63 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ $i(v1) | ~ $i(v0) | ~ % 13.55/2.63 | transfinite_sequence_of(v1, v0) | transfinite_sequence(v1)) % 13.55/2.63 | % 13.55/2.63 | ALPHA: (redefinition_k2_ordinal1) implies: % 13.55/2.63 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (tseq_dom_restriction(v0, % 13.55/2.63 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ~ transfinite_sequence(v0) | % 13.55/2.63 | ~ relation(v0) | ~ ordinal(v1) | ~ function(v0) | % 13.55/2.63 | (relation_dom_restriction(v0, v1) = v2 & $i(v2))) % 13.55/2.63 | % 13.55/2.63 | DELTA: instantiating (t48_ordinal1) with fresh symbols all_59_0, all_59_1, % 13.55/2.63 | all_59_2, all_59_3 gives: % 13.55/2.63 | (6) tseq_dom_restriction(all_59_2, all_59_1) = all_59_0 & $i(all_59_0) & % 13.55/2.63 | $i(all_59_1) & $i(all_59_2) & $i(all_59_3) & % 13.55/2.63 | transfinite_sequence_of(all_59_2, all_59_3) & ordinal(all_59_1) & ~ % 13.55/2.63 | transfinite_sequence_of(all_59_0, all_59_3) % 13.55/2.63 | % 13.55/2.63 | ALPHA: (6) implies: % 13.55/2.63 | (7) ~ transfinite_sequence_of(all_59_0, all_59_3) % 13.55/2.63 | (8) ordinal(all_59_1) % 13.55/2.63 | (9) transfinite_sequence_of(all_59_2, all_59_3) % 13.55/2.63 | (10) $i(all_59_3) % 13.55/2.63 | (11) $i(all_59_2) % 13.55/2.63 | (12) $i(all_59_1) % 13.55/2.63 | (13) tseq_dom_restriction(all_59_2, all_59_1) = all_59_0 % 13.55/2.63 | % 13.55/2.64 | GROUND_INST: instantiating (4) with all_59_3, all_59_2, simplifying with (9), % 13.55/2.64 | (10), (11) gives: % 13.55/2.64 | (14) transfinite_sequence(all_59_2) % 13.55/2.64 | % 13.55/2.64 | GROUND_INST: instantiating (3) with all_59_3, all_59_2, simplifying with (9), % 13.55/2.64 | (10), (11) gives: % 13.55/2.64 | (15) relation(all_59_2) % 13.55/2.64 | % 13.55/2.64 | GROUND_INST: instantiating (2) with all_59_3, all_59_2, simplifying with (9), % 13.55/2.64 | (10), (11) gives: % 13.55/2.64 | (16) function(all_59_2) % 13.55/2.64 | % 13.55/2.64 | GROUND_INST: instantiating (dt_k2_ordinal1) with all_59_2, all_59_1, all_59_0, % 13.55/2.64 | simplifying with (8), (11), (12), (13), (14), (15), (16) gives: % 13.55/2.64 | (17) ? [v0: $i] : (relation_rng(all_59_2) = v0 & $i(v0) & % 13.55/2.64 | transfinite_sequence_of(all_59_0, v0)) % 13.55/2.64 | % 13.55/2.64 | GROUND_INST: instantiating (5) with all_59_2, all_59_1, all_59_0, simplifying % 13.55/2.64 | with (8), (11), (12), (13), (14), (15), (16) gives: % 13.55/2.64 | (18) relation_dom_restriction(all_59_2, all_59_1) = all_59_0 & $i(all_59_0) % 13.55/2.64 | % 13.55/2.64 | ALPHA: (18) implies: % 13.55/2.64 | (19) $i(all_59_0) % 13.55/2.64 | % 13.55/2.64 | DELTA: instantiating (17) with fresh symbol all_79_0 gives: % 13.55/2.64 | (20) relation_rng(all_59_2) = all_79_0 & $i(all_79_0) & % 13.55/2.64 | transfinite_sequence_of(all_59_0, all_79_0) % 13.55/2.64 | % 13.55/2.64 | ALPHA: (20) implies: % 13.55/2.64 | (21) transfinite_sequence_of(all_59_0, all_79_0) % 13.55/2.64 | (22) $i(all_79_0) % 13.55/2.64 | (23) relation_rng(all_59_2) = all_79_0 % 13.55/2.64 | % 13.55/2.64 | GROUND_INST: instantiating (1) with all_59_3, all_59_2, all_79_0, simplifying % 13.55/2.64 | with (9), (10), (11), (14), (15), (16), (23) gives: % 13.55/2.64 | (24) subset(all_79_0, all_59_3) % 13.55/2.64 | % 13.55/2.64 | GROUND_INST: instantiating (t47_ordinal1) with all_79_0, all_59_3, all_59_0, % 13.55/2.64 | simplifying with (7), (10), (19), (21), (22), (24) gives: % 13.55/2.64 | (25) $false % 13.55/2.64 | % 13.55/2.64 | CLOSE: (25) is inconsistent. % 13.55/2.64 | % 13.55/2.64 End of proof % 13.55/2.64 % SZS output end Proof for theBenchmark % 13.55/2.64 % 13.55/2.64 2048ms %------------------------------------------------------------------------------