TSTP Solution File: SET024+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET024+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 : n024.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 15:23:13 EDT 2023
% Result : Theorem 13.56s 2.67s
% Output : Proof 19.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET024+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n024.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 11:33:54 EDT 2023
% 0.13/0.35 % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.03/1.23 Prover 1: Preprocessing ...
% 3.03/1.23 Prover 4: Preprocessing ...
% 3.63/1.27 Prover 2: Preprocessing ...
% 3.63/1.27 Prover 6: Preprocessing ...
% 3.63/1.27 Prover 3: Preprocessing ...
% 3.63/1.27 Prover 0: Preprocessing ...
% 3.63/1.27 Prover 5: Preprocessing ...
% 8.17/1.96 Prover 1: Warning: ignoring some quantifiers
% 9.65/2.06 Prover 3: Warning: ignoring some quantifiers
% 9.65/2.09 Prover 3: Constructing countermodel ...
% 9.65/2.09 Prover 5: Proving ...
% 9.65/2.09 Prover 1: Constructing countermodel ...
% 9.65/2.10 Prover 6: Proving ...
% 10.10/2.13 Prover 4: Warning: ignoring some quantifiers
% 10.35/2.18 Prover 4: Constructing countermodel ...
% 10.35/2.20 Prover 2: Proving ...
% 10.89/2.27 Prover 0: Proving ...
% 13.56/2.66 Prover 0: proved (2021ms)
% 13.56/2.66
% 13.56/2.67 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.56/2.67
% 13.56/2.67 Prover 3: stopped
% 13.56/2.68 Prover 2: stopped
% 13.56/2.69 Prover 5: stopped
% 13.56/2.70 Prover 6: stopped
% 14.44/2.71 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.44/2.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.44/2.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.44/2.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.44/2.71 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.61/2.73 Prover 10: Preprocessing ...
% 14.61/2.74 Prover 7: Preprocessing ...
% 14.61/2.74 Prover 8: Preprocessing ...
% 14.61/2.77 Prover 11: Preprocessing ...
% 14.61/2.80 Prover 13: Preprocessing ...
% 15.73/2.89 Prover 10: Warning: ignoring some quantifiers
% 15.73/2.93 Prover 10: Constructing countermodel ...
% 15.73/2.93 Prover 7: Warning: ignoring some quantifiers
% 16.34/2.98 Prover 7: Constructing countermodel ...
% 16.86/3.03 Prover 11: Warning: ignoring some quantifiers
% 16.86/3.05 Prover 8: Warning: ignoring some quantifiers
% 16.86/3.05 Prover 11: Constructing countermodel ...
% 16.86/3.07 Prover 8: Constructing countermodel ...
% 16.86/3.08 Prover 13: Warning: ignoring some quantifiers
% 16.86/3.11 Prover 13: Constructing countermodel ...
% 18.00/3.29 Prover 7: Found proof (size 10)
% 18.00/3.29 Prover 7: proved (621ms)
% 18.00/3.29 Prover 10: gave up
% 18.00/3.29 Prover 11: stopped
% 18.00/3.29 Prover 13: stopped
% 18.00/3.29 Prover 8: stopped
% 18.00/3.29 Prover 4: stopped
% 18.00/3.29 Prover 1: stopped
% 18.00/3.29
% 18.00/3.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 18.00/3.29
% 18.00/3.29 % SZS output start Proof for theBenchmark
% 18.00/3.30 Assumptions after simplification:
% 18.00/3.30 ---------------------------------
% 18.00/3.30
% 18.00/3.30 (set_in_its_singleton)
% 18.71/3.32 $i(universal_class) & ? [v0: $i] : ? [v1: $i] : (singleton(v0) = v1 & $i(v1)
% 18.71/3.32 & $i(v0) & member(v0, universal_class) & ~ member(v0, v1))
% 18.71/3.32
% 18.71/3.32 (singleton_set_defn)
% 18.71/3.32 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 18.71/3.33 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 18.71/3.33 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1)))
% 18.71/3.33
% 18.71/3.33 (unordered_pair_defn)
% 18.71/3.33 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 18.71/3.33 (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 18.71/3.33 | ~ $i(v0) | ~ member(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 18.71/3.33 ! [v3: $i] : ( ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 18.71/3.33 $i(v0) | ~ member(v0, v3) | member(v0, universal_class)) & ! [v0: $i] : !
% 18.71/3.33 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | ~ $i(v1) | ~
% 18.71/3.33 $i(v0) | ~ member(v0, universal_class) | member(v0, v2)) & ! [v0: $i] : !
% 18.71/3.33 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~
% 18.71/3.33 $i(v0) | ~ member(v0, universal_class) | member(v0, v2))
% 18.71/3.33
% 18.71/3.33 Further assumptions not needed in the proof:
% 18.71/3.33 --------------------------------------------
% 18.71/3.33 apply_defn, choice, class_elements_are_sets, complement, compose_defn1,
% 18.71/3.33 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of,
% 18.71/3.33 element_relation, element_relation_defn, extensionality, first_second, flip,
% 18.71/3.33 flip_defn, function_defn, identity_relation, image_defn, inductive_defn,
% 18.71/3.33 infinity, intersection, inverse_defn, null_class_defn, ordered_pair_defn,
% 18.71/3.33 power_class, power_class_defn, range_of_defn, regularity, replacement,
% 18.71/3.33 restrict_defn, rotate, rotate_defn, subclass_defn, successor_defn,
% 18.71/3.33 successor_relation_defn1, successor_relation_defn2, sum_class, sum_class_defn,
% 18.71/3.33 union_defn, unordered_pair
% 18.71/3.33
% 18.71/3.33 Those formulas are unsatisfiable:
% 18.71/3.33 ---------------------------------
% 18.71/3.33
% 18.71/3.33 Begin of proof
% 18.71/3.33 |
% 18.71/3.33 | ALPHA: (unordered_pair_defn) implies:
% 18.71/3.33 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) =
% 18.71/3.33 | v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, universal_class) |
% 18.71/3.33 | member(v0, v2))
% 18.71/3.33 |
% 18.71/3.33 | ALPHA: (singleton_set_defn) implies:
% 18.71/3.33 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 18.71/3.33 | (unordered_pair(v0, v0) = v1 & $i(v1)))
% 18.71/3.33 |
% 18.71/3.33 | ALPHA: (set_in_its_singleton) implies:
% 18.71/3.33 | (3) ? [v0: $i] : ? [v1: $i] : (singleton(v0) = v1 & $i(v1) & $i(v0) &
% 18.71/3.33 | member(v0, universal_class) & ~ member(v0, v1))
% 18.71/3.33 |
% 18.71/3.34 | DELTA: instantiating (3) with fresh symbols all_41_0, all_41_1 gives:
% 18.71/3.34 | (4) singleton(all_41_1) = all_41_0 & $i(all_41_0) & $i(all_41_1) &
% 18.71/3.34 | member(all_41_1, universal_class) & ~ member(all_41_1, all_41_0)
% 18.71/3.34 |
% 18.71/3.34 | ALPHA: (4) implies:
% 18.71/3.34 | (5) ~ member(all_41_1, all_41_0)
% 18.71/3.34 | (6) member(all_41_1, universal_class)
% 18.71/3.34 | (7) $i(all_41_1)
% 18.71/3.34 | (8) singleton(all_41_1) = all_41_0
% 18.71/3.34 |
% 18.71/3.34 | GROUND_INST: instantiating (2) with all_41_1, all_41_0, simplifying with (7),
% 18.71/3.34 | (8) gives:
% 18.71/3.34 | (9) unordered_pair(all_41_1, all_41_1) = all_41_0 & $i(all_41_0)
% 18.71/3.34 |
% 18.71/3.34 | ALPHA: (9) implies:
% 18.71/3.34 | (10) unordered_pair(all_41_1, all_41_1) = all_41_0
% 18.71/3.34 |
% 18.71/3.34 | GROUND_INST: instantiating (1) with all_41_1, all_41_1, all_41_0, simplifying
% 18.71/3.34 | with (5), (6), (7), (10) gives:
% 18.71/3.34 | (11) $false
% 18.71/3.34 |
% 18.71/3.34 | CLOSE: (11) is inconsistent.
% 18.71/3.34 |
% 18.71/3.34 End of proof
% 19.08/3.34 % SZS output end Proof for theBenchmark
% 19.08/3.34
% 19.08/3.34 2721ms
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