TSTP Solution File: SET072+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET072+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 : n013.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 15:23:35 EDT 2023
% Result : Theorem 19.39s 3.47s
% Output : Proof 23.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET072+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.17/0.33 % Computer : n013.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Sat Aug 26 09:56:32 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 4.02/1.28 Prover 4: Preprocessing ...
% 4.02/1.28 Prover 1: Preprocessing ...
% 4.02/1.32 Prover 0: Preprocessing ...
% 4.02/1.32 Prover 3: Preprocessing ...
% 4.02/1.32 Prover 6: Preprocessing ...
% 4.02/1.32 Prover 5: Preprocessing ...
% 4.02/1.32 Prover 2: Preprocessing ...
% 8.72/2.02 Prover 1: Warning: ignoring some quantifiers
% 8.72/2.05 Prover 3: Warning: ignoring some quantifiers
% 8.72/2.07 Prover 1: Constructing countermodel ...
% 8.72/2.08 Prover 3: Constructing countermodel ...
% 8.72/2.09 Prover 5: Proving ...
% 8.72/2.10 Prover 4: Warning: ignoring some quantifiers
% 8.72/2.10 Prover 6: Proving ...
% 8.72/2.12 Prover 4: Constructing countermodel ...
% 10.08/2.17 Prover 2: Proving ...
% 10.08/2.18 Prover 0: Proving ...
% 19.39/3.46 Prover 5: proved (2830ms)
% 19.39/3.46
% 19.39/3.47 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.39/3.47
% 19.39/3.48 Prover 0: stopped
% 19.39/3.48 Prover 2: stopped
% 19.39/3.49 Prover 3: stopped
% 19.39/3.51 Prover 6: stopped
% 19.39/3.51 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 19.39/3.51 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 19.39/3.51 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 19.39/3.51 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 19.39/3.51 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 19.39/3.56 Prover 7: Preprocessing ...
% 19.39/3.59 Prover 8: Preprocessing ...
% 20.87/3.60 Prover 10: Preprocessing ...
% 20.87/3.60 Prover 13: Preprocessing ...
% 21.04/3.61 Prover 11: Preprocessing ...
% 21.87/3.74 Prover 10: Warning: ignoring some quantifiers
% 21.87/3.75 Prover 7: Warning: ignoring some quantifiers
% 21.87/3.75 Prover 10: Constructing countermodel ...
% 21.87/3.76 Prover 7: Constructing countermodel ...
% 21.87/3.77 Prover 13: Warning: ignoring some quantifiers
% 21.87/3.79 Prover 13: Constructing countermodel ...
% 22.44/3.81 Prover 8: Warning: ignoring some quantifiers
% 22.44/3.82 Prover 8: Constructing countermodel ...
% 22.44/3.84 Prover 11: Warning: ignoring some quantifiers
% 22.44/3.85 Prover 11: Constructing countermodel ...
% 23.16/3.90 Prover 10: Found proof (size 18)
% 23.16/3.90 Prover 10: proved (409ms)
% 23.16/3.90 Prover 7: stopped
% 23.16/3.90 Prover 11: stopped
% 23.16/3.90 Prover 13: stopped
% 23.16/3.90 Prover 8: stopped
% 23.16/3.90 Prover 4: stopped
% 23.16/3.90 Prover 1: stopped
% 23.16/3.90
% 23.16/3.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.16/3.90
% 23.36/3.91 % SZS output start Proof for theBenchmark
% 23.36/3.91 Assumptions after simplification:
% 23.36/3.91 ---------------------------------
% 23.36/3.91
% 23.36/3.91 (right_cancellation)
% 23.45/3.94 $i(universal_class) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] :
% 23.45/3.94 ( ~ (v1 = v0) & unordered_pair(v1, v2) = v3 & unordered_pair(v0, v2) = v3 &
% 23.45/3.94 $i(v3) & $i(v2) & $i(v1) & $i(v0) & member(v1, universal_class) & member(v0,
% 23.45/3.94 universal_class))
% 23.45/3.94
% 23.45/3.94 (unordered_pair_defn)
% 23.45/3.94 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 23.45/3.94 (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 23.45/3.94 | ~ $i(v0) | ~ member(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 23.45/3.94 ! [v3: $i] : ( ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 23.45/3.94 $i(v0) | ~ member(v0, v3) | member(v0, universal_class)) & ! [v0: $i] : !
% 23.45/3.94 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | ~ $i(v1) | ~
% 23.45/3.94 $i(v0) | ~ member(v0, universal_class) | member(v0, v2)) & ! [v0: $i] : !
% 23.45/3.94 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~
% 23.45/3.94 $i(v0) | ~ member(v0, universal_class) | member(v0, v2))
% 23.45/3.94
% 23.45/3.94 Further assumptions not needed in the proof:
% 23.45/3.94 --------------------------------------------
% 23.45/3.94 apply_defn, choice, class_elements_are_sets, complement, compose_defn1,
% 23.45/3.94 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of,
% 23.45/3.94 element_relation, element_relation_defn, extensionality, first_second, flip,
% 23.45/3.94 flip_defn, function_defn, identity_relation, image_defn, inductive_defn,
% 23.45/3.94 infinity, intersection, inverse_defn, null_class_defn, ordered_pair_defn,
% 23.45/3.94 power_class, power_class_defn, range_of_defn, regularity, replacement,
% 23.45/3.94 restrict_defn, rotate, rotate_defn, singleton_set_defn, subclass_defn,
% 23.45/3.94 successor_defn, successor_relation_defn1, successor_relation_defn2, sum_class,
% 23.45/3.94 sum_class_defn, union_defn, unordered_pair
% 23.45/3.94
% 23.45/3.94 Those formulas are unsatisfiable:
% 23.45/3.94 ---------------------------------
% 23.45/3.94
% 23.45/3.94 Begin of proof
% 23.45/3.94 |
% 23.45/3.94 | ALPHA: (unordered_pair_defn) implies:
% 23.45/3.94 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) =
% 23.45/3.94 | v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, universal_class) |
% 23.45/3.94 | member(v0, v2))
% 23.45/3.95 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 =
% 23.45/3.95 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 23.45/3.95 | $i(v0) | ~ member(v0, v3))
% 23.45/3.95 |
% 23.45/3.95 | ALPHA: (right_cancellation) implies:
% 23.45/3.95 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ( ~ (v1 = v0) &
% 23.45/3.95 | unordered_pair(v1, v2) = v3 & unordered_pair(v0, v2) = v3 & $i(v3) &
% 23.45/3.95 | $i(v2) & $i(v1) & $i(v0) & member(v1, universal_class) & member(v0,
% 23.45/3.95 | universal_class))
% 23.45/3.95 |
% 23.45/3.95 | DELTA: instantiating (3) with fresh symbols all_59_0, all_59_1, all_59_2,
% 23.45/3.95 | all_59_3 gives:
% 23.45/3.95 | (4) ~ (all_59_2 = all_59_3) & unordered_pair(all_59_2, all_59_1) =
% 23.45/3.95 | all_59_0 & unordered_pair(all_59_3, all_59_1) = all_59_0 & $i(all_59_0)
% 23.45/3.95 | & $i(all_59_1) & $i(all_59_2) & $i(all_59_3) & member(all_59_2,
% 23.45/3.95 | universal_class) & member(all_59_3, universal_class)
% 23.45/3.95 |
% 23.45/3.95 | ALPHA: (4) implies:
% 23.45/3.95 | (5) ~ (all_59_2 = all_59_3)
% 23.45/3.95 | (6) member(all_59_3, universal_class)
% 23.45/3.95 | (7) member(all_59_2, universal_class)
% 23.45/3.95 | (8) $i(all_59_3)
% 23.45/3.95 | (9) $i(all_59_2)
% 23.45/3.95 | (10) $i(all_59_1)
% 23.45/3.95 | (11) unordered_pair(all_59_3, all_59_1) = all_59_0
% 23.45/3.95 | (12) unordered_pair(all_59_2, all_59_1) = all_59_0
% 23.45/3.95 |
% 23.45/3.95 | GROUND_INST: instantiating (1) with all_59_3, all_59_1, all_59_0, simplifying
% 23.45/3.95 | with (6), (8), (10), (11) gives:
% 23.45/3.95 | (13) member(all_59_3, all_59_0)
% 23.45/3.95 |
% 23.45/3.95 | GROUND_INST: instantiating (1) with all_59_2, all_59_1, all_59_0, simplifying
% 23.45/3.95 | with (7), (9), (10), (12) gives:
% 23.45/3.95 | (14) member(all_59_2, all_59_0)
% 23.45/3.95 |
% 23.45/3.95 | GROUND_INST: instantiating (2) with all_59_3, all_59_2, all_59_1, all_59_0,
% 23.45/3.95 | simplifying with (8), (9), (10), (12), (13) gives:
% 23.45/3.95 | (15) all_59_1 = all_59_3 | all_59_2 = all_59_3
% 23.45/3.95 |
% 23.45/3.95 | GROUND_INST: instantiating (2) with all_59_2, all_59_3, all_59_1, all_59_0,
% 23.45/3.95 | simplifying with (8), (9), (10), (11), (14) gives:
% 23.45/3.95 | (16) all_59_1 = all_59_2 | all_59_2 = all_59_3
% 23.45/3.95 |
% 23.45/3.95 | BETA: splitting (16) gives:
% 23.45/3.95 |
% 23.45/3.95 | Case 1:
% 23.45/3.95 | |
% 23.45/3.95 | | (17) all_59_1 = all_59_2
% 23.45/3.95 | |
% 23.45/3.95 | | BETA: splitting (15) gives:
% 23.45/3.95 | |
% 23.45/3.95 | | Case 1:
% 23.45/3.95 | | |
% 23.45/3.95 | | | (18) all_59_1 = all_59_3
% 23.45/3.95 | | |
% 23.45/3.95 | | | COMBINE_EQS: (17), (18) imply:
% 23.45/3.95 | | | (19) all_59_2 = all_59_3
% 23.45/3.95 | | |
% 23.45/3.95 | | | SIMP: (19) implies:
% 23.45/3.95 | | | (20) all_59_2 = all_59_3
% 23.45/3.95 | | |
% 23.45/3.95 | | | REDUCE: (5), (20) imply:
% 23.45/3.95 | | | (21) $false
% 23.45/3.96 | | |
% 23.45/3.96 | | | CLOSE: (21) is inconsistent.
% 23.45/3.96 | | |
% 23.45/3.96 | | Case 2:
% 23.45/3.96 | | |
% 23.45/3.96 | | | (22) all_59_2 = all_59_3
% 23.45/3.96 | | |
% 23.45/3.96 | | | REDUCE: (5), (22) imply:
% 23.45/3.96 | | | (23) $false
% 23.45/3.96 | | |
% 23.45/3.96 | | | CLOSE: (23) is inconsistent.
% 23.45/3.96 | | |
% 23.45/3.96 | | End of split
% 23.45/3.96 | |
% 23.45/3.96 | Case 2:
% 23.45/3.96 | |
% 23.45/3.96 | | (24) all_59_2 = all_59_3
% 23.45/3.96 | |
% 23.45/3.96 | | REDUCE: (5), (24) imply:
% 23.45/3.96 | | (25) $false
% 23.45/3.96 | |
% 23.45/3.96 | | CLOSE: (25) is inconsistent.
% 23.45/3.96 | |
% 23.45/3.96 | End of split
% 23.45/3.96 |
% 23.45/3.96 End of proof
% 23.45/3.96 % SZS output end Proof for theBenchmark
% 23.45/3.96
% 23.45/3.96 3354ms
%------------------------------------------------------------------------------