TSTP Solution File: SET054+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET054+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 : n031.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 15:23:25 EDT 2023
% Result : Theorem 10.53s 2.25s
% Output : Proof 13.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET054+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.16/0.34 % Computer : n031.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 15:13:38 EDT 2023
% 0.16/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.99/1.18 Prover 1: Preprocessing ...
% 2.99/1.19 Prover 4: Preprocessing ...
% 2.99/1.22 Prover 0: Preprocessing ...
% 2.99/1.22 Prover 3: Preprocessing ...
% 2.99/1.22 Prover 5: Preprocessing ...
% 2.99/1.22 Prover 6: Preprocessing ...
% 2.99/1.22 Prover 2: Preprocessing ...
% 8.85/1.97 Prover 1: Warning: ignoring some quantifiers
% 8.85/1.99 Prover 3: Warning: ignoring some quantifiers
% 8.85/2.01 Prover 5: Proving ...
% 8.85/2.03 Prover 3: Constructing countermodel ...
% 8.85/2.03 Prover 1: Constructing countermodel ...
% 8.85/2.04 Prover 4: Warning: ignoring some quantifiers
% 8.85/2.05 Prover 6: Proving ...
% 8.85/2.11 Prover 2: Proving ...
% 8.85/2.12 Prover 4: Constructing countermodel ...
% 10.53/2.18 Prover 0: Proving ...
% 10.53/2.24 Prover 3: proved (1592ms)
% 10.53/2.24
% 10.53/2.25 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.53/2.25
% 10.53/2.25 Prover 5: stopped
% 10.53/2.25 Prover 2: stopped
% 11.16/2.27 Prover 0: stopped
% 11.16/2.28 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.16/2.28 Prover 6: proved (1589ms)
% 11.16/2.28
% 11.16/2.28 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.16/2.28
% 11.29/2.28 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 11.29/2.28 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 11.29/2.28 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 11.29/2.28 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.29/2.31 Prover 7: Preprocessing ...
% 11.67/2.34 Prover 8: Preprocessing ...
% 11.67/2.35 Prover 10: Preprocessing ...
% 11.67/2.36 Prover 11: Preprocessing ...
% 11.67/2.36 Prover 13: Preprocessing ...
% 12.32/2.44 Prover 1: Found proof (size 6)
% 12.32/2.44 Prover 1: proved (1796ms)
% 12.32/2.44 Prover 4: stopped
% 12.32/2.44 Prover 11: stopped
% 12.32/2.46 Prover 13: stopped
% 12.32/2.48 Prover 7: Warning: ignoring some quantifiers
% 12.80/2.48 Prover 10: Warning: ignoring some quantifiers
% 12.80/2.50 Prover 7: Constructing countermodel ...
% 12.80/2.50 Prover 10: Constructing countermodel ...
% 12.80/2.51 Prover 7: stopped
% 12.80/2.52 Prover 10: stopped
% 12.80/2.53 Prover 8: Warning: ignoring some quantifiers
% 12.80/2.54 Prover 8: Constructing countermodel ...
% 12.80/2.55 Prover 8: stopped
% 12.80/2.55
% 12.80/2.55 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.80/2.55
% 12.80/2.55 % SZS output start Proof for theBenchmark
% 12.80/2.56 Assumptions after simplification:
% 12.80/2.56 ---------------------------------
% 12.80/2.56
% 12.80/2.56 (extensionality)
% 13.37/2.58 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (subclass(v0, v1) = 0) | ~ $i(v1) |
% 13.37/2.58 ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & subclass(v1, v0) = v2)) & ! [v0:
% 13.37/2.58 $i] : ! [v1: int] : (v1 = 0 | ~ (subclass(v0, v0) = v1) | ~ $i(v0))
% 13.37/2.58
% 13.37/2.58 (reflexivity_of_subclass)
% 13.37/2.58 ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subclass(v0, v0) = v1 & $i(v0))
% 13.37/2.58
% 13.37/2.58 Further assumptions not needed in the proof:
% 13.37/2.58 --------------------------------------------
% 13.37/2.58 apply_defn, choice, class_elements_are_sets, complement, compose_defn1,
% 13.37/2.58 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of,
% 13.37/2.58 element_relation, element_relation_defn, first_second, flip, flip_defn,
% 13.37/2.58 function_defn, identity_relation, image_defn, inductive_defn, infinity,
% 13.37/2.58 intersection, inverse_defn, null_class_defn, ordered_pair_defn, power_class,
% 13.37/2.58 power_class_defn, range_of_defn, regularity, replacement, restrict_defn, rotate,
% 13.37/2.58 rotate_defn, singleton_set_defn, subclass_defn, successor_defn,
% 13.37/2.58 successor_relation_defn1, successor_relation_defn2, sum_class, sum_class_defn,
% 13.37/2.58 union_defn, unordered_pair, unordered_pair_defn
% 13.37/2.58
% 13.37/2.58 Those formulas are unsatisfiable:
% 13.37/2.58 ---------------------------------
% 13.37/2.58
% 13.37/2.58 Begin of proof
% 13.37/2.58 |
% 13.37/2.58 | ALPHA: (extensionality) implies:
% 13.37/2.59 | (1) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (subclass(v0, v0) = v1) | ~
% 13.37/2.59 | $i(v0))
% 13.37/2.59 |
% 13.37/2.59 | DELTA: instantiating (reflexivity_of_subclass) with fresh symbols all_40_0,
% 13.37/2.59 | all_40_1 gives:
% 13.37/2.59 | (2) ~ (all_40_0 = 0) & subclass(all_40_1, all_40_1) = all_40_0 &
% 13.37/2.59 | $i(all_40_1)
% 13.37/2.59 |
% 13.37/2.59 | ALPHA: (2) implies:
% 13.37/2.59 | (3) ~ (all_40_0 = 0)
% 13.37/2.59 | (4) $i(all_40_1)
% 13.37/2.59 | (5) subclass(all_40_1, all_40_1) = all_40_0
% 13.37/2.59 |
% 13.37/2.59 | GROUND_INST: instantiating (1) with all_40_1, all_40_0, simplifying with (4),
% 13.37/2.59 | (5) gives:
% 13.37/2.59 | (6) all_40_0 = 0
% 13.37/2.59 |
% 13.37/2.59 | REDUCE: (3), (6) imply:
% 13.37/2.59 | (7) $false
% 13.37/2.59 |
% 13.37/2.59 | CLOSE: (7) is inconsistent.
% 13.37/2.59 |
% 13.37/2.59 End of proof
% 13.37/2.59 % SZS output end Proof for theBenchmark
% 13.37/2.59
% 13.37/2.59 1970ms
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