%------------------------------------------------------------------------------ % File : Princess---230619 % Problem : SET063+1 : TPTP v8.1.2. Bugfixed v5.4.0. % Transfm : none % Format : tptp % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % Computer : n018.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 15:23:30 EDT 2023 % Result : Theorem 20.16s 3.60s % Output : Proof 31.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : SET063+1 : TPTP v8.1.2. Bugfixed v5.4.0. % 0.00/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s % 0.12/0.31 % Computer : n018.cluster.edu % 0.12/0.31 % Model : x86_64 x86_64 % 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.31 % Memory : 8042.1875MB % 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.31 % CPULimit : 300 % 0.12/0.31 % WCLimit : 300 % 0.12/0.31 % DateTime : Sat Aug 26 09:03:59 EDT 2023 % 0.12/0.31 % CPUTime : % 0.16/0.60 ________ _____ % 0.16/0.60 ___ __ \_________(_)________________________________ % 0.16/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/ % 0.16/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ ) % 0.16/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/ % 0.16/0.60 % 0.16/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic % 0.16/0.60 (2023-06-19) % 0.16/0.60 % 0.16/0.60 (c) Philipp Rümmer, 2009-2023 % 0.16/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen, % 0.16/0.60 Amanda Stjerna. % 0.16/0.60 Free software under BSD-3-Clause. % 0.16/0.60 % 0.16/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml % 0.16/0.60 % 0.16/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.16/0.61 Running up to 7 provers in parallel. % 0.16/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893 % 0.16/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423 % 0.16/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996 % 0.16/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994 % 0.16/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288 % 0.16/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365 % 0.16/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696 % 3.38/1.27 Prover 4: Preprocessing ... % 3.38/1.27 Prover 1: Preprocessing ... % 3.87/1.32 Prover 2: Preprocessing ... % 3.87/1.32 Prover 3: Preprocessing ... % 3.87/1.32 Prover 5: Preprocessing ... % 3.87/1.32 Prover 0: Preprocessing ... % 3.87/1.32 Prover 6: Preprocessing ... % 10.00/2.28 Prover 1: Warning: ignoring some quantifiers % 12.23/2.48 Prover 5: Proving ... % 12.23/2.48 Prover 3: Warning: ignoring some quantifiers % 12.23/2.49 Prover 1: Constructing countermodel ... % 12.23/2.50 Prover 6: Proving ... % 12.23/2.51 Prover 3: Constructing countermodel ... % 12.23/2.54 Prover 4: Warning: ignoring some quantifiers % 12.96/2.61 Prover 4: Constructing countermodel ... % 13.47/2.69 Prover 2: Proving ... % 14.03/2.74 Prover 0: Proving ... % 20.16/3.59 Prover 0: proved (2971ms) % 20.16/3.60 % 20.16/3.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 20.16/3.60 % 20.16/3.60 Prover 3: stopped % 20.16/3.60 Prover 5: stopped % 20.16/3.60 Prover 2: stopped % 20.61/3.62 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089 % 20.61/3.62 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470 % 20.61/3.62 Prover 6: stopped % 20.61/3.62 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125 % 20.61/3.62 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984 % 20.61/3.62 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443 % 20.61/3.73 Prover 8: Preprocessing ... % 20.61/3.73 Prover 7: Preprocessing ... % 20.61/3.82 Prover 11: Preprocessing ... % 20.61/3.82 Prover 13: Preprocessing ... % 20.61/3.82 Prover 10: Preprocessing ... % 22.95/4.00 Prover 7: Warning: ignoring some quantifiers % 22.95/4.01 Prover 8: Warning: ignoring some quantifiers % 22.95/4.02 Prover 7: Constructing countermodel ... % 23.77/4.06 Prover 8: Constructing countermodel ... % 24.07/4.10 Prover 10: Warning: ignoring some quantifiers % 24.45/4.15 Prover 10: Constructing countermodel ... % 24.57/4.17 Prover 11: Warning: ignoring some quantifiers % 24.57/4.18 Prover 13: Warning: ignoring some quantifiers % 24.57/4.20 Prover 13: Constructing countermodel ... % 25.06/4.24 Prover 11: Constructing countermodel ... % 26.75/4.53 Prover 10: gave up % 26.75/4.56 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683 % 26.75/4.62 Prover 16: Preprocessing ... % 28.86/4.82 Prover 16: Warning: ignoring some quantifiers % 28.86/4.83 Prover 16: Constructing countermodel ... % 31.25/5.08 Prover 4: Found proof (size 22) % 31.25/5.08 Prover 4: proved (4444ms) % 31.25/5.08 Prover 1: stopped % 31.25/5.08 Prover 11: stopped % 31.25/5.08 Prover 16: stopped % 31.25/5.08 Prover 7: stopped % 31.25/5.08 Prover 13: stopped % 31.25/5.09 Prover 8: stopped % 31.25/5.09 % 31.25/5.09 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p % 31.25/5.09 % 31.25/5.09 % SZS output start Proof for theBenchmark % 31.25/5.10 Assumptions after simplification: % 31.25/5.10 --------------------------------- % 31.25/5.10 % 31.25/5.10 (corollary_of_null_class_is_subclass) % 31.25/5.13 $i(null_class) & ? [v0: $i] : ( ~ (v0 = null_class) & subclass(v0, % 31.25/5.13 null_class) = 0 & $i(v0)) % 31.25/5.13 % 31.25/5.13 (extensionality) % 31.25/5.13 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subclass(v1, v0) = 0) | ~ $i(v1) | % 31.25/5.13 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subclass(v0, v1) = v2)) & ! [v0: % 31.25/5.13 $i] : ! [v1: $i] : (v1 = v0 | ~ (subclass(v0, v1) = 0) | ~ $i(v1) | ~ % 31.25/5.13 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subclass(v1, v0) = v2)) & ! [v0: $i] % 31.25/5.13 : ! [v1: int] : (v1 = 0 | ~ (subclass(v0, v0) = v1) | ~ $i(v0)) % 31.25/5.13 % 31.25/5.13 (null_class_defn) % 31.71/5.14 $i(null_class) & ! [v0: $i] : ( ~ (member(v0, null_class) = 0) | ~ $i(v0)) % 31.71/5.14 % 31.71/5.14 (subclass_defn) % 31.71/5.14 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ % 31.71/5.14 (subclass(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | % 31.71/5.14 ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] % 31.71/5.14 : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subclass(v0, v1) = v2) | ~ % 31.71/5.14 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, % 31.71/5.14 v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : % 31.71/5.14 ! [v2: $i] : ( ~ (subclass(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) % 31.71/5.14 | ~ $i(v1) | ~ $i(v0) | member(v2, v1) = 0) % 31.71/5.14 % 31.71/5.14 Further assumptions not needed in the proof: % 31.71/5.14 -------------------------------------------- % 31.71/5.14 apply_defn, choice, class_elements_are_sets, complement, compose_defn1, % 31.71/5.14 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of, % 31.71/5.14 element_relation, element_relation_defn, first_second, flip, flip_defn, % 31.71/5.14 function_defn, identity_relation, image_defn, inductive_defn, infinity, % 31.71/5.14 intersection, inverse_defn, ordered_pair_defn, power_class, power_class_defn, % 31.71/5.14 range_of_defn, regularity, replacement, restrict_defn, rotate, rotate_defn, % 31.71/5.14 singleton_set_defn, successor_defn, successor_relation_defn1, % 31.71/5.14 successor_relation_defn2, sum_class, sum_class_defn, union_defn, unordered_pair, % 31.71/5.14 unordered_pair_defn % 31.71/5.14 % 31.71/5.14 Those formulas are unsatisfiable: % 31.71/5.14 --------------------------------- % 31.71/5.14 % 31.71/5.14 Begin of proof % 31.71/5.14 | % 31.71/5.14 | ALPHA: (subclass_defn) implies: % 31.71/5.15 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subclass(v0, % 31.71/5.15 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : % 31.71/5.15 | ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) % 31.71/5.15 | % 31.71/5.15 | ALPHA: (extensionality) implies: % 31.71/5.15 | (2) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subclass(v1, v0) = 0) | ~ % 31.71/5.15 | $i(v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subclass(v0, v1) = % 31.71/5.15 | v2)) % 31.71/5.15 | % 31.71/5.15 | ALPHA: (null_class_defn) implies: % 31.71/5.15 | (3) ! [v0: $i] : ( ~ (member(v0, null_class) = 0) | ~ $i(v0)) % 31.71/5.15 | % 31.71/5.15 | ALPHA: (corollary_of_null_class_is_subclass) implies: % 31.71/5.15 | (4) $i(null_class) % 31.71/5.15 | (5) ? [v0: $i] : ( ~ (v0 = null_class) & subclass(v0, null_class) = 0 & % 31.71/5.15 | $i(v0)) % 31.71/5.15 | % 31.71/5.15 | DELTA: instantiating (5) with fresh symbol all_38_0 gives: % 31.71/5.15 | (6) ~ (all_38_0 = null_class) & subclass(all_38_0, null_class) = 0 & % 31.71/5.15 | $i(all_38_0) % 31.71/5.15 | % 31.71/5.15 | ALPHA: (6) implies: % 31.71/5.15 | (7) ~ (all_38_0 = null_class) % 31.71/5.15 | (8) $i(all_38_0) % 31.71/5.15 | (9) subclass(all_38_0, null_class) = 0 % 31.71/5.15 | % 31.71/5.15 | GROUND_INST: instantiating (2) with null_class, all_38_0, simplifying with % 31.71/5.15 | (4), (8), (9) gives: % 31.71/5.15 | (10) all_38_0 = null_class | ? [v0: int] : ( ~ (v0 = 0) & % 31.71/5.15 | subclass(null_class, all_38_0) = v0) % 31.71/5.15 | % 31.71/5.15 | BETA: splitting (10) gives: % 31.71/5.15 | % 31.71/5.15 | Case 1: % 31.71/5.15 | | % 31.71/5.15 | | (11) all_38_0 = null_class % 31.71/5.15 | | % 31.71/5.15 | | REDUCE: (7), (11) imply: % 31.71/5.15 | | (12) $false % 31.71/5.16 | | % 31.71/5.16 | | CLOSE: (12) is inconsistent. % 31.71/5.16 | | % 31.71/5.16 | Case 2: % 31.71/5.16 | | % 31.71/5.16 | | (13) ? [v0: int] : ( ~ (v0 = 0) & subclass(null_class, all_38_0) = v0) % 31.71/5.16 | | % 31.71/5.16 | | DELTA: instantiating (13) with fresh symbol all_115_0 gives: % 31.71/5.16 | | (14) ~ (all_115_0 = 0) & subclass(null_class, all_38_0) = all_115_0 % 31.71/5.16 | | % 31.71/5.16 | | ALPHA: (14) implies: % 31.71/5.16 | | (15) ~ (all_115_0 = 0) % 31.71/5.16 | | (16) subclass(null_class, all_38_0) = all_115_0 % 31.71/5.16 | | % 31.71/5.16 | | GROUND_INST: instantiating (1) with null_class, all_38_0, all_115_0, % 31.71/5.16 | | simplifying with (4), (8), (16) gives: % 31.71/5.16 | | (17) all_115_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & % 31.71/5.16 | | member(v0, all_38_0) = v1 & member(v0, null_class) = 0 & $i(v0)) % 31.71/5.16 | | % 31.71/5.16 | | BETA: splitting (17) gives: % 31.71/5.16 | | % 31.71/5.16 | | Case 1: % 31.71/5.16 | | | % 31.71/5.16 | | | (18) all_115_0 = 0 % 31.71/5.16 | | | % 31.71/5.16 | | | REDUCE: (15), (18) imply: % 31.71/5.16 | | | (19) $false % 31.71/5.16 | | | % 31.71/5.16 | | | CLOSE: (19) is inconsistent. % 31.71/5.16 | | | % 31.71/5.16 | | Case 2: % 31.71/5.16 | | | % 31.71/5.16 | | | (20) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_38_0) = % 31.71/5.16 | | | v1 & member(v0, null_class) = 0 & $i(v0)) % 31.71/5.16 | | | % 31.71/5.16 | | | DELTA: instantiating (20) with fresh symbols all_254_0, all_254_1 gives: % 31.71/5.16 | | | (21) ~ (all_254_0 = 0) & member(all_254_1, all_38_0) = all_254_0 & % 31.71/5.16 | | | member(all_254_1, null_class) = 0 & $i(all_254_1) % 31.71/5.16 | | | % 31.71/5.16 | | | ALPHA: (21) implies: % 31.71/5.16 | | | (22) $i(all_254_1) % 31.71/5.16 | | | (23) member(all_254_1, null_class) = 0 % 31.71/5.16 | | | % 31.71/5.16 | | | GROUND_INST: instantiating (3) with all_254_1, simplifying with (22), (23) % 31.71/5.16 | | | gives: % 31.71/5.16 | | | (24) $false % 31.71/5.16 | | | % 31.71/5.16 | | | CLOSE: (24) is inconsistent. % 31.71/5.16 | | | % 31.71/5.16 | | End of split % 31.71/5.16 | | % 31.71/5.16 | End of split % 31.71/5.16 | % 31.71/5.16 End of proof % 31.71/5.16 % SZS output end Proof for theBenchmark % 31.71/5.16 % 31.71/5.16 4563ms %------------------------------------------------------------------------------