TSTP Solution File: SET091+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET091+1 : TPTP v8.1.2. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n016.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 15:23:44 EDT 2023
% Result : Theorem 14.07s 2.65s
% Output : Proof 18.07s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET091+1 : TPTP v8.1.2. Bugfixed v7.3.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34 % Computer : n016.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Sat Aug 26 12:13:11 EDT 2023
% 0.16/0.34 % 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.
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.14/1.16 Prover 4: Preprocessing ...
% 3.48/1.18 Prover 1: Preprocessing ...
% 3.48/1.21 Prover 5: Preprocessing ...
% 3.48/1.21 Prover 6: Preprocessing ...
% 3.48/1.21 Prover 3: Preprocessing ...
% 3.48/1.21 Prover 2: Preprocessing ...
% 3.48/1.21 Prover 0: Preprocessing ...
% 9.20/1.99 Prover 1: Warning: ignoring some quantifiers
% 9.20/2.00 Prover 5: Proving ...
% 9.20/2.01 Prover 6: Proving ...
% 9.76/2.05 Prover 4: Warning: ignoring some quantifiers
% 9.76/2.06 Prover 1: Constructing countermodel ...
% 9.76/2.08 Prover 3: Warning: ignoring some quantifiers
% 9.76/2.11 Prover 3: Constructing countermodel ...
% 10.32/2.13 Prover 4: Constructing countermodel ...
% 10.32/2.17 Prover 2: Proving ...
% 10.71/2.23 Prover 0: Proving ...
% 13.84/2.63 Prover 0: proved (2009ms)
% 13.84/2.64
% 14.07/2.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 14.07/2.65
% 14.07/2.65 Prover 2: stopped
% 14.07/2.65 Prover 5: stopped
% 14.07/2.66 Prover 6: stopped
% 14.07/2.67 Prover 3: stopped
% 14.07/2.67 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.07/2.67 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.07/2.67 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.07/2.67 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.07/2.68 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.07/2.70 Prover 7: Preprocessing ...
% 14.63/2.75 Prover 11: Preprocessing ...
% 14.63/2.75 Prover 10: Preprocessing ...
% 14.63/2.76 Prover 8: Preprocessing ...
% 14.63/2.78 Prover 13: Preprocessing ...
% 15.68/2.92 Prover 10: Warning: ignoring some quantifiers
% 15.68/2.95 Prover 10: Constructing countermodel ...
% 15.68/2.96 Prover 7: Warning: ignoring some quantifiers
% 15.68/2.99 Prover 7: Constructing countermodel ...
% 15.68/3.01 Prover 13: Warning: ignoring some quantifiers
% 15.68/3.04 Prover 13: Constructing countermodel ...
% 16.89/3.08 Prover 8: Warning: ignoring some quantifiers
% 16.89/3.10 Prover 8: Constructing countermodel ...
% 16.89/3.11 Prover 11: Warning: ignoring some quantifiers
% 17.44/3.12 Prover 11: Constructing countermodel ...
% 18.07/3.21 Prover 10: Found proof (size 14)
% 18.07/3.21 Prover 10: proved (540ms)
% 18.07/3.21 Prover 11: stopped
% 18.07/3.21 Prover 13: stopped
% 18.07/3.21 Prover 8: stopped
% 18.07/3.21 Prover 1: stopped
% 18.07/3.21 Prover 4: stopped
% 18.07/3.21 Prover 7: stopped
% 18.07/3.21
% 18.07/3.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.07/3.21
% 18.07/3.22 % SZS output start Proof for theBenchmark
% 18.07/3.22 Assumptions after simplification:
% 18.07/3.22 ---------------------------------
% 18.07/3.22
% 18.07/3.22 (member_universal_self)
% 18.07/3.24 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (member_of(v0)
% 18.07/3.24 = v1) | ~ $i(v0) | member(v1, universal_class))
% 18.07/3.24
% 18.07/3.24 (member_when_not_a_singleton)
% 18.07/3.24 $i(universal_class) & ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) &
% 18.07/3.24 member_of(v0) = v1 & $i(v1) & $i(v0) & ! [v2: $i] : ( ~ (singleton(v2) =
% 18.07/3.24 v0) | ~ $i(v2) | ~ member(v2, universal_class)))
% 18.07/3.24
% 18.07/3.24 (singleton_self)
% 18.07/3.24 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (member_of(v0) = v1) | ~ $i(v0) |
% 18.07/3.24 singleton(v1) = v0)
% 18.07/3.24
% 18.07/3.24 Further assumptions not needed in the proof:
% 18.07/3.24 --------------------------------------------
% 18.07/3.24 apply_defn, choice, class_elements_are_sets, complement, compose_defn1,
% 18.07/3.24 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of,
% 18.07/3.24 element_relation, element_relation_defn, extensionality, first_second, flip,
% 18.07/3.24 flip_defn, function_defn, identity_relation, image_defn, inductive_defn,
% 18.07/3.24 infinity, intersection, inverse_defn, member_singleton_singleton,
% 18.07/3.24 member_singleton_universal, null_class_defn, ordered_pair_defn, power_class,
% 18.07/3.24 power_class_defn, range_of_defn, regularity, replacement, restrict_defn, rotate,
% 18.07/3.24 rotate_defn, singleton_set_defn, subclass_defn, successor_defn,
% 18.07/3.24 successor_relation_defn1, successor_relation_defn2, sum_class, sum_class_defn,
% 18.07/3.24 union_defn, unordered_pair, unordered_pair_defn
% 18.07/3.24
% 18.07/3.24 Those formulas are unsatisfiable:
% 18.07/3.24 ---------------------------------
% 18.07/3.24
% 18.07/3.24 Begin of proof
% 18.07/3.25 |
% 18.07/3.25 | ALPHA: (member_universal_self) implies:
% 18.07/3.25 | (1) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (member_of(v0) = v1) | ~
% 18.07/3.25 | $i(v0) | member(v1, universal_class))
% 18.07/3.25 |
% 18.07/3.25 | ALPHA: (member_when_not_a_singleton) implies:
% 18.07/3.25 | (2) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & member_of(v0) = v1 & $i(v1)
% 18.07/3.25 | & $i(v0) & ! [v2: $i] : ( ~ (singleton(v2) = v0) | ~ $i(v2) | ~
% 18.07/3.25 | member(v2, universal_class)))
% 18.07/3.25 |
% 18.07/3.25 | DELTA: instantiating (2) with fresh symbols all_54_0, all_54_1 gives:
% 18.07/3.25 | (3) ~ (all_54_0 = all_54_1) & member_of(all_54_1) = all_54_0 &
% 18.07/3.25 | $i(all_54_0) & $i(all_54_1) & ! [v0: $i] : ( ~ (singleton(v0) =
% 18.07/3.25 | all_54_1) | ~ $i(v0) | ~ member(v0, universal_class))
% 18.07/3.25 |
% 18.07/3.25 | ALPHA: (3) implies:
% 18.07/3.25 | (4) ~ (all_54_0 = all_54_1)
% 18.07/3.25 | (5) $i(all_54_1)
% 18.07/3.25 | (6) $i(all_54_0)
% 18.07/3.25 | (7) member_of(all_54_1) = all_54_0
% 18.07/3.25 | (8) ! [v0: $i] : ( ~ (singleton(v0) = all_54_1) | ~ $i(v0) | ~
% 18.07/3.25 | member(v0, universal_class))
% 18.07/3.25 |
% 18.07/3.25 | GROUND_INST: instantiating (singleton_self) with all_54_1, all_54_0,
% 18.07/3.25 | simplifying with (5), (7) gives:
% 18.07/3.25 | (9) all_54_0 = all_54_1 | singleton(all_54_0) = all_54_1
% 18.07/3.25 |
% 18.07/3.25 | GROUND_INST: instantiating (1) with all_54_1, all_54_0, simplifying with (5),
% 18.07/3.25 | (7) gives:
% 18.07/3.25 | (10) all_54_0 = all_54_1 | member(all_54_0, universal_class)
% 18.07/3.25 |
% 18.07/3.25 | BETA: splitting (10) gives:
% 18.07/3.25 |
% 18.07/3.25 | Case 1:
% 18.07/3.25 | |
% 18.07/3.25 | | (11) member(all_54_0, universal_class)
% 18.07/3.25 | |
% 18.07/3.25 | | BETA: splitting (9) gives:
% 18.07/3.25 | |
% 18.07/3.25 | | Case 1:
% 18.07/3.25 | | |
% 18.07/3.25 | | | (12) singleton(all_54_0) = all_54_1
% 18.07/3.25 | | |
% 18.07/3.26 | | | GROUND_INST: instantiating (8) with all_54_0, simplifying with (6), (11),
% 18.07/3.26 | | | (12) gives:
% 18.07/3.26 | | | (13) $false
% 18.07/3.26 | | |
% 18.07/3.26 | | | CLOSE: (13) is inconsistent.
% 18.07/3.26 | | |
% 18.07/3.26 | | Case 2:
% 18.07/3.26 | | |
% 18.07/3.26 | | | (14) all_54_0 = all_54_1
% 18.07/3.26 | | |
% 18.07/3.26 | | | REDUCE: (4), (14) imply:
% 18.07/3.26 | | | (15) $false
% 18.07/3.26 | | |
% 18.07/3.26 | | | CLOSE: (15) is inconsistent.
% 18.07/3.26 | | |
% 18.07/3.26 | | End of split
% 18.07/3.26 | |
% 18.07/3.26 | Case 2:
% 18.07/3.26 | |
% 18.07/3.26 | | (16) all_54_0 = all_54_1
% 18.07/3.26 | |
% 18.07/3.26 | | REDUCE: (4), (16) imply:
% 18.07/3.26 | | (17) $false
% 18.07/3.26 | |
% 18.07/3.26 | | CLOSE: (17) is inconsistent.
% 18.07/3.26 | |
% 18.07/3.26 | End of split
% 18.07/3.26 |
% 18.07/3.26 End of proof
% 18.07/3.26 % SZS output end Proof for theBenchmark
% 18.07/3.26
% 18.07/3.26 2651ms
%------------------------------------------------------------------------------