TSTP Solution File: SET062+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET062+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 : 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 15:23:29 EDT 2023
% Result : Theorem 11.82s 2.33s
% Output : Proof 13.74s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET062+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n022.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 : Sat Aug 26 12:23:40 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.30/1.14 Prover 4: Preprocessing ...
% 3.30/1.14 Prover 1: Preprocessing ...
% 3.30/1.18 Prover 6: Preprocessing ...
% 3.30/1.18 Prover 5: Preprocessing ...
% 3.30/1.18 Prover 2: Preprocessing ...
% 3.30/1.18 Prover 3: Preprocessing ...
% 3.30/1.18 Prover 0: Preprocessing ...
% 8.42/1.90 Prover 3: Warning: ignoring some quantifiers
% 8.91/1.91 Prover 1: Warning: ignoring some quantifiers
% 8.91/1.91 Prover 5: Proving ...
% 8.91/1.93 Prover 3: Constructing countermodel ...
% 8.91/1.94 Prover 1: Constructing countermodel ...
% 8.91/1.96 Prover 6: Proving ...
% 9.36/1.99 Prover 4: Warning: ignoring some quantifiers
% 9.36/2.04 Prover 2: Proving ...
% 9.36/2.05 Prover 4: Constructing countermodel ...
% 9.36/2.13 Prover 0: Proving ...
% 11.82/2.33 Prover 6: proved (1694ms)
% 11.82/2.33
% 11.82/2.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.82/2.33
% 11.82/2.33 Prover 3: stopped
% 11.82/2.35 Prover 0: stopped
% 11.82/2.35 Prover 5: stopped
% 11.82/2.35 Prover 2: stopped
% 12.24/2.37 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 12.24/2.37 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.24/2.37 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 12.24/2.37 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 12.24/2.37 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 12.24/2.39 Prover 7: Preprocessing ...
% 12.24/2.41 Prover 8: Preprocessing ...
% 12.24/2.41 Prover 11: Preprocessing ...
% 12.24/2.42 Prover 10: Preprocessing ...
% 12.24/2.43 Prover 13: Preprocessing ...
% 12.24/2.44 Prover 1: Found proof (size 13)
% 12.24/2.44 Prover 1: proved (1815ms)
% 12.24/2.45 Prover 4: stopped
% 12.97/2.47 Prover 10: stopped
% 12.97/2.49 Prover 7: stopped
% 12.97/2.49 Prover 11: stopped
% 13.21/2.50 Prover 13: stopped
% 13.46/2.57 Prover 8: Warning: ignoring some quantifiers
% 13.46/2.59 Prover 8: Constructing countermodel ...
% 13.46/2.59 Prover 8: stopped
% 13.46/2.59
% 13.46/2.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.46/2.59
% 13.46/2.59 % SZS output start Proof for theBenchmark
% 13.46/2.60 Assumptions after simplification:
% 13.46/2.60 ---------------------------------
% 13.46/2.60
% 13.46/2.60 (null_class_defn)
% 13.74/2.62 $i(null_class) & ! [v0: $i] : ( ~ (member(v0, null_class) = 0) | ~ $i(v0))
% 13.74/2.62
% 13.74/2.62 (null_class_is_subclass)
% 13.74/2.62 $i(null_class) & ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 13.74/2.62 subclass(null_class, v0) = v1 & $i(v0))
% 13.74/2.62
% 13.74/2.62 (subclass_defn)
% 13.74/2.62 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subclass(v0, v1) =
% 13.74/2.62 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 13.74/2.62 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 13.74/2.62 [v1: $i] : ( ~ (subclass(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] :
% 13.74/2.62 ( ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 13.74/2.63
% 13.74/2.63 Further assumptions not needed in the proof:
% 13.74/2.63 --------------------------------------------
% 13.74/2.63 apply_defn, choice, class_elements_are_sets, complement, compose_defn1,
% 13.74/2.63 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of,
% 13.74/2.63 element_relation, element_relation_defn, extensionality, first_second, flip,
% 13.74/2.63 flip_defn, function_defn, identity_relation, image_defn, inductive_defn,
% 13.74/2.63 infinity, intersection, inverse_defn, ordered_pair_defn, power_class,
% 13.74/2.63 power_class_defn, range_of_defn, regularity, replacement, restrict_defn, rotate,
% 13.74/2.63 rotate_defn, singleton_set_defn, successor_defn, successor_relation_defn1,
% 13.74/2.63 successor_relation_defn2, sum_class, sum_class_defn, union_defn, unordered_pair,
% 13.74/2.63 unordered_pair_defn
% 13.74/2.63
% 13.74/2.63 Those formulas are unsatisfiable:
% 13.74/2.63 ---------------------------------
% 13.74/2.63
% 13.74/2.63 Begin of proof
% 13.74/2.63 |
% 13.74/2.63 | ALPHA: (subclass_defn) implies:
% 13.74/2.63 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subclass(v0,
% 13.74/2.63 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 13.74/2.63 | ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 13.74/2.63 |
% 13.74/2.63 | ALPHA: (null_class_defn) implies:
% 13.74/2.63 | (2) ! [v0: $i] : ( ~ (member(v0, null_class) = 0) | ~ $i(v0))
% 13.74/2.63 |
% 13.74/2.63 | ALPHA: (null_class_is_subclass) implies:
% 13.74/2.63 | (3) $i(null_class)
% 13.74/2.63 | (4) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subclass(null_class, v0) =
% 13.74/2.63 | v1 & $i(v0))
% 13.74/2.63 |
% 13.74/2.63 | DELTA: instantiating (4) with fresh symbols all_38_0, all_38_1 gives:
% 13.74/2.63 | (5) ~ (all_38_0 = 0) & subclass(null_class, all_38_1) = all_38_0 &
% 13.74/2.63 | $i(all_38_1)
% 13.74/2.63 |
% 13.74/2.63 | ALPHA: (5) implies:
% 13.74/2.63 | (6) ~ (all_38_0 = 0)
% 13.74/2.63 | (7) $i(all_38_1)
% 13.74/2.63 | (8) subclass(null_class, all_38_1) = all_38_0
% 13.74/2.63 |
% 13.74/2.64 | GROUND_INST: instantiating (1) with null_class, all_38_1, all_38_0,
% 13.74/2.64 | simplifying with (3), (7), (8) gives:
% 13.74/2.64 | (9) all_38_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 13.74/2.64 | all_38_1) = v1 & member(v0, null_class) = 0 & $i(v0))
% 13.74/2.64 |
% 13.74/2.64 | BETA: splitting (9) gives:
% 13.74/2.64 |
% 13.74/2.64 | Case 1:
% 13.74/2.64 | |
% 13.74/2.64 | | (10) all_38_0 = 0
% 13.74/2.64 | |
% 13.74/2.64 | | REDUCE: (6), (10) imply:
% 13.74/2.64 | | (11) $false
% 13.74/2.64 | |
% 13.74/2.64 | | CLOSE: (11) is inconsistent.
% 13.74/2.64 | |
% 13.74/2.64 | Case 2:
% 13.74/2.64 | |
% 13.74/2.64 | | (12) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_38_1) =
% 13.74/2.64 | | v1 & member(v0, null_class) = 0 & $i(v0))
% 13.74/2.64 | |
% 13.74/2.64 | | DELTA: instantiating (12) with fresh symbols all_103_0, all_103_1 gives:
% 13.74/2.64 | | (13) ~ (all_103_0 = 0) & member(all_103_1, all_38_1) = all_103_0 &
% 13.74/2.64 | | member(all_103_1, null_class) = 0 & $i(all_103_1)
% 13.74/2.64 | |
% 13.74/2.64 | | ALPHA: (13) implies:
% 13.74/2.64 | | (14) $i(all_103_1)
% 13.74/2.64 | | (15) member(all_103_1, null_class) = 0
% 13.74/2.64 | |
% 13.74/2.64 | | GROUND_INST: instantiating (2) with all_103_1, simplifying with (14), (15)
% 13.74/2.64 | | gives:
% 13.74/2.64 | | (16) $false
% 13.74/2.64 | |
% 13.74/2.64 | | CLOSE: (16) is inconsistent.
% 13.74/2.64 | |
% 13.74/2.64 | End of split
% 13.74/2.64 |
% 13.74/2.64 End of proof
% 13.74/2.64 % SZS output end Proof for theBenchmark
% 13.74/2.64
% 13.74/2.64 2030ms
%------------------------------------------------------------------------------