TSTP Solution File: SET079+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET079+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 : n023.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 15:23:38 EDT 2023
% Result : Theorem 64.04s 9.01s
% Output : Proof 68.50s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.07 % Problem : SET079+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.01/0.08 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.07/0.27 % Computer : n023.cluster.edu
% 0.07/0.27 % Model : x86_64 x86_64
% 0.07/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27 % Memory : 8042.1875MB
% 0.07/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27 % CPULimit : 300
% 0.07/0.27 % WCLimit : 300
% 0.07/0.27 % DateTime : Sat Aug 26 11:10:26 EDT 2023
% 0.07/0.27 % CPUTime :
% 0.11/0.54 ________ _____
% 0.11/0.54 ___ __ \_________(_)________________________________
% 0.11/0.54 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.11/0.54 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.11/0.54 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.11/0.54
% 0.11/0.54 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.11/0.54 (2023-06-19)
% 0.11/0.54
% 0.11/0.54 (c) Philipp Rümmer, 2009-2023
% 0.11/0.54 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.11/0.54 Amanda Stjerna.
% 0.11/0.54 Free software under BSD-3-Clause.
% 0.11/0.54
% 0.11/0.54 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.11/0.54
% 0.11/0.54 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.11/0.55 Running up to 7 provers in parallel.
% 0.11/0.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.11/0.56 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.11/0.56 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.11/0.56 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.11/0.56 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.11/0.56 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.11/0.56 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.12/1.12 Prover 4: Preprocessing ...
% 3.12/1.12 Prover 1: Preprocessing ...
% 3.12/1.15 Prover 2: Preprocessing ...
% 3.12/1.15 Prover 3: Preprocessing ...
% 3.12/1.15 Prover 5: Preprocessing ...
% 3.12/1.15 Prover 6: Preprocessing ...
% 3.12/1.15 Prover 0: Preprocessing ...
% 9.07/1.93 Prover 1: Warning: ignoring some quantifiers
% 9.07/1.93 Prover 4: Warning: ignoring some quantifiers
% 9.07/1.95 Prover 5: Proving ...
% 9.07/1.96 Prover 3: Warning: ignoring some quantifiers
% 9.07/1.97 Prover 6: Proving ...
% 9.07/1.98 Prover 1: Constructing countermodel ...
% 9.07/1.98 Prover 3: Constructing countermodel ...
% 9.71/2.02 Prover 4: Constructing countermodel ...
% 9.71/2.05 Prover 2: Proving ...
% 10.54/2.11 Prover 0: Proving ...
% 64.04/9.01 Prover 5: proved (8447ms)
% 64.04/9.01
% 64.04/9.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 64.04/9.01
% 64.04/9.01 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 64.04/9.01 Prover 2: stopped
% 64.38/9.02 Prover 6: stopped
% 64.38/9.03 Prover 3: stopped
% 64.38/9.03 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 64.38/9.03 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 64.38/9.03 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 64.55/9.06 Prover 0: stopped
% 64.55/9.07 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 65.27/9.16 Prover 8: Preprocessing ...
% 65.27/9.16 Prover 11: Preprocessing ...
% 65.27/9.17 Prover 7: Preprocessing ...
% 65.71/9.20 Prover 10: Preprocessing ...
% 65.71/9.23 Prover 13: Preprocessing ...
% 66.58/9.31 Prover 7: Warning: ignoring some quantifiers
% 66.58/9.32 Prover 8: Warning: ignoring some quantifiers
% 66.58/9.32 Prover 7: Constructing countermodel ...
% 66.58/9.32 Prover 8: Constructing countermodel ...
% 66.58/9.32 Prover 10: Warning: ignoring some quantifiers
% 66.78/9.34 Prover 10: Constructing countermodel ...
% 66.78/9.38 Prover 11: Warning: ignoring some quantifiers
% 66.78/9.39 Prover 11: Constructing countermodel ...
% 66.78/9.41 Prover 13: Warning: ignoring some quantifiers
% 66.78/9.42 Prover 13: Constructing countermodel ...
% 68.00/9.52 Prover 7: Found proof (size 12)
% 68.00/9.52 Prover 7: proved (510ms)
% 68.00/9.52 Prover 11: stopped
% 68.00/9.52 Prover 13: stopped
% 68.00/9.52 Prover 8: stopped
% 68.00/9.52 Prover 10: stopped
% 68.00/9.53 Prover 4: stopped
% 68.00/9.53 Prover 1: stopped
% 68.00/9.53
% 68.00/9.53 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 68.00/9.53
% 68.00/9.53 % SZS output start Proof for theBenchmark
% 68.00/9.54 Assumptions after simplification:
% 68.00/9.54 ---------------------------------
% 68.00/9.54
% 68.00/9.54 (corollary_to_set_in_its_singleton)
% 68.00/9.56 $i(null_class) & $i(universal_class) & ? [v0: $i] : (singleton(v0) =
% 68.00/9.56 null_class & $i(v0) & member(v0, universal_class))
% 68.00/9.56
% 68.00/9.56 (null_class_defn)
% 68.46/9.56 $i(null_class) & ! [v0: $i] : ( ~ $i(v0) | ~ member(v0, null_class))
% 68.46/9.56
% 68.46/9.56 (singleton_set_defn)
% 68.46/9.57 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 68.46/9.57 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 68.46/9.57 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1)))
% 68.46/9.57
% 68.46/9.57 (unordered_pair_defn)
% 68.46/9.57 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 68.46/9.57 (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 68.46/9.57 | ~ $i(v0) | ~ member(v0, v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 68.46/9.57 ! [v3: $i] : ( ~ (unordered_pair(v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 68.46/9.57 $i(v0) | ~ member(v0, v3) | member(v0, universal_class)) & ! [v0: $i] : !
% 68.46/9.57 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) = v2) | ~ $i(v1) | ~
% 68.46/9.57 $i(v0) | ~ member(v0, universal_class) | member(v0, v2)) & ! [v0: $i] : !
% 68.46/9.57 [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v0, v1) = v2) | ~ $i(v1) | ~
% 68.46/9.57 $i(v0) | ~ member(v0, universal_class) | member(v0, v2))
% 68.46/9.57
% 68.46/9.57 Further assumptions not needed in the proof:
% 68.46/9.57 --------------------------------------------
% 68.50/9.57 apply_defn, choice, class_elements_are_sets, complement, compose_defn1,
% 68.50/9.57 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of,
% 68.50/9.57 element_relation, element_relation_defn, extensionality, first_second, flip,
% 68.50/9.57 flip_defn, function_defn, identity_relation, image_defn, inductive_defn,
% 68.50/9.57 infinity, intersection, inverse_defn, ordered_pair_defn, power_class,
% 68.50/9.57 power_class_defn, range_of_defn, regularity, replacement, restrict_defn, rotate,
% 68.50/9.57 rotate_defn, subclass_defn, successor_defn, successor_relation_defn1,
% 68.50/9.57 successor_relation_defn2, sum_class, sum_class_defn, union_defn, unordered_pair
% 68.50/9.57
% 68.50/9.57 Those formulas are unsatisfiable:
% 68.50/9.57 ---------------------------------
% 68.50/9.57
% 68.50/9.57 Begin of proof
% 68.50/9.57 |
% 68.50/9.57 | ALPHA: (unordered_pair_defn) implies:
% 68.50/9.57 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (unordered_pair(v1, v0) =
% 68.50/9.57 | v2) | ~ $i(v1) | ~ $i(v0) | ~ member(v0, universal_class) |
% 68.50/9.57 | member(v0, v2))
% 68.50/9.57 |
% 68.50/9.57 | ALPHA: (singleton_set_defn) implies:
% 68.50/9.58 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 68.50/9.58 | (unordered_pair(v0, v0) = v1 & $i(v1)))
% 68.50/9.58 |
% 68.50/9.58 | ALPHA: (null_class_defn) implies:
% 68.50/9.58 | (3) ! [v0: $i] : ( ~ $i(v0) | ~ member(v0, null_class))
% 68.50/9.58 |
% 68.50/9.58 | ALPHA: (corollary_to_set_in_its_singleton) implies:
% 68.50/9.58 | (4) ? [v0: $i] : (singleton(v0) = null_class & $i(v0) & member(v0,
% 68.50/9.58 | universal_class))
% 68.50/9.58 |
% 68.50/9.58 | DELTA: instantiating (4) with fresh symbol all_41_0 gives:
% 68.50/9.58 | (5) singleton(all_41_0) = null_class & $i(all_41_0) & member(all_41_0,
% 68.50/9.58 | universal_class)
% 68.50/9.58 |
% 68.50/9.58 | ALPHA: (5) implies:
% 68.50/9.58 | (6) member(all_41_0, universal_class)
% 68.50/9.58 | (7) $i(all_41_0)
% 68.50/9.58 | (8) singleton(all_41_0) = null_class
% 68.50/9.58 |
% 68.50/9.58 | GROUND_INST: instantiating (3) with all_41_0, simplifying with (7) gives:
% 68.50/9.58 | (9) ~ member(all_41_0, null_class)
% 68.50/9.58 |
% 68.50/9.58 | GROUND_INST: instantiating (2) with all_41_0, null_class, simplifying with
% 68.50/9.58 | (7), (8) gives:
% 68.50/9.58 | (10) unordered_pair(all_41_0, all_41_0) = null_class & $i(null_class)
% 68.50/9.58 |
% 68.50/9.58 | ALPHA: (10) implies:
% 68.50/9.58 | (11) unordered_pair(all_41_0, all_41_0) = null_class
% 68.50/9.58 |
% 68.50/9.58 | GROUND_INST: instantiating (1) with all_41_0, all_41_0, null_class,
% 68.50/9.58 | simplifying with (6), (7), (9), (11) gives:
% 68.50/9.58 | (12) $false
% 68.50/9.58 |
% 68.50/9.58 | CLOSE: (12) is inconsistent.
% 68.50/9.58 |
% 68.50/9.58 End of proof
% 68.50/9.58 % SZS output end Proof for theBenchmark
% 68.50/9.58
% 68.50/9.58 9042ms
%------------------------------------------------------------------------------