TSTP Solution File: SET076+1 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET076+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 : n031.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 15:23:37 EDT 2023
% Result : Theorem 19.40s 3.52s
% Output : Proof 64.99s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : SET076+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.09/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n031.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Sat Aug 26 15:54:38 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.18/0.64 ________ _____
% 0.18/0.64 ___ __ \_________(_)________________________________
% 0.18/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.18/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.18/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.18/0.64
% 0.18/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.64 (2023-06-19)
% 0.18/0.64
% 0.18/0.64 (c) Philipp Rümmer, 2009-2023
% 0.18/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.64 Amanda Stjerna.
% 0.18/0.64 Free software under BSD-3-Clause.
% 0.18/0.64
% 0.18/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.64
% 0.18/0.64 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.18/0.66 Running up to 7 provers in parallel.
% 0.18/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.18/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.18/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.18/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.18/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.18/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.18/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.12/1.33 Prover 4: Preprocessing ...
% 3.12/1.34 Prover 1: Preprocessing ...
% 3.92/1.40 Prover 6: Preprocessing ...
% 3.92/1.40 Prover 0: Preprocessing ...
% 3.92/1.40 Prover 3: Preprocessing ...
% 3.92/1.40 Prover 5: Preprocessing ...
% 3.92/1.40 Prover 2: Preprocessing ...
% 11.57/2.45 Prover 1: Warning: ignoring some quantifiers
% 12.21/2.49 Prover 6: Proving ...
% 12.21/2.51 Prover 3: Warning: ignoring some quantifiers
% 12.21/2.52 Prover 5: Proving ...
% 12.21/2.54 Prover 1: Constructing countermodel ...
% 12.21/2.56 Prover 3: Constructing countermodel ...
% 13.09/2.62 Prover 4: Warning: ignoring some quantifiers
% 13.09/2.69 Prover 4: Constructing countermodel ...
% 13.09/2.70 Prover 2: Proving ...
% 13.09/2.83 Prover 0: Proving ...
% 19.40/3.52 Prover 6: proved (2840ms)
% 19.40/3.52
% 19.40/3.52 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.40/3.52
% 19.40/3.53 Prover 5: stopped
% 19.40/3.53 Prover 2: stopped
% 19.40/3.53 Prover 0: stopped
% 19.40/3.54 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 19.40/3.54 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 19.40/3.54 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 19.40/3.54 Prover 3: stopped
% 19.40/3.54 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 19.40/3.55 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 20.43/3.69 Prover 10: Preprocessing ...
% 20.95/3.71 Prover 7: Preprocessing ...
% 20.95/3.72 Prover 8: Preprocessing ...
% 20.95/3.73 Prover 13: Preprocessing ...
% 20.95/3.76 Prover 11: Preprocessing ...
% 22.39/3.98 Prover 10: Warning: ignoring some quantifiers
% 23.24/4.01 Prover 10: Constructing countermodel ...
% 23.24/4.04 Prover 13: Warning: ignoring some quantifiers
% 23.24/4.05 Prover 8: Warning: ignoring some quantifiers
% 23.24/4.08 Prover 7: Warning: ignoring some quantifiers
% 23.24/4.08 Prover 13: Constructing countermodel ...
% 23.24/4.10 Prover 8: Constructing countermodel ...
% 23.98/4.14 Prover 7: Constructing countermodel ...
% 24.64/4.19 Prover 11: Warning: ignoring some quantifiers
% 24.64/4.21 Prover 11: Constructing countermodel ...
% 26.53/4.47 Prover 10: gave up
% 26.53/4.49 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 27.25/4.57 Prover 16: Preprocessing ...
% 29.49/4.86 Prover 16: Warning: ignoring some quantifiers
% 29.49/4.89 Prover 16: Constructing countermodel ...
% 62.95/9.23 Prover 13: stopped
% 62.95/9.24 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 62.95/9.27 Prover 11: Found proof (size 60)
% 62.95/9.27 Prover 11: proved (5726ms)
% 62.95/9.27 Prover 7: stopped
% 62.95/9.27 Prover 16: stopped
% 62.95/9.27 Prover 4: stopped
% 62.95/9.28 Prover 8: stopped
% 62.95/9.28 Prover 1: stopped
% 63.42/9.31 Prover 19: Preprocessing ...
% 63.42/9.48 Prover 19: Warning: ignoring some quantifiers
% 64.20/9.50 Prover 19: Constructing countermodel ...
% 64.20/9.51 Prover 19: stopped
% 64.20/9.51
% 64.20/9.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 64.20/9.51
% 64.20/9.52 % SZS output start Proof for theBenchmark
% 64.20/9.52 Assumptions after simplification:
% 64.20/9.52 ---------------------------------
% 64.20/9.52
% 64.20/9.52 (complement)
% 64.20/9.57 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] :
% 64.20/9.57 (v3 = 0 | ~ (complement(v0) = v2) | ~ (member(v1, v2) = v3) | ~ $i(v1) | ~
% 64.20/9.57 $i(v0) | ? [v4: int] : ? [v5: int] : ((v5 = 0 & member(v1, v0) = 0) | ( ~
% 64.20/9.57 (v4 = 0) & member(v1, universal_class) = v4))) & ! [v0: $i] : ! [v1:
% 64.20/9.57 $i] : ! [v2: int] : (v2 = 0 | ~ (member(v1, v0) = v2) | ~ $i(v1) | ~
% 64.20/9.57 $i(v0) | ? [v3: int] : ? [v4: $i] : ? [v5: int] : ((v5 = 0 &
% 64.20/9.57 complement(v0) = v4 & member(v1, v4) = 0 & $i(v4)) | ( ~ (v3 = 0) &
% 64.20/9.57 member(v1, universal_class) = v3))) & ! [v0: $i] : ! [v1: $i] : !
% 64.20/9.57 [v2: $i] : ( ~ (complement(v0) = v2) | ~ (member(v1, v2) = 0) | ~ $i(v1) |
% 64.20/9.57 ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & member(v1, v0) = v3 & member(v1,
% 64.20/9.57 universal_class) = 0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 64.20/9.57 (member(v1, v0) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 64.20/9.57 ? [v5: int] : ((v5 = 0 & ~ (v2 = 0) & member(v1, universal_class) = 0) | (
% 64.20/9.57 ~ (v4 = 0) & complement(v0) = v3 & member(v1, v3) = v4 & $i(v3))))
% 64.20/9.57
% 64.20/9.57 (element_relation_defn)
% 64.20/9.58 $i(element_relation) & $i(universal_class) & ! [v0: $i] : ! [v1: $i] : !
% 64.20/9.58 [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 64.20/9.58 int] : ? [v4: int] : ? [v5: int] : ((v5 = 0 & v4 = 0 & member(v1,
% 64.20/9.58 universal_class) = 0 & member(v0, v1) = 0) | ( ~ (v3 = 0) & member(v2,
% 64.20/9.58 element_relation) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 64.20/9.58 ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ?
% 64.20/9.58 [v4: int] : ? [v5: int] : ((v5 = 0 & member(v2, element_relation) = 0) | (
% 64.20/9.58 ~ (v4 = 0) & member(v0, v1) = v4) | ( ~ (v3 = 0) & member(v1,
% 64.20/9.58 universal_class) = v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] :
% 64.20/9.58 ( ~ (member(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int]
% 64.20/9.58 : ? [v5: int] : ((v5 = 0 & v2 = 0 & member(v1, universal_class) = 0) | ( ~
% 64.20/9.58 (v4 = 0) & ordered_pair(v0, v1) = v3 & member(v3, element_relation) = v4
% 64.20/9.58 & $i(v3)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (member(v0, v1) = 0) | ~
% 64.20/9.58 $i(v1) | ~ $i(v0) | ? [v2: int] : ? [v3: $i] : ? [v4: int] : ((v4 = 0 &
% 64.20/9.58 ordered_pair(v0, v1) = v3 & member(v3, element_relation) = 0 & $i(v3)) |
% 64.20/9.58 ( ~ (v2 = 0) & member(v1, universal_class) = v2)))
% 64.20/9.58
% 64.20/9.58 (subclass_defn)
% 64.20/9.58 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 64.20/9.58 (subclass(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 64.20/9.58 ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i]
% 64.20/9.58 : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subclass(v0, v1) = v2) | ~
% 64.20/9.58 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3,
% 64.20/9.58 v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] :
% 64.20/9.58 ! [v2: $i] : ( ~ (subclass(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2)
% 64.20/9.58 | ~ $i(v1) | ~ $i(v0) | member(v2, v1) = 0)
% 64.20/9.58
% 64.20/9.58 (unordered_pair_defn)
% 64.79/9.59 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] :
% 64.79/9.59 (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3) | ~
% 64.79/9.59 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0,
% 64.79/9.59 universal_class) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 64.79/9.59 [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) =
% 64.79/9.59 v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0,
% 64.79/9.59 universal_class) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 64.79/9.59 [v3: $i] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~
% 64.79/9.59 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : !
% 64.79/9.59 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (unordered_pair(v1, v2) = v3) | ~
% 64.79/9.59 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | member(v0,
% 64.79/9.59 universal_class) = 0)
% 64.79/9.59
% 64.79/9.59 (unordered_pair_is_subset)
% 64.79/9.59 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: int] : ( ~ (v4
% 64.79/9.59 = 0) & unordered_pair(v0, v1) = v3 & subclass(v3, v2) = v4 & member(v1,
% 64.79/9.59 v2) = 0 & member(v0, v2) = 0 & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 64.79/9.59
% 64.79/9.59 (function-axioms)
% 64.79/9.60 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 64.79/9.60 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0)) & ! [v0:
% 64.79/9.60 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2)
% 64.79/9.61 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 64.79/9.61 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3,
% 64.79/9.61 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 64.79/9.61 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~
% 64.79/9.61 (compose(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 64.79/9.61 $i] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0)) & !
% 64.79/9.61 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3,
% 64.79/9.61 v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 64.79/9.61 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~
% 64.79/9.61 (intersection(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 64.79/9.61 [v3: $i] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3,
% 64.79/9.61 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 64.79/9.61 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & !
% 64.79/9.61 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 64.79/9.61 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 64.79/9.61 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 64.79/9.61 : (v1 = v0 | ~ (subclass(v3, v2) = v1) | ~ (subclass(v3, v2) = v0)) & !
% 64.79/9.61 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 64.79/9.61 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & !
% 64.79/9.61 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 64.79/9.61 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: $i] : ! [v1:
% 64.79/9.61 $i] : ! [v2: $i] : (v1 = v0 | ~ (power_class(v2) = v1) | ~
% 64.79/9.61 (power_class(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 64.79/9.61 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0)) & ! [v0:
% 64.79/9.61 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 64.79/9.61 ~ (inductive(v2) = v1) | ~ (inductive(v2) = v0)) & ! [v0: $i] : ! [v1:
% 64.79/9.61 $i] : ! [v2: $i] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) =
% 64.79/9.61 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 64.79/9.61 (inverse(v2) = v1) | ~ (inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 64.79/9.61 [v2: $i] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0)) & !
% 64.79/9.61 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (flip(v2) = v1) | ~
% 64.79/9.61 (flip(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 64.79/9.61 (rotate(v2) = v1) | ~ (rotate(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 64.79/9.61 [v2: $i] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0)) & !
% 64.79/9.61 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (complement(v2) = v1) |
% 64.79/9.61 ~ (complement(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 64.79/9.61 v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 64.79/9.61 : ! [v2: $i] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0)) & !
% 64.79/9.61 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 64.79/9.61 (singleton(v2) = v0))
% 64.79/9.61
% 64.79/9.61 Further assumptions not needed in the proof:
% 64.79/9.61 --------------------------------------------
% 64.79/9.61 apply_defn, choice, class_elements_are_sets, compose_defn1, compose_defn2,
% 64.79/9.61 cross_product, cross_product_defn, disjoint_defn, domain_of, element_relation,
% 64.79/9.61 extensionality, first_second, flip, flip_defn, function_defn, identity_relation,
% 64.79/9.61 image_defn, inductive_defn, infinity, intersection, inverse_defn,
% 64.79/9.61 null_class_defn, ordered_pair_defn, power_class, power_class_defn,
% 64.79/9.61 range_of_defn, regularity, replacement, restrict_defn, rotate, rotate_defn,
% 64.79/9.61 singleton_set_defn, successor_defn, successor_relation_defn1,
% 64.79/9.61 successor_relation_defn2, sum_class, sum_class_defn, union_defn, unordered_pair
% 64.79/9.61
% 64.79/9.61 Those formulas are unsatisfiable:
% 64.79/9.61 ---------------------------------
% 64.79/9.61
% 64.79/9.61 Begin of proof
% 64.79/9.61 |
% 64.79/9.61 | ALPHA: (subclass_defn) implies:
% 64.79/9.61 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subclass(v0,
% 64.79/9.61 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 64.79/9.61 | ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 64.79/9.61 |
% 64.79/9.61 | ALPHA: (unordered_pair_defn) implies:
% 64.79/9.61 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 64.79/9.61 | (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) |
% 64.79/9.61 | ~ $i(v1) | ~ $i(v0) | member(v0, universal_class) = 0)
% 64.79/9.62 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 =
% 64.79/9.62 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~
% 64.79/9.62 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 64.79/9.62 |
% 64.79/9.62 | ALPHA: (element_relation_defn) implies:
% 64.94/9.62 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (member(v0, v1) = v2) |
% 64.94/9.62 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: int] :
% 64.94/9.62 | ((v5 = 0 & v2 = 0 & member(v1, universal_class) = 0) | ( ~ (v4 = 0) &
% 64.94/9.62 | ordered_pair(v0, v1) = v3 & member(v3, element_relation) = v4 &
% 64.94/9.62 | $i(v3))))
% 64.94/9.62 |
% 64.94/9.62 | ALPHA: (complement) implies:
% 64.94/9.62 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (member(v1, v0) = v2) |
% 64.94/9.62 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ? [v5: int] :
% 64.94/9.62 | ((v5 = 0 & ~ (v2 = 0) & member(v1, universal_class) = 0) | ( ~ (v4 =
% 64.94/9.62 | 0) & complement(v0) = v3 & member(v1, v3) = v4 & $i(v3))))
% 64.94/9.62 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (member(v1, v0)
% 64.94/9.62 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ? [v4: $i] : ?
% 64.94/9.62 | [v5: int] : ((v5 = 0 & complement(v0) = v4 & member(v1, v4) = 0 &
% 64.94/9.62 | $i(v4)) | ( ~ (v3 = 0) & member(v1, universal_class) = v3)))
% 64.94/9.62 |
% 64.94/9.62 | ALPHA: (function-axioms) implies:
% 64.94/9.62 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (complement(v2)
% 64.94/9.62 | = v1) | ~ (complement(v2) = v0))
% 64.94/9.63 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 64.94/9.63 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 64.94/9.63 | = v0))
% 64.94/9.63 |
% 64.94/9.63 | DELTA: instantiating (unordered_pair_is_subset) with fresh symbols all_50_0,
% 64.94/9.63 | all_50_1, all_50_2, all_50_3, all_50_4 gives:
% 64.99/9.63 | (9) ~ (all_50_0 = 0) & unordered_pair(all_50_4, all_50_3) = all_50_1 &
% 64.99/9.63 | subclass(all_50_1, all_50_2) = all_50_0 & member(all_50_3, all_50_2) =
% 64.99/9.63 | 0 & member(all_50_4, all_50_2) = 0 & $i(all_50_1) & $i(all_50_2) &
% 64.99/9.63 | $i(all_50_3) & $i(all_50_4)
% 64.99/9.63 |
% 64.99/9.63 | ALPHA: (9) implies:
% 64.99/9.63 | (10) ~ (all_50_0 = 0)
% 64.99/9.63 | (11) $i(all_50_4)
% 64.99/9.63 | (12) $i(all_50_3)
% 64.99/9.63 | (13) $i(all_50_2)
% 64.99/9.63 | (14) $i(all_50_1)
% 64.99/9.63 | (15) member(all_50_4, all_50_2) = 0
% 64.99/9.63 | (16) member(all_50_3, all_50_2) = 0
% 64.99/9.63 | (17) subclass(all_50_1, all_50_2) = all_50_0
% 64.99/9.63 | (18) unordered_pair(all_50_4, all_50_3) = all_50_1
% 64.99/9.63 |
% 64.99/9.63 | GROUND_INST: instantiating (5) with all_50_2, all_50_4, 0, simplifying with
% 64.99/9.63 | (11), (13), (15) gives:
% 64.99/9.63 | (19) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & complement(all_50_2) = v0
% 64.99/9.63 | & member(all_50_4, v0) = v1 & $i(v0))
% 64.99/9.63 |
% 64.99/9.63 | GROUND_INST: instantiating (5) with all_50_2, all_50_3, 0, simplifying with
% 64.99/9.63 | (12), (13), (16) gives:
% 64.99/9.63 | (20) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & complement(all_50_2) = v0
% 64.99/9.63 | & member(all_50_3, v0) = v1 & $i(v0))
% 64.99/9.63 |
% 64.99/9.63 | GROUND_INST: instantiating (1) with all_50_1, all_50_2, all_50_0, simplifying
% 64.99/9.63 | with (13), (14), (17) gives:
% 64.99/9.64 | (21) all_50_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 64.99/9.64 | all_50_1) = 0 & member(v0, all_50_2) = v1 & $i(v0))
% 64.99/9.64 |
% 64.99/9.64 | DELTA: instantiating (20) with fresh symbols all_87_0, all_87_1 gives:
% 64.99/9.64 | (22) ~ (all_87_0 = 0) & complement(all_50_2) = all_87_1 & member(all_50_3,
% 64.99/9.64 | all_87_1) = all_87_0 & $i(all_87_1)
% 64.99/9.64 |
% 64.99/9.64 | ALPHA: (22) implies:
% 64.99/9.64 | (23) ~ (all_87_0 = 0)
% 64.99/9.64 | (24) member(all_50_3, all_87_1) = all_87_0
% 64.99/9.64 | (25) complement(all_50_2) = all_87_1
% 64.99/9.64 |
% 64.99/9.64 | DELTA: instantiating (19) with fresh symbols all_89_0, all_89_1 gives:
% 64.99/9.64 | (26) ~ (all_89_0 = 0) & complement(all_50_2) = all_89_1 & member(all_50_4,
% 64.99/9.64 | all_89_1) = all_89_0 & $i(all_89_1)
% 64.99/9.64 |
% 64.99/9.64 | ALPHA: (26) implies:
% 64.99/9.64 | (27) ~ (all_89_0 = 0)
% 64.99/9.64 | (28) member(all_50_4, all_89_1) = all_89_0
% 64.99/9.64 | (29) complement(all_50_2) = all_89_1
% 64.99/9.64 |
% 64.99/9.64 | BETA: splitting (21) gives:
% 64.99/9.64 |
% 64.99/9.64 | Case 1:
% 64.99/9.64 | |
% 64.99/9.64 | | (30) all_50_0 = 0
% 64.99/9.64 | |
% 64.99/9.64 | | REDUCE: (10), (30) imply:
% 64.99/9.64 | | (31) $false
% 64.99/9.64 | |
% 64.99/9.64 | | CLOSE: (31) is inconsistent.
% 64.99/9.64 | |
% 64.99/9.64 | Case 2:
% 64.99/9.64 | |
% 64.99/9.64 | | (32) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_50_1) = 0
% 64.99/9.64 | | & member(v0, all_50_2) = v1 & $i(v0))
% 64.99/9.64 | |
% 64.99/9.64 | | DELTA: instantiating (32) with fresh symbols all_117_0, all_117_1 gives:
% 64.99/9.64 | | (33) ~ (all_117_0 = 0) & member(all_117_1, all_50_1) = 0 &
% 64.99/9.64 | | member(all_117_1, all_50_2) = all_117_0 & $i(all_117_1)
% 64.99/9.64 | |
% 64.99/9.64 | | ALPHA: (33) implies:
% 64.99/9.64 | | (34) ~ (all_117_0 = 0)
% 64.99/9.64 | | (35) $i(all_117_1)
% 64.99/9.64 | | (36) member(all_117_1, all_50_2) = all_117_0
% 64.99/9.64 | | (37) member(all_117_1, all_50_1) = 0
% 64.99/9.64 | |
% 64.99/9.64 | | GROUND_INST: instantiating (7) with all_87_1, all_89_1, all_50_2,
% 64.99/9.64 | | simplifying with (25), (29) gives:
% 64.99/9.64 | | (38) all_89_1 = all_87_1
% 64.99/9.64 | |
% 64.99/9.64 | | REDUCE: (28), (38) imply:
% 64.99/9.65 | | (39) member(all_50_4, all_87_1) = all_89_0
% 64.99/9.65 | |
% 64.99/9.65 | | GROUND_INST: instantiating (6) with all_50_2, all_117_1, all_117_0,
% 64.99/9.65 | | simplifying with (13), (35), (36) gives:
% 64.99/9.65 | | (40) all_117_0 = 0 | ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v2 = 0
% 64.99/9.65 | | & complement(all_50_2) = v1 & member(all_117_1, v1) = 0 &
% 64.99/9.65 | | $i(v1)) | ( ~ (v0 = 0) & member(all_117_1, universal_class) =
% 64.99/9.65 | | v0))
% 64.99/9.65 | |
% 64.99/9.65 | | GROUND_INST: instantiating (4) with all_117_1, all_50_2, all_117_0,
% 64.99/9.65 | | simplifying with (13), (35), (36) gives:
% 64.99/9.65 | | (41) ? [v0: $i] : ? [v1: int] : ? [v2: int] : ((v2 = 0 & all_117_0 = 0
% 64.99/9.65 | | & member(all_50_2, universal_class) = 0) | ( ~ (v1 = 0) &
% 64.99/9.65 | | ordered_pair(all_117_1, all_50_2) = v0 & member(v0,
% 64.99/9.65 | | element_relation) = v1 & $i(v0)))
% 64.99/9.65 | |
% 64.99/9.65 | | GROUND_INST: instantiating (3) with all_117_1, all_50_4, all_50_3, all_50_1,
% 64.99/9.65 | | simplifying with (11), (12), (18), (35), (37) gives:
% 64.99/9.65 | | (42) all_117_1 = all_50_3 | all_117_1 = all_50_4
% 64.99/9.65 | |
% 64.99/9.65 | | GROUND_INST: instantiating (2) with all_117_1, all_50_4, all_50_3, all_50_1,
% 64.99/9.65 | | simplifying with (11), (12), (18), (35), (37) gives:
% 64.99/9.65 | | (43) member(all_117_1, universal_class) = 0
% 64.99/9.65 | |
% 64.99/9.65 | | DELTA: instantiating (41) with fresh symbols all_185_0, all_185_1, all_185_2
% 64.99/9.65 | | gives:
% 64.99/9.65 | | (44) (all_185_0 = 0 & all_117_0 = 0 & member(all_50_2, universal_class) =
% 64.99/9.65 | | 0) | ( ~ (all_185_1 = 0) & ordered_pair(all_117_1, all_50_2) =
% 64.99/9.65 | | all_185_2 & member(all_185_2, element_relation) = all_185_1 &
% 64.99/9.65 | | $i(all_185_2))
% 64.99/9.65 | |
% 64.99/9.65 | | BETA: splitting (40) gives:
% 64.99/9.65 | |
% 64.99/9.65 | | Case 1:
% 64.99/9.65 | | |
% 64.99/9.65 | | | (45) all_117_0 = 0
% 64.99/9.65 | | |
% 64.99/9.65 | | | REDUCE: (34), (45) imply:
% 64.99/9.65 | | | (46) $false
% 64.99/9.65 | | |
% 64.99/9.65 | | | CLOSE: (46) is inconsistent.
% 64.99/9.65 | | |
% 64.99/9.65 | | Case 2:
% 64.99/9.65 | | |
% 64.99/9.66 | | | (47) ? [v0: int] : ? [v1: $i] : ? [v2: int] : ((v2 = 0 &
% 64.99/9.66 | | | complement(all_50_2) = v1 & member(all_117_1, v1) = 0 &
% 64.99/9.66 | | | $i(v1)) | ( ~ (v0 = 0) & member(all_117_1, universal_class) =
% 64.99/9.66 | | | v0))
% 64.99/9.66 | | |
% 64.99/9.66 | | | DELTA: instantiating (47) with fresh symbols all_251_0, all_251_1,
% 64.99/9.66 | | | all_251_2 gives:
% 64.99/9.66 | | | (48) (all_251_0 = 0 & complement(all_50_2) = all_251_1 &
% 64.99/9.66 | | | member(all_117_1, all_251_1) = 0 & $i(all_251_1)) | ( ~
% 64.99/9.66 | | | (all_251_2 = 0) & member(all_117_1, universal_class) =
% 64.99/9.66 | | | all_251_2)
% 64.99/9.66 | | |
% 64.99/9.66 | | | BETA: splitting (48) gives:
% 64.99/9.66 | | |
% 64.99/9.66 | | | Case 1:
% 64.99/9.66 | | | |
% 64.99/9.66 | | | | (49) all_251_0 = 0 & complement(all_50_2) = all_251_1 &
% 64.99/9.66 | | | | member(all_117_1, all_251_1) = 0 & $i(all_251_1)
% 64.99/9.66 | | | |
% 64.99/9.66 | | | | ALPHA: (49) implies:
% 64.99/9.66 | | | | (50) member(all_117_1, all_251_1) = 0
% 64.99/9.66 | | | | (51) complement(all_50_2) = all_251_1
% 64.99/9.66 | | | |
% 64.99/9.66 | | | | BETA: splitting (44) gives:
% 64.99/9.66 | | | |
% 64.99/9.66 | | | | Case 1:
% 64.99/9.66 | | | | |
% 64.99/9.66 | | | | | (52) all_185_0 = 0 & all_117_0 = 0 & member(all_50_2,
% 64.99/9.66 | | | | | universal_class) = 0
% 64.99/9.66 | | | | |
% 64.99/9.66 | | | | | ALPHA: (52) implies:
% 64.99/9.66 | | | | | (53) all_117_0 = 0
% 64.99/9.66 | | | | |
% 64.99/9.66 | | | | | REDUCE: (34), (53) imply:
% 64.99/9.66 | | | | | (54) $false
% 64.99/9.66 | | | | |
% 64.99/9.66 | | | | | CLOSE: (54) is inconsistent.
% 64.99/9.66 | | | | |
% 64.99/9.66 | | | | Case 2:
% 64.99/9.66 | | | | |
% 64.99/9.66 | | | | |
% 64.99/9.66 | | | | | GROUND_INST: instantiating (7) with all_87_1, all_251_1, all_50_2,
% 64.99/9.66 | | | | | simplifying with (25), (51) gives:
% 64.99/9.66 | | | | | (55) all_251_1 = all_87_1
% 64.99/9.66 | | | | |
% 64.99/9.66 | | | | | REDUCE: (50), (55) imply:
% 64.99/9.66 | | | | | (56) member(all_117_1, all_87_1) = 0
% 64.99/9.66 | | | | |
% 64.99/9.66 | | | | | BETA: splitting (42) gives:
% 64.99/9.66 | | | | |
% 64.99/9.66 | | | | | Case 1:
% 64.99/9.66 | | | | | |
% 64.99/9.66 | | | | | | (57) all_117_1 = all_50_3
% 64.99/9.66 | | | | | |
% 64.99/9.66 | | | | | | REDUCE: (56), (57) imply:
% 64.99/9.66 | | | | | | (58) member(all_50_3, all_87_1) = 0
% 64.99/9.66 | | | | | |
% 64.99/9.66 | | | | | | GROUND_INST: instantiating (8) with all_87_0, 0, all_87_1, all_50_3,
% 64.99/9.66 | | | | | | simplifying with (24), (58) gives:
% 64.99/9.66 | | | | | | (59) all_87_0 = 0
% 64.99/9.66 | | | | | |
% 64.99/9.66 | | | | | | REDUCE: (23), (59) imply:
% 64.99/9.66 | | | | | | (60) $false
% 64.99/9.66 | | | | | |
% 64.99/9.66 | | | | | | CLOSE: (60) is inconsistent.
% 64.99/9.66 | | | | | |
% 64.99/9.66 | | | | | Case 2:
% 64.99/9.66 | | | | | |
% 64.99/9.66 | | | | | | (61) all_117_1 = all_50_4
% 64.99/9.66 | | | | | |
% 64.99/9.66 | | | | | | REDUCE: (56), (61) imply:
% 64.99/9.66 | | | | | | (62) member(all_50_4, all_87_1) = 0
% 64.99/9.66 | | | | | |
% 64.99/9.66 | | | | | | GROUND_INST: instantiating (8) with all_89_0, 0, all_87_1, all_50_4,
% 64.99/9.66 | | | | | | simplifying with (39), (62) gives:
% 64.99/9.66 | | | | | | (63) all_89_0 = 0
% 64.99/9.66 | | | | | |
% 64.99/9.66 | | | | | | REDUCE: (27), (63) imply:
% 64.99/9.66 | | | | | | (64) $false
% 64.99/9.66 | | | | | |
% 64.99/9.66 | | | | | | CLOSE: (64) is inconsistent.
% 64.99/9.66 | | | | | |
% 64.99/9.66 | | | | | End of split
% 64.99/9.66 | | | | |
% 64.99/9.66 | | | | End of split
% 64.99/9.66 | | | |
% 64.99/9.66 | | | Case 2:
% 64.99/9.66 | | | |
% 64.99/9.66 | | | | (65) ~ (all_251_2 = 0) & member(all_117_1, universal_class) =
% 64.99/9.66 | | | | all_251_2
% 64.99/9.66 | | | |
% 64.99/9.66 | | | | ALPHA: (65) implies:
% 64.99/9.66 | | | | (66) ~ (all_251_2 = 0)
% 64.99/9.66 | | | | (67) member(all_117_1, universal_class) = all_251_2
% 64.99/9.66 | | | |
% 64.99/9.66 | | | | GROUND_INST: instantiating (8) with 0, all_251_2, universal_class,
% 64.99/9.66 | | | | all_117_1, simplifying with (43), (67) gives:
% 64.99/9.66 | | | | (68) all_251_2 = 0
% 64.99/9.66 | | | |
% 64.99/9.66 | | | | REDUCE: (66), (68) imply:
% 64.99/9.66 | | | | (69) $false
% 64.99/9.66 | | | |
% 64.99/9.67 | | | | CLOSE: (69) is inconsistent.
% 64.99/9.67 | | | |
% 64.99/9.67 | | | End of split
% 64.99/9.67 | | |
% 64.99/9.67 | | End of split
% 64.99/9.67 | |
% 64.99/9.67 | End of split
% 64.99/9.67 |
% 64.99/9.67 End of proof
% 64.99/9.67 % SZS output end Proof for theBenchmark
% 64.99/9.67
% 64.99/9.67 9025ms
%------------------------------------------------------------------------------