TSTP Solution File: SET025+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET025+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 : n015.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 15:23:14 EDT 2023
% Result : Theorem 13.26s 2.58s
% Output : Proof 18.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET025+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 : n015.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 16:36:23 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.60 ________ _____
% 0.21/0.60 ___ __ \_________(_)________________________________
% 0.21/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.60
% 0.21/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.60 (2023-06-19)
% 0.21/0.60
% 0.21/0.60 (c) Philipp Rümmer, 2009-2023
% 0.21/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.60 Amanda Stjerna.
% 0.21/0.60 Free software under BSD-3-Clause.
% 0.21/0.60
% 0.21/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.60
% 0.21/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.21/0.62 Running up to 7 provers in parallel.
% 0.21/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.21/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 3.18/1.18 Prover 1: Preprocessing ...
% 3.18/1.18 Prover 4: Preprocessing ...
% 3.64/1.22 Prover 0: Preprocessing ...
% 3.64/1.22 Prover 2: Preprocessing ...
% 3.64/1.22 Prover 6: Preprocessing ...
% 3.64/1.22 Prover 5: Preprocessing ...
% 3.64/1.22 Prover 3: Preprocessing ...
% 8.90/1.99 Prover 1: Warning: ignoring some quantifiers
% 8.90/2.03 Prover 3: Warning: ignoring some quantifiers
% 8.90/2.06 Prover 3: Constructing countermodel ...
% 8.90/2.08 Prover 6: Proving ...
% 8.90/2.08 Prover 5: Proving ...
% 8.90/2.09 Prover 1: Constructing countermodel ...
% 8.90/2.14 Prover 4: Warning: ignoring some quantifiers
% 10.43/2.19 Prover 4: Constructing countermodel ...
% 10.43/2.22 Prover 2: Proving ...
% 11.55/2.33 Prover 0: Proving ...
% 13.26/2.58 Prover 5: proved (1947ms)
% 13.26/2.58
% 13.26/2.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.26/2.58
% 13.26/2.58 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.26/2.58 Prover 3: stopped
% 13.26/2.59 Prover 6: stopped
% 13.26/2.59 Prover 2: stopped
% 13.26/2.59 Prover 0: stopped
% 13.26/2.59 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.26/2.59 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.26/2.59 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.26/2.59 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.39/2.68 Prover 11: Preprocessing ...
% 14.39/2.68 Prover 7: Preprocessing ...
% 14.39/2.71 Prover 8: Preprocessing ...
% 14.39/2.71 Prover 13: Preprocessing ...
% 14.39/2.71 Prover 10: Preprocessing ...
% 15.09/2.87 Prover 7: Warning: ignoring some quantifiers
% 15.09/2.88 Prover 10: Warning: ignoring some quantifiers
% 15.09/2.90 Prover 7: Constructing countermodel ...
% 15.09/2.91 Prover 10: Constructing countermodel ...
% 16.44/2.96 Prover 8: Warning: ignoring some quantifiers
% 16.44/2.96 Prover 13: Warning: ignoring some quantifiers
% 16.56/2.97 Prover 8: Constructing countermodel ...
% 16.56/2.98 Prover 13: Constructing countermodel ...
% 17.08/3.05 Prover 11: Warning: ignoring some quantifiers
% 17.08/3.07 Prover 11: Constructing countermodel ...
% 18.17/3.20 Prover 7: Found proof (size 11)
% 18.17/3.20 Prover 7: proved (614ms)
% 18.17/3.20 Prover 10: stopped
% 18.17/3.20 Prover 13: stopped
% 18.17/3.20 Prover 11: stopped
% 18.17/3.20 Prover 8: stopped
% 18.17/3.21 Prover 4: stopped
% 18.17/3.21 Prover 1: stopped
% 18.17/3.21
% 18.17/3.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.17/3.21
% 18.17/3.21 % SZS output start Proof for theBenchmark
% 18.17/3.22 Assumptions after simplification:
% 18.17/3.22 ---------------------------------
% 18.17/3.22
% 18.17/3.22 (ordered_pair_defn)
% 18.17/3.24 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (singleton(v1) =
% 18.17/3.24 v2) | ~ (unordered_pair(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 18.17/3.24 $i] : ? [v5: $i] : (ordered_pair(v0, v1) = v4 & singleton(v0) = v5 &
% 18.17/3.24 unordered_pair(v5, v3) = v4 & $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1:
% 18.17/3.24 $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 18.17/3.24 | ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : (singleton(v1) = v4 &
% 18.17/3.24 singleton(v0) = v3 & unordered_pair(v3, v5) = v2 & unordered_pair(v0, v4)
% 18.17/3.24 = v5 & $i(v5) & $i(v4) & $i(v3) & $i(v2)))
% 18.17/3.24
% 18.17/3.24 (ordered_pair_is_set)
% 18.17/3.24 $i(universal_class) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 18.17/3.24 (ordered_pair(v0, v1) = v2 & $i(v2) & $i(v1) & $i(v0) & ~ member(v2,
% 18.17/3.24 universal_class))
% 18.17/3.24
% 18.17/3.24 (unordered_pair)
% 18.17/3.24 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 18.17/3.24 (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | member(v2,
% 18.17/3.24 universal_class))
% 18.17/3.24
% 18.17/3.24 Further assumptions not needed in the proof:
% 18.17/3.24 --------------------------------------------
% 18.17/3.25 apply_defn, choice, class_elements_are_sets, complement, compose_defn1,
% 18.17/3.25 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of,
% 18.17/3.25 element_relation, element_relation_defn, extensionality, first_second, flip,
% 18.17/3.25 flip_defn, function_defn, identity_relation, image_defn, inductive_defn,
% 18.17/3.25 infinity, intersection, inverse_defn, null_class_defn, power_class,
% 18.17/3.25 power_class_defn, range_of_defn, regularity, replacement, restrict_defn, rotate,
% 18.17/3.25 rotate_defn, singleton_set_defn, subclass_defn, successor_defn,
% 18.17/3.25 successor_relation_defn1, successor_relation_defn2, sum_class, sum_class_defn,
% 18.17/3.25 union_defn, unordered_pair_defn
% 18.17/3.25
% 18.17/3.25 Those formulas are unsatisfiable:
% 18.17/3.25 ---------------------------------
% 18.17/3.25
% 18.17/3.25 Begin of proof
% 18.17/3.25 |
% 18.17/3.25 | ALPHA: (unordered_pair) implies:
% 18.17/3.25 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 18.17/3.25 | v2) | ~ $i(v1) | ~ $i(v0) | member(v2, universal_class))
% 18.17/3.25 |
% 18.17/3.25 | ALPHA: (ordered_pair_defn) implies:
% 18.17/3.25 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 18.17/3.25 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 18.17/3.25 | $i] : (singleton(v1) = v4 & singleton(v0) = v3 & unordered_pair(v3,
% 18.17/3.25 | v5) = v2 & unordered_pair(v0, v4) = v5 & $i(v5) & $i(v4) & $i(v3)
% 18.17/3.25 | & $i(v2)))
% 18.17/3.25 |
% 18.17/3.25 | ALPHA: (ordered_pair_is_set) implies:
% 18.17/3.25 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (ordered_pair(v0, v1) = v2 &
% 18.17/3.25 | $i(v2) & $i(v1) & $i(v0) & ~ member(v2, universal_class))
% 18.17/3.25 |
% 18.17/3.25 | DELTA: instantiating (3) with fresh symbols all_41_0, all_41_1, all_41_2
% 18.17/3.25 | gives:
% 18.17/3.25 | (4) ordered_pair(all_41_2, all_41_1) = all_41_0 & $i(all_41_0) &
% 18.17/3.25 | $i(all_41_1) & $i(all_41_2) & ~ member(all_41_0, universal_class)
% 18.17/3.25 |
% 18.17/3.25 | ALPHA: (4) implies:
% 18.17/3.25 | (5) ~ member(all_41_0, universal_class)
% 18.17/3.25 | (6) $i(all_41_2)
% 18.17/3.25 | (7) $i(all_41_1)
% 18.17/3.25 | (8) ordered_pair(all_41_2, all_41_1) = all_41_0
% 18.17/3.25 |
% 18.17/3.25 | GROUND_INST: instantiating (2) with all_41_2, all_41_1, all_41_0, simplifying
% 18.17/3.25 | with (6), (7), (8) gives:
% 18.17/3.26 | (9) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (singleton(all_41_1) = v1 &
% 18.17/3.26 | singleton(all_41_2) = v0 & unordered_pair(v0, v2) = all_41_0 &
% 18.17/3.26 | unordered_pair(all_41_2, v1) = v2 & $i(v2) & $i(v1) & $i(v0) &
% 18.17/3.26 | $i(all_41_0))
% 18.17/3.26 |
% 18.55/3.26 | DELTA: instantiating (9) with fresh symbols all_96_0, all_96_1, all_96_2
% 18.55/3.26 | gives:
% 18.55/3.26 | (10) singleton(all_41_1) = all_96_1 & singleton(all_41_2) = all_96_2 &
% 18.55/3.26 | unordered_pair(all_96_2, all_96_0) = all_41_0 &
% 18.55/3.26 | unordered_pair(all_41_2, all_96_1) = all_96_0 & $i(all_96_0) &
% 18.55/3.26 | $i(all_96_1) & $i(all_96_2) & $i(all_41_0)
% 18.55/3.26 |
% 18.55/3.26 | ALPHA: (10) implies:
% 18.55/3.26 | (11) $i(all_96_2)
% 18.55/3.26 | (12) $i(all_96_0)
% 18.55/3.26 | (13) unordered_pair(all_96_2, all_96_0) = all_41_0
% 18.55/3.26 |
% 18.55/3.26 | GROUND_INST: instantiating (1) with all_96_2, all_96_0, all_41_0, simplifying
% 18.55/3.26 | with (5), (11), (12), (13) gives:
% 18.55/3.26 | (14) $false
% 18.55/3.26 |
% 18.55/3.26 | CLOSE: (14) is inconsistent.
% 18.55/3.26 |
% 18.55/3.26 End of proof
% 18.55/3.26 % SZS output end Proof for theBenchmark
% 18.55/3.26
% 18.55/3.26 2655ms
%------------------------------------------------------------------------------