TSTP Solution File: SET074+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET074+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 : n025.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 15:23:36 EDT 2023
% Result : Theorem 16.55s 2.96s
% Output : Proof 19.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET074+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 : n025.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 09:23:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.60 (c) Philipp Rümmer, 2009-2023
% 0.20/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.60 Amanda Stjerna.
% 0.20/0.60 Free software under BSD-3-Clause.
% 0.20/0.60
% 0.20/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.60
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.26/1.15 Prover 4: Preprocessing ...
% 3.26/1.17 Prover 1: Preprocessing ...
% 3.73/1.20 Prover 5: Preprocessing ...
% 3.73/1.20 Prover 6: Preprocessing ...
% 3.73/1.21 Prover 0: Preprocessing ...
% 3.73/1.21 Prover 3: Preprocessing ...
% 3.73/1.21 Prover 2: Preprocessing ...
% 9.65/2.09 Prover 1: Warning: ignoring some quantifiers
% 9.65/2.10 Prover 3: Warning: ignoring some quantifiers
% 10.27/2.11 Prover 5: Proving ...
% 10.27/2.13 Prover 3: Constructing countermodel ...
% 10.27/2.13 Prover 6: Proving ...
% 10.49/2.14 Prover 1: Constructing countermodel ...
% 10.49/2.15 Prover 4: Warning: ignoring some quantifiers
% 10.49/2.18 Prover 4: Constructing countermodel ...
% 10.49/2.20 Prover 2: Proving ...
% 11.16/2.26 Prover 0: Proving ...
% 16.55/2.96 Prover 5: proved (2332ms)
% 16.55/2.96
% 16.55/2.96 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 16.55/2.96
% 16.55/2.97 Prover 2: stopped
% 16.55/2.97 Prover 6: stopped
% 16.55/2.98 Prover 0: stopped
% 16.55/2.98 Prover 3: stopped
% 16.95/2.99 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 16.95/2.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 16.95/2.99 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 16.95/2.99 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 16.95/2.99 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 16.95/3.03 Prover 11: Preprocessing ...
% 16.95/3.04 Prover 8: Preprocessing ...
% 17.45/3.06 Prover 7: Preprocessing ...
% 17.52/3.06 Prover 13: Preprocessing ...
% 17.52/3.07 Prover 10: Preprocessing ...
% 18.15/3.21 Prover 8: Warning: ignoring some quantifiers
% 18.15/3.23 Prover 7: Warning: ignoring some quantifiers
% 18.86/3.25 Prover 8: Constructing countermodel ...
% 18.86/3.25 Prover 7: Constructing countermodel ...
% 18.86/3.28 Prover 10: Warning: ignoring some quantifiers
% 18.86/3.29 Prover 11: Warning: ignoring some quantifiers
% 19.28/3.31 Prover 11: Constructing countermodel ...
% 19.28/3.32 Prover 10: Constructing countermodel ...
% 19.28/3.34 Prover 13: Warning: ignoring some quantifiers
% 19.28/3.36 Prover 13: Constructing countermodel ...
% 19.28/3.42 Prover 10: Found proof (size 8)
% 19.28/3.42 Prover 10: proved (438ms)
% 19.28/3.42 Prover 11: stopped
% 19.28/3.42 Prover 4: stopped
% 19.28/3.42 Prover 13: stopped
% 19.28/3.42 Prover 7: stopped
% 19.28/3.42 Prover 1: stopped
% 19.28/3.42 Prover 8: stopped
% 19.28/3.42
% 19.28/3.42 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.28/3.42
% 19.28/3.42 % SZS output start Proof for theBenchmark
% 19.28/3.43 Assumptions after simplification:
% 19.28/3.43 ---------------------------------
% 19.28/3.43
% 19.28/3.43 (corollary1_2)
% 19.28/3.45 $i(null_class) & $i(universal_class) & ? [v0: $i] : ? [v1: $i] :
% 19.28/3.45 (unordered_pair(v0, v1) = null_class & $i(v1) & $i(v0) & member(v1,
% 19.28/3.45 universal_class))
% 19.28/3.45
% 19.28/3.45 (null_class_defn)
% 19.28/3.45 $i(null_class) & ! [v0: $i] : ( ~ $i(v0) | ~ member(v0, null_class))
% 19.28/3.45
% 19.28/3.45 (unordered_pair_defn)
% 19.28/3.46 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 19.28/3.46 (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 19.28/3.46 | ~ $i(v0) | ~ member(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 19.28/3.46 ! [v3: $i] : ( ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 19.28/3.46 $i(v0) | ~ member(v0, v3) | member(v0, universal_class)) & ! [v0: $i] : !
% 19.28/3.46 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | ~ $i(v1) | ~
% 19.28/3.46 $i(v0) | ~ member(v0, universal_class) | member(v0, v2)) & ! [v0: $i] : !
% 19.28/3.46 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~
% 19.28/3.46 $i(v0) | ~ member(v0, universal_class) | member(v0, v2))
% 19.28/3.46
% 19.28/3.46 Further assumptions not needed in the proof:
% 19.28/3.46 --------------------------------------------
% 19.28/3.46 apply_defn, choice, class_elements_are_sets, complement, compose_defn1,
% 19.28/3.46 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of,
% 19.28/3.46 element_relation, element_relation_defn, extensionality, first_second, flip,
% 19.28/3.46 flip_defn, function_defn, identity_relation, image_defn, inductive_defn,
% 19.28/3.46 infinity, intersection, inverse_defn, ordered_pair_defn, power_class,
% 19.28/3.46 power_class_defn, range_of_defn, regularity, replacement, restrict_defn, rotate,
% 19.28/3.46 rotate_defn, singleton_set_defn, subclass_defn, successor_defn,
% 19.28/3.46 successor_relation_defn1, successor_relation_defn2, sum_class, sum_class_defn,
% 19.28/3.46 union_defn, unordered_pair
% 19.28/3.46
% 19.28/3.46 Those formulas are unsatisfiable:
% 19.28/3.46 ---------------------------------
% 19.28/3.46
% 19.28/3.46 Begin of proof
% 19.28/3.46 |
% 19.28/3.46 | ALPHA: (unordered_pair_defn) implies:
% 19.28/3.46 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) =
% 19.28/3.46 | v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, universal_class) |
% 19.28/3.46 | member(v0, v2))
% 19.28/3.46 |
% 19.28/3.46 | ALPHA: (null_class_defn) implies:
% 19.28/3.46 | (2) ! [v0: $i] : ( ~ $i(v0) | ~ member(v0, null_class))
% 19.28/3.46 |
% 19.28/3.46 | ALPHA: (corollary1_2) implies:
% 19.28/3.46 | (3) ? [v0: $i] : ? [v1: $i] : (unordered_pair(v0, v1) = null_class &
% 19.28/3.46 | $i(v1) & $i(v0) & member(v1, universal_class))
% 19.28/3.46 |
% 19.28/3.46 | DELTA: instantiating (3) with fresh symbols all_41_0, all_41_1 gives:
% 19.28/3.46 | (4) unordered_pair(all_41_1, all_41_0) = null_class & $i(all_41_0) &
% 19.28/3.46 | $i(all_41_1) & member(all_41_0, universal_class)
% 19.28/3.46 |
% 19.28/3.46 | ALPHA: (4) implies:
% 19.28/3.46 | (5) member(all_41_0, universal_class)
% 19.28/3.46 | (6) $i(all_41_1)
% 19.28/3.46 | (7) $i(all_41_0)
% 19.28/3.46 | (8) unordered_pair(all_41_1, all_41_0) = null_class
% 19.28/3.46 |
% 19.28/3.47 | GROUND_INST: instantiating (1) with all_41_0, all_41_1, null_class,
% 19.28/3.47 | simplifying with (5), (6), (7), (8) gives:
% 19.28/3.47 | (9) member(all_41_0, null_class)
% 19.28/3.47 |
% 19.28/3.47 | GROUND_INST: instantiating (2) with all_41_0, simplifying with (7), (9) gives:
% 19.28/3.47 | (10) $false
% 19.28/3.47 |
% 19.28/3.47 | CLOSE: (10) is inconsistent.
% 19.28/3.47 |
% 19.28/3.47 End of proof
% 19.28/3.47 % SZS output end Proof for theBenchmark
% 19.28/3.47
% 19.28/3.47 2868ms
%------------------------------------------------------------------------------