TSTP Solution File: SET086+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET086+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 15:23:41 EDT 2023
% Result : Theorem 13.43s 2.61s
% Output : Proof 17.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET086+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.34 % Computer : n025.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 12:10:22 EDT 2023
% 0.14/0.34 % 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
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.05/1.13 Prover 1: Preprocessing ...
% 3.05/1.13 Prover 4: Preprocessing ...
% 3.60/1.17 Prover 0: Preprocessing ...
% 3.60/1.17 Prover 5: Preprocessing ...
% 3.60/1.17 Prover 2: Preprocessing ...
% 3.60/1.17 Prover 6: Preprocessing ...
% 3.60/1.17 Prover 3: Preprocessing ...
% 9.57/2.19 Prover 1: Warning: ignoring some quantifiers
% 9.57/2.23 Prover 3: Warning: ignoring some quantifiers
% 10.26/2.24 Prover 6: Proving ...
% 10.26/2.24 Prover 5: Proving ...
% 10.26/2.27 Prover 1: Constructing countermodel ...
% 10.26/2.29 Prover 3: Constructing countermodel ...
% 11.83/2.35 Prover 4: Warning: ignoring some quantifiers
% 11.83/2.41 Prover 2: Proving ...
% 12.67/2.48 Prover 4: Constructing countermodel ...
% 13.43/2.58 Prover 0: Proving ...
% 13.43/2.61 Prover 3: proved (1978ms)
% 13.43/2.61
% 13.43/2.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 13.43/2.61
% 13.72/2.63 Prover 5: stopped
% 13.72/2.63 Prover 0: stopped
% 13.72/2.63 Prover 6: stopped
% 13.72/2.63 Prover 2: stopped
% 13.85/2.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 13.85/2.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 13.85/2.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 13.85/2.64 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 13.85/2.65 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.39/2.74 Prover 8: Preprocessing ...
% 14.39/2.75 Prover 7: Preprocessing ...
% 14.39/2.75 Prover 10: Preprocessing ...
% 14.39/2.76 Prover 11: Preprocessing ...
% 14.39/2.76 Prover 13: Preprocessing ...
% 15.79/3.02 Prover 10: Warning: ignoring some quantifiers
% 16.63/3.06 Prover 7: Warning: ignoring some quantifiers
% 16.63/3.07 Prover 1: Found proof (size 12)
% 16.63/3.07 Prover 1: proved (2448ms)
% 16.63/3.07 Prover 4: Found proof (size 19)
% 16.63/3.07 Prover 4: proved (2449ms)
% 16.89/3.09 Prover 10: Constructing countermodel ...
% 16.89/3.09 Prover 13: Warning: ignoring some quantifiers
% 16.89/3.09 Prover 7: Constructing countermodel ...
% 16.89/3.10 Prover 8: Warning: ignoring some quantifiers
% 16.89/3.11 Prover 10: stopped
% 16.89/3.12 Prover 7: stopped
% 16.89/3.13 Prover 11: Warning: ignoring some quantifiers
% 16.89/3.13 Prover 13: Constructing countermodel ...
% 16.89/3.13 Prover 8: Constructing countermodel ...
% 16.89/3.14 Prover 13: stopped
% 17.34/3.14 Prover 11: Constructing countermodel ...
% 17.34/3.14 Prover 8: stopped
% 17.42/3.17 Prover 11: stopped
% 17.42/3.17
% 17.42/3.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.42/3.17
% 17.42/3.17 % SZS output start Proof for theBenchmark
% 17.42/3.18 Assumptions after simplification:
% 17.42/3.18 ---------------------------------
% 17.42/3.18
% 17.42/3.18 (member_of_substitution)
% 17.42/3.21 $i(universal_class) & ? [v0: $i] : ($i(v0) & ! [v1: $i] : ( ~ (member(v1,
% 17.42/3.21 universal_class) = 0) | ~ $i(v1) | ? [v2: $i] : ( ~ (v2 = v0) &
% 17.42/3.21 singleton(v1) = v2 & $i(v2))) & ? [v1: $i] : (singleton(v1) = v0 &
% 17.42/3.21 member(v1, universal_class) = 0 & $i(v1)))
% 17.42/3.21
% 17.42/3.21 (function-axioms)
% 17.69/3.23 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 17.69/3.23 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0)) & ! [v0:
% 17.69/3.23 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2)
% 17.69/3.23 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 17.69/3.23 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3,
% 17.69/3.23 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.69/3.23 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~
% 17.69/3.23 (compose(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 17.69/3.23 $i] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0)) & !
% 17.69/3.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3,
% 17.69/3.23 v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.69/3.23 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~
% 17.69/3.23 (intersection(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 17.69/3.23 [v3: $i] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3,
% 17.69/3.23 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 17.69/3.23 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & !
% 17.69/3.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 17.69/3.23 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 17.69/3.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 17.69/3.23 : (v1 = v0 | ~ (subclass(v3, v2) = v1) | ~ (subclass(v3, v2) = v0)) & !
% 17.69/3.23 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 17.69/3.23 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & !
% 17.69/3.23 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 17.69/3.23 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: $i] : ! [v1:
% 17.69/3.23 $i] : ! [v2: $i] : (v1 = v0 | ~ (power_class(v2) = v1) | ~
% 17.69/3.23 (power_class(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 17.69/3.23 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0)) & ! [v0:
% 17.69/3.23 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 17.69/3.23 ~ (inductive(v2) = v1) | ~ (inductive(v2) = v0)) & ! [v0: $i] : ! [v1:
% 17.69/3.23 $i] : ! [v2: $i] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) =
% 17.69/3.23 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.69/3.23 (inverse(v2) = v1) | ~ (inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.69/3.23 [v2: $i] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0)) & !
% 17.69/3.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (flip(v2) = v1) | ~
% 17.69/3.23 (flip(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 17.69/3.23 (rotate(v2) = v1) | ~ (rotate(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 17.69/3.23 [v2: $i] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0)) & !
% 17.69/3.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (complement(v2) = v1) |
% 17.69/3.23 ~ (complement(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 17.69/3.23 v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 17.69/3.23 : ! [v2: $i] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0)) & !
% 17.69/3.23 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 17.69/3.23 (singleton(v2) = v0))
% 17.69/3.23
% 17.69/3.23 Further assumptions not needed in the proof:
% 17.69/3.23 --------------------------------------------
% 17.69/3.23 apply_defn, choice, class_elements_are_sets, complement, compose_defn1,
% 17.69/3.23 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of,
% 17.69/3.23 element_relation, element_relation_defn, extensionality, first_second, flip,
% 17.69/3.23 flip_defn, function_defn, identity_relation, image_defn, inductive_defn,
% 17.69/3.23 infinity, intersection, inverse_defn, null_class_defn, ordered_pair_defn,
% 17.69/3.23 power_class, power_class_defn, range_of_defn, regularity, replacement,
% 17.69/3.23 restrict_defn, rotate, rotate_defn, singleton_set_defn, subclass_defn,
% 17.69/3.23 successor_defn, successor_relation_defn1, successor_relation_defn2, sum_class,
% 17.69/3.23 sum_class_defn, union_defn, unordered_pair, unordered_pair_defn
% 17.69/3.23
% 17.69/3.23 Those formulas are unsatisfiable:
% 17.69/3.23 ---------------------------------
% 17.69/3.23
% 17.69/3.23 Begin of proof
% 17.69/3.23 |
% 17.69/3.23 | ALPHA: (member_of_substitution) implies:
% 17.69/3.24 | (1) ? [v0: $i] : ($i(v0) & ! [v1: $i] : ( ~ (member(v1, universal_class)
% 17.69/3.24 | = 0) | ~ $i(v1) | ? [v2: $i] : ( ~ (v2 = v0) & singleton(v1) =
% 17.69/3.24 | v2 & $i(v2))) & ? [v1: $i] : (singleton(v1) = v0 & member(v1,
% 17.69/3.24 | universal_class) = 0 & $i(v1)))
% 17.69/3.24 |
% 17.69/3.24 | ALPHA: (function-axioms) implies:
% 17.69/3.24 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2)
% 17.69/3.24 | = v1) | ~ (singleton(v2) = v0))
% 17.69/3.24 |
% 17.69/3.24 | DELTA: instantiating (1) with fresh symbol all_56_0 gives:
% 17.69/3.24 | (3) $i(all_56_0) & ! [v0: $i] : ( ~ (member(v0, universal_class) = 0) | ~
% 17.69/3.24 | $i(v0) | ? [v1: any] : ( ~ (v1 = all_56_0) & singleton(v0) = v1 &
% 17.69/3.24 | $i(v1))) & ? [v0: $i] : (singleton(v0) = all_56_0 & member(v0,
% 17.69/3.24 | universal_class) = 0 & $i(v0))
% 17.69/3.24 |
% 17.69/3.24 | ALPHA: (3) implies:
% 17.69/3.24 | (4) ! [v0: $i] : ( ~ (member(v0, universal_class) = 0) | ~ $i(v0) | ?
% 17.69/3.24 | [v1: any] : ( ~ (v1 = all_56_0) & singleton(v0) = v1 & $i(v1)))
% 17.69/3.24 | (5) ? [v0: $i] : (singleton(v0) = all_56_0 & member(v0, universal_class) =
% 17.69/3.24 | 0 & $i(v0))
% 17.69/3.24 |
% 17.69/3.24 | DELTA: instantiating (5) with fresh symbol all_68_0 gives:
% 17.69/3.24 | (6) singleton(all_68_0) = all_56_0 & member(all_68_0, universal_class) = 0
% 17.69/3.24 | & $i(all_68_0)
% 17.69/3.24 |
% 17.69/3.24 | ALPHA: (6) implies:
% 17.69/3.25 | (7) $i(all_68_0)
% 17.69/3.25 | (8) member(all_68_0, universal_class) = 0
% 17.69/3.25 | (9) singleton(all_68_0) = all_56_0
% 17.69/3.25 |
% 17.69/3.25 | GROUND_INST: instantiating (4) with all_68_0, simplifying with (7), (8) gives:
% 17.69/3.25 | (10) ? [v0: any] : ( ~ (v0 = all_56_0) & singleton(all_68_0) = v0 &
% 17.69/3.25 | $i(v0))
% 17.69/3.25 |
% 17.69/3.25 | DELTA: instantiating (10) with fresh symbol all_90_0 gives:
% 17.69/3.25 | (11) ~ (all_90_0 = all_56_0) & singleton(all_68_0) = all_90_0 &
% 17.69/3.25 | $i(all_90_0)
% 17.69/3.25 |
% 17.69/3.25 | ALPHA: (11) implies:
% 17.69/3.25 | (12) ~ (all_90_0 = all_56_0)
% 17.87/3.25 | (13) singleton(all_68_0) = all_90_0
% 17.87/3.25 |
% 17.87/3.25 | GROUND_INST: instantiating (2) with all_56_0, all_90_0, all_68_0, simplifying
% 17.87/3.25 | with (9), (13) gives:
% 17.87/3.25 | (14) all_90_0 = all_56_0
% 17.87/3.25 |
% 17.87/3.25 | REDUCE: (12), (14) imply:
% 17.87/3.25 | (15) $false
% 17.87/3.25 |
% 17.87/3.25 | CLOSE: (15) is inconsistent.
% 17.87/3.25 |
% 17.87/3.25 End of proof
% 17.87/3.25 % SZS output end Proof for theBenchmark
% 17.87/3.25
% 17.87/3.25 2646ms
%------------------------------------------------------------------------------