TSTP Solution File: SET095+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET095+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 15:23:45 EDT 2023
% Result : Theorem 14.02s 2.63s
% Output : Proof 22.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : SET095+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.13/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.14/0.36 % Computer : n031.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sat Aug 26 12:48:38 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.22/0.62 ________ _____
% 0.22/0.62 ___ __ \_________(_)________________________________
% 0.22/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.22/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.22/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.22/0.62
% 0.22/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.22/0.62 (2023-06-19)
% 0.22/0.62
% 0.22/0.62 (c) Philipp Rümmer, 2009-2023
% 0.22/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.22/0.62 Amanda Stjerna.
% 0.22/0.62 Free software under BSD-3-Clause.
% 0.22/0.62
% 0.22/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.22/0.62
% 0.22/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.22/0.63 Running up to 7 provers in parallel.
% 0.22/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.16/1.16 Prover 1: Preprocessing ...
% 3.64/1.16 Prover 4: Preprocessing ...
% 3.64/1.21 Prover 6: Preprocessing ...
% 3.64/1.21 Prover 0: Preprocessing ...
% 3.64/1.21 Prover 3: Preprocessing ...
% 3.64/1.21 Prover 5: Preprocessing ...
% 3.64/1.21 Prover 2: Preprocessing ...
% 9.50/1.98 Prover 1: Warning: ignoring some quantifiers
% 9.50/2.04 Prover 5: Proving ...
% 9.50/2.05 Prover 4: Warning: ignoring some quantifiers
% 9.50/2.05 Prover 1: Constructing countermodel ...
% 9.50/2.06 Prover 6: Proving ...
% 9.50/2.08 Prover 3: Warning: ignoring some quantifiers
% 9.90/2.13 Prover 3: Constructing countermodel ...
% 9.90/2.14 Prover 4: Constructing countermodel ...
% 10.73/2.20 Prover 2: Proving ...
% 11.77/2.30 Prover 0: Proving ...
% 14.02/2.62 Prover 0: proved (1987ms)
% 14.02/2.63
% 14.02/2.63 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.02/2.63
% 14.02/2.63 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.02/2.63 Prover 3: stopped
% 14.02/2.64 Prover 2: stopped
% 14.02/2.64 Prover 5: stopped
% 14.02/2.64 Prover 6: stopped
% 14.02/2.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.02/2.64 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.02/2.64 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 14.02/2.64 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 14.42/2.70 Prover 8: Preprocessing ...
% 14.42/2.71 Prover 7: Preprocessing ...
% 14.42/2.71 Prover 10: Preprocessing ...
% 14.42/2.75 Prover 11: Preprocessing ...
% 14.42/2.77 Prover 13: Preprocessing ...
% 16.28/2.93 Prover 10: Warning: ignoring some quantifiers
% 16.59/2.96 Prover 10: Constructing countermodel ...
% 16.59/2.99 Prover 7: Warning: ignoring some quantifiers
% 16.59/3.01 Prover 8: Warning: ignoring some quantifiers
% 16.59/3.02 Prover 8: Constructing countermodel ...
% 17.39/3.04 Prover 7: Constructing countermodel ...
% 17.82/3.10 Prover 13: Warning: ignoring some quantifiers
% 17.82/3.12 Prover 13: Constructing countermodel ...
% 18.24/3.18 Prover 11: Warning: ignoring some quantifiers
% 18.24/3.19 Prover 11: Constructing countermodel ...
% 18.88/3.28 Prover 10: gave up
% 18.88/3.30 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 19.58/3.40 Prover 16: Preprocessing ...
% 20.26/3.61 Prover 16: Warning: ignoring some quantifiers
% 21.57/3.62 Prover 16: Constructing countermodel ...
% 22.37/3.73 Prover 4: Found proof (size 41)
% 22.37/3.73 Prover 4: proved (3093ms)
% 22.37/3.73 Prover 1: stopped
% 22.37/3.73 Prover 11: stopped
% 22.37/3.73 Prover 13: stopped
% 22.37/3.73 Prover 8: stopped
% 22.37/3.73 Prover 7: stopped
% 22.37/3.73 Prover 16: stopped
% 22.37/3.74
% 22.37/3.74 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.37/3.74
% 22.37/3.74 % SZS output start Proof for theBenchmark
% 22.37/3.75 Assumptions after simplification:
% 22.37/3.75 ---------------------------------
% 22.37/3.75
% 22.37/3.75 (element_relation_defn)
% 22.37/3.78 $i(element_relation) & $i(universal_class) & ! [v0: $i] : ! [v1: $i] : !
% 22.37/3.78 [v2: $i] : ( ~ (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 22.37/3.78 any] : ? [v4: any] : ? [v5: any] : (member(v2, element_relation) = v5 &
% 22.37/3.78 member(v1, universal_class) = v3 & member(v0, v1) = v4 & ( ~ (v4 = 0) | ~
% 22.37/3.78 (v3 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 22.37/3.78 (ordered_pair(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4:
% 22.37/3.78 any] : ? [v5: any] : (member(v2, element_relation) = v3 & member(v1,
% 22.37/3.78 universal_class) = v4 & member(v0, v1) = v5 & ( ~ (v3 = 0) | (v5 = 0 &
% 22.37/3.78 v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 22.37/3.78 (member(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] :
% 22.37/3.78 ? [v5: any] : (ordered_pair(v0, v1) = v3 & member(v3, element_relation) =
% 22.37/3.78 v4 & member(v1, universal_class) = v5 & $i(v3) & ( ~ (v4 = 0) | (v5 = 0 &
% 22.37/3.78 v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (member(v0, v1) = 0) | ~
% 22.37/3.78 $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 22.37/3.78 (ordered_pair(v0, v1) = v3 & member(v3, element_relation) = v4 & member(v1,
% 22.37/3.78 universal_class) = v2 & $i(v3) & ( ~ (v2 = 0) | v4 = 0)))
% 22.37/3.78
% 22.37/3.78 (property_of_singletons2)
% 22.37/3.78 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 22.37/3.78 singleton(v0) = v2 & subclass(v2, v1) = v3 & member(v0, v1) = 0 & $i(v2) &
% 22.37/3.78 $i(v1) & $i(v0))
% 22.37/3.78
% 22.37/3.78 (singleton_set_defn)
% 22.37/3.78 ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 22.37/3.78 (unordered_pair(v0, v0) = v1 & $i(v1))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 22.37/3.78 (unordered_pair(v0, v0) = v1) | ~ $i(v0) | (singleton(v0) = v1 & $i(v1)))
% 22.37/3.78
% 22.37/3.78 (subclass_defn)
% 22.37/3.79 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 22.37/3.79 (subclass(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 22.37/3.79 ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i]
% 22.37/3.79 : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subclass(v0, v1) = v2) | ~
% 22.37/3.79 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3,
% 22.37/3.79 v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] :
% 22.37/3.79 ! [v2: $i] : ( ~ (subclass(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2)
% 22.37/3.79 | ~ $i(v1) | ~ $i(v0) | member(v2, v1) = 0)
% 22.37/3.79
% 22.37/3.79 (unordered_pair_defn)
% 22.37/3.79 $i(universal_class) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] :
% 22.37/3.79 (v3 = 0 | ~ (unordered_pair(v1, v0) = v2) | ~ (member(v0, v2) = v3) | ~
% 22.37/3.79 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0,
% 22.37/3.79 universal_class) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 22.37/3.79 [v3: int] : (v3 = 0 | ~ (unordered_pair(v0, v1) = v2) | ~ (member(v0, v2) =
% 22.37/3.79 v3) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v0,
% 22.37/3.79 universal_class) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 22.37/3.79 [v3: $i] : (v2 = v0 | v1 = v0 | ~ (unordered_pair(v1, v2) = v3) | ~
% 22.37/3.79 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0)) & ! [v0: $i] : !
% 22.37/3.79 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (unordered_pair(v1, v2) = v3) | ~
% 22.37/3.79 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | member(v0,
% 22.37/3.79 universal_class) = 0)
% 22.37/3.79
% 22.37/3.79 (function-axioms)
% 22.84/3.80 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 22.84/3.80 | ~ (restrict(v4, v3, v2) = v1) | ~ (restrict(v4, v3, v2) = v0)) & ! [v0:
% 22.84/3.80 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (apply(v3, v2)
% 22.84/3.80 = v1) | ~ (apply(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 22.84/3.80 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3,
% 22.84/3.80 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 22.84/3.80 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (compose(v3, v2) = v1) | ~
% 22.84/3.80 (compose(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 22.84/3.80 $i] : (v1 = v0 | ~ (image(v3, v2) = v1) | ~ (image(v3, v2) = v0)) & !
% 22.84/3.80 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3,
% 22.84/3.80 v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 22.84/3.80 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~
% 22.84/3.80 (intersection(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 22.84/3.80 [v3: $i] : (v1 = v0 | ~ (cross_product(v3, v2) = v1) | ~ (cross_product(v3,
% 22.84/3.80 v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1
% 22.84/3.80 = v0 | ~ (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0)) & !
% 22.84/3.80 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.84/3.80 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 22.84/3.80 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 22.84/3.80 : (v1 = v0 | ~ (subclass(v3, v2) = v1) | ~ (subclass(v3, v2) = v0)) & !
% 22.84/3.80 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 22.84/3.80 $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & !
% 22.84/3.80 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0
% 22.84/3.80 | ~ (function(v2) = v1) | ~ (function(v2) = v0)) & ! [v0: $i] : ! [v1:
% 22.84/3.80 $i] : ! [v2: $i] : (v1 = v0 | ~ (power_class(v2) = v1) | ~
% 22.84/3.80 (power_class(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 22.84/3.80 | ~ (sum_class(v2) = v1) | ~ (sum_class(v2) = v0)) & ! [v0:
% 22.84/3.80 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 |
% 22.84/3.80 ~ (inductive(v2) = v1) | ~ (inductive(v2) = v0)) & ! [v0: $i] : ! [v1:
% 22.84/3.80 $i] : ! [v2: $i] : (v1 = v0 | ~ (range_of(v2) = v1) | ~ (range_of(v2) =
% 22.84/3.80 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 22.84/3.80 (inverse(v2) = v1) | ~ (inverse(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 22.84/3.80 [v2: $i] : (v1 = v0 | ~ (successor(v2) = v1) | ~ (successor(v2) = v0)) & !
% 22.84/3.80 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (flip(v2) = v1) | ~
% 22.84/3.80 (flip(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~
% 22.84/3.80 (rotate(v2) = v1) | ~ (rotate(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 22.84/3.80 [v2: $i] : (v1 = v0 | ~ (domain_of(v2) = v1) | ~ (domain_of(v2) = v0)) & !
% 22.84/3.80 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (complement(v2) = v1) |
% 22.84/3.80 ~ (complement(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 22.84/3.80 v0 | ~ (first(v2) = v1) | ~ (first(v2) = v0)) & ! [v0: $i] : ! [v1: $i]
% 22.84/3.80 : ! [v2: $i] : (v1 = v0 | ~ (second(v2) = v1) | ~ (second(v2) = v0)) & !
% 22.84/3.80 [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) | ~
% 22.84/3.80 (singleton(v2) = v0))
% 22.84/3.80
% 22.84/3.80 Further assumptions not needed in the proof:
% 22.84/3.80 --------------------------------------------
% 22.84/3.80 apply_defn, choice, class_elements_are_sets, complement, compose_defn1,
% 22.84/3.80 compose_defn2, cross_product, cross_product_defn, disjoint_defn, domain_of,
% 22.84/3.80 element_relation, extensionality, first_second, flip, flip_defn, function_defn,
% 22.84/3.80 identity_relation, image_defn, inductive_defn, infinity, intersection,
% 22.84/3.80 inverse_defn, null_class_defn, ordered_pair_defn, power_class, power_class_defn,
% 22.84/3.80 range_of_defn, regularity, replacement, restrict_defn, rotate, rotate_defn,
% 22.84/3.80 successor_defn, successor_relation_defn1, successor_relation_defn2, sum_class,
% 22.84/3.80 sum_class_defn, union_defn, unordered_pair
% 22.84/3.80
% 22.84/3.80 Those formulas are unsatisfiable:
% 22.84/3.80 ---------------------------------
% 22.84/3.80
% 22.84/3.80 Begin of proof
% 22.84/3.80 |
% 22.84/3.80 | ALPHA: (subclass_defn) implies:
% 22.84/3.81 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subclass(v0,
% 22.84/3.81 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 22.84/3.81 | ( ~ (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 22.84/3.81 |
% 22.84/3.81 | ALPHA: (unordered_pair_defn) implies:
% 22.84/3.81 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v2 = v0 | v1 =
% 22.84/3.81 | v0 | ~ (unordered_pair(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~
% 22.84/3.81 | $i(v2) | ~ $i(v1) | ~ $i(v0))
% 22.84/3.81 |
% 22.84/3.81 | ALPHA: (singleton_set_defn) implies:
% 22.84/3.81 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (singleton(v0) = v1) | ~ $i(v0) |
% 22.84/3.81 | (unordered_pair(v0, v0) = v1 & $i(v1)))
% 22.84/3.81 |
% 22.84/3.81 | ALPHA: (element_relation_defn) implies:
% 22.84/3.81 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (member(v0, v1) = 0) | ~ $i(v1) | ~
% 22.84/3.81 | $i(v0) | ? [v2: any] : ? [v3: $i] : ? [v4: any] :
% 22.84/3.81 | (ordered_pair(v0, v1) = v3 & member(v3, element_relation) = v4 &
% 22.84/3.81 | member(v1, universal_class) = v2 & $i(v3) & ( ~ (v2 = 0) | v4 =
% 22.84/3.81 | 0)))
% 22.84/3.81 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (member(v0, v1) = v2) |
% 22.84/3.81 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: any] : ? [v5: any] :
% 22.84/3.81 | (ordered_pair(v0, v1) = v3 & member(v3, element_relation) = v4 &
% 22.84/3.81 | member(v1, universal_class) = v5 & $i(v3) & ( ~ (v4 = 0) | (v5 = 0
% 22.84/3.81 | & v2 = 0))))
% 22.84/3.81 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 22.84/3.81 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5:
% 22.84/3.81 | any] : (member(v2, element_relation) = v3 & member(v1,
% 22.84/3.81 | universal_class) = v4 & member(v0, v1) = v5 & ( ~ (v3 = 0) | (v5
% 22.84/3.81 | = 0 & v4 = 0))))
% 22.84/3.81 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ordered_pair(v0, v1) =
% 22.84/3.81 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : ? [v5:
% 22.84/3.81 | any] : (member(v2, element_relation) = v5 & member(v1,
% 22.84/3.81 | universal_class) = v3 & member(v0, v1) = v4 & ( ~ (v4 = 0) | ~
% 22.84/3.81 | (v3 = 0) | v5 = 0)))
% 22.84/3.81 |
% 22.84/3.81 | ALPHA: (function-axioms) implies:
% 22.84/3.82 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 22.84/3.82 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 22.84/3.82 | = v0))
% 22.84/3.82 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.84/3.82 | (ordered_pair(v3, v2) = v1) | ~ (ordered_pair(v3, v2) = v0))
% 22.84/3.82 |
% 22.84/3.82 | DELTA: instantiating (property_of_singletons2) with fresh symbols all_47_0,
% 22.84/3.82 | all_47_1, all_47_2, all_47_3 gives:
% 22.84/3.82 | (10) ~ (all_47_0 = 0) & singleton(all_47_3) = all_47_1 &
% 22.84/3.82 | subclass(all_47_1, all_47_2) = all_47_0 & member(all_47_3, all_47_2) =
% 22.84/3.82 | 0 & $i(all_47_1) & $i(all_47_2) & $i(all_47_3)
% 22.84/3.82 |
% 22.84/3.82 | ALPHA: (10) implies:
% 22.84/3.82 | (11) ~ (all_47_0 = 0)
% 22.84/3.82 | (12) $i(all_47_3)
% 22.84/3.82 | (13) $i(all_47_2)
% 22.84/3.82 | (14) $i(all_47_1)
% 22.84/3.82 | (15) member(all_47_3, all_47_2) = 0
% 22.84/3.82 | (16) subclass(all_47_1, all_47_2) = all_47_0
% 22.84/3.82 | (17) singleton(all_47_3) = all_47_1
% 22.84/3.82 |
% 22.84/3.82 | GROUND_INST: instantiating (4) with all_47_3, all_47_2, simplifying with (12),
% 22.84/3.82 | (13), (15) gives:
% 22.84/3.82 | (18) ? [v0: any] : ? [v1: $i] : ? [v2: any] : (ordered_pair(all_47_3,
% 22.84/3.82 | all_47_2) = v1 & member(v1, element_relation) = v2 &
% 22.84/3.82 | member(all_47_2, universal_class) = v0 & $i(v1) & ( ~ (v0 = 0) | v2
% 22.84/3.82 | = 0))
% 22.84/3.82 |
% 22.84/3.82 | GROUND_INST: instantiating (5) with all_47_3, all_47_2, 0, simplifying with
% 22.84/3.82 | (12), (13), (15) gives:
% 22.84/3.82 | (19) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (ordered_pair(all_47_3,
% 22.84/3.82 | all_47_2) = v0 & member(v0, element_relation) = v1 &
% 22.84/3.82 | member(all_47_2, universal_class) = v2 & $i(v0) & ( ~ (v1 = 0) | v2
% 22.84/3.82 | = 0))
% 22.84/3.82 |
% 22.84/3.82 | GROUND_INST: instantiating (1) with all_47_1, all_47_2, all_47_0, simplifying
% 22.84/3.82 | with (13), (14), (16) gives:
% 22.84/3.82 | (20) all_47_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 22.84/3.82 | all_47_1) = 0 & member(v0, all_47_2) = v1 & $i(v0))
% 22.84/3.82 |
% 22.84/3.82 | GROUND_INST: instantiating (3) with all_47_3, all_47_1, simplifying with (12),
% 22.84/3.82 | (17) gives:
% 22.84/3.82 | (21) unordered_pair(all_47_3, all_47_3) = all_47_1 & $i(all_47_1)
% 22.84/3.82 |
% 22.84/3.82 | ALPHA: (21) implies:
% 22.84/3.82 | (22) unordered_pair(all_47_3, all_47_3) = all_47_1
% 22.84/3.82 |
% 22.84/3.82 | DELTA: instantiating (18) with fresh symbols all_99_0, all_99_1, all_99_2
% 22.84/3.83 | gives:
% 22.84/3.83 | (23) ordered_pair(all_47_3, all_47_2) = all_99_1 & member(all_99_1,
% 22.84/3.83 | element_relation) = all_99_0 & member(all_47_2, universal_class) =
% 22.84/3.83 | all_99_2 & $i(all_99_1) & ( ~ (all_99_2 = 0) | all_99_0 = 0)
% 22.84/3.83 |
% 22.84/3.83 | ALPHA: (23) implies:
% 22.84/3.83 | (24) ordered_pair(all_47_3, all_47_2) = all_99_1
% 22.84/3.83 |
% 22.84/3.83 | DELTA: instantiating (19) with fresh symbols all_103_0, all_103_1, all_103_2
% 22.84/3.83 | gives:
% 22.84/3.83 | (25) ordered_pair(all_47_3, all_47_2) = all_103_2 & member(all_103_2,
% 22.84/3.83 | element_relation) = all_103_1 & member(all_47_2, universal_class) =
% 22.84/3.83 | all_103_0 & $i(all_103_2) & ( ~ (all_103_1 = 0) | all_103_0 = 0)
% 22.84/3.83 |
% 22.84/3.83 | ALPHA: (25) implies:
% 22.84/3.83 | (26) ordered_pair(all_47_3, all_47_2) = all_103_2
% 22.84/3.83 |
% 22.84/3.83 | BETA: splitting (20) gives:
% 22.84/3.83 |
% 22.84/3.83 | Case 1:
% 22.84/3.83 | |
% 22.84/3.83 | | (27) all_47_0 = 0
% 22.84/3.83 | |
% 22.84/3.83 | | REDUCE: (11), (27) imply:
% 22.84/3.83 | | (28) $false
% 22.84/3.83 | |
% 22.84/3.83 | | CLOSE: (28) is inconsistent.
% 22.84/3.83 | |
% 22.84/3.83 | Case 2:
% 22.84/3.83 | |
% 22.84/3.83 | | (29) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_47_1) = 0
% 22.84/3.83 | | & member(v0, all_47_2) = v1 & $i(v0))
% 22.84/3.83 | |
% 22.84/3.83 | | DELTA: instantiating (29) with fresh symbols all_125_0, all_125_1 gives:
% 22.84/3.83 | | (30) ~ (all_125_0 = 0) & member(all_125_1, all_47_1) = 0 &
% 22.84/3.83 | | member(all_125_1, all_47_2) = all_125_0 & $i(all_125_1)
% 22.84/3.83 | |
% 22.84/3.83 | | ALPHA: (30) implies:
% 22.84/3.83 | | (31) ~ (all_125_0 = 0)
% 22.84/3.83 | | (32) $i(all_125_1)
% 22.84/3.83 | | (33) member(all_125_1, all_47_2) = all_125_0
% 22.84/3.83 | | (34) member(all_125_1, all_47_1) = 0
% 22.84/3.83 | |
% 22.84/3.83 | | GROUND_INST: instantiating (9) with all_99_1, all_103_2, all_47_2, all_47_3,
% 22.84/3.83 | | simplifying with (24), (26) gives:
% 22.84/3.83 | | (35) all_103_2 = all_99_1
% 22.84/3.83 | |
% 22.84/3.83 | | GROUND_INST: instantiating (2) with all_125_1, all_47_3, all_47_3, all_47_1,
% 22.84/3.83 | | simplifying with (12), (22), (32), (34) gives:
% 22.84/3.83 | | (36) all_125_1 = all_47_3
% 22.84/3.83 | |
% 22.84/3.83 | | GROUND_INST: instantiating (7) with all_47_3, all_47_2, all_99_1,
% 22.84/3.83 | | simplifying with (12), (13), (24) gives:
% 22.84/3.83 | | (37) ? [v0: any] : ? [v1: any] : ? [v2: any] : (member(all_99_1,
% 22.84/3.83 | | element_relation) = v2 & member(all_47_2, universal_class) = v0
% 22.84/3.83 | | & member(all_47_3, all_47_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) |
% 22.84/3.83 | | v2 = 0))
% 22.84/3.83 | |
% 22.84/3.83 | | GROUND_INST: instantiating (6) with all_47_3, all_47_2, all_99_1,
% 22.84/3.83 | | simplifying with (12), (13), (24) gives:
% 22.84/3.84 | | (38) ? [v0: any] : ? [v1: any] : ? [v2: any] : (member(all_99_1,
% 22.84/3.84 | | element_relation) = v0 & member(all_47_2, universal_class) = v1
% 22.84/3.84 | | & member(all_47_3, all_47_2) = v2 & ( ~ (v0 = 0) | (v2 = 0 & v1 =
% 22.84/3.84 | | 0)))
% 22.84/3.84 | |
% 22.84/3.84 | | DELTA: instantiating (38) with fresh symbols all_209_0, all_209_1, all_209_2
% 22.84/3.84 | | gives:
% 22.84/3.84 | | (39) member(all_99_1, element_relation) = all_209_2 & member(all_47_2,
% 22.84/3.84 | | universal_class) = all_209_1 & member(all_47_3, all_47_2) =
% 22.84/3.84 | | all_209_0 & ( ~ (all_209_2 = 0) | (all_209_0 = 0 & all_209_1 = 0))
% 22.84/3.84 | |
% 22.84/3.84 | | ALPHA: (39) implies:
% 22.84/3.84 | | (40) member(all_47_3, all_47_2) = all_209_0
% 22.84/3.84 | |
% 22.84/3.84 | | DELTA: instantiating (37) with fresh symbols all_211_0, all_211_1, all_211_2
% 22.84/3.84 | | gives:
% 22.84/3.84 | | (41) member(all_99_1, element_relation) = all_211_0 & member(all_47_2,
% 22.84/3.84 | | universal_class) = all_211_2 & member(all_47_3, all_47_2) =
% 22.84/3.84 | | all_211_1 & ( ~ (all_211_1 = 0) | ~ (all_211_2 = 0) | all_211_0 =
% 22.84/3.84 | | 0)
% 22.84/3.84 | |
% 22.84/3.84 | | ALPHA: (41) implies:
% 22.84/3.84 | | (42) member(all_47_3, all_47_2) = all_211_1
% 22.84/3.84 | |
% 22.84/3.84 | | REDUCE: (33), (36) imply:
% 22.84/3.84 | | (43) member(all_47_3, all_47_2) = all_125_0
% 22.84/3.84 | |
% 22.84/3.84 | | GROUND_INST: instantiating (8) with 0, all_211_1, all_47_2, all_47_3,
% 22.84/3.84 | | simplifying with (15), (42) gives:
% 22.84/3.84 | | (44) all_211_1 = 0
% 22.84/3.84 | |
% 22.84/3.84 | | GROUND_INST: instantiating (8) with all_209_0, all_211_1, all_47_2,
% 22.84/3.84 | | all_47_3, simplifying with (40), (42) gives:
% 22.84/3.84 | | (45) all_211_1 = all_209_0
% 22.84/3.84 | |
% 22.84/3.84 | | GROUND_INST: instantiating (8) with all_125_0, all_211_1, all_47_2,
% 22.84/3.84 | | all_47_3, simplifying with (42), (43) gives:
% 22.84/3.84 | | (46) all_211_1 = all_125_0
% 22.84/3.84 | |
% 22.84/3.84 | | COMBINE_EQS: (45), (46) imply:
% 22.84/3.84 | | (47) all_209_0 = all_125_0
% 22.84/3.84 | |
% 22.84/3.84 | | COMBINE_EQS: (44), (45) imply:
% 22.84/3.84 | | (48) all_209_0 = 0
% 22.84/3.84 | |
% 22.84/3.84 | | COMBINE_EQS: (47), (48) imply:
% 22.84/3.84 | | (49) all_125_0 = 0
% 22.84/3.84 | |
% 22.84/3.84 | | REDUCE: (31), (49) imply:
% 22.84/3.84 | | (50) $false
% 22.84/3.84 | |
% 22.84/3.84 | | CLOSE: (50) is inconsistent.
% 22.84/3.84 | |
% 22.84/3.84 | End of split
% 22.84/3.84 |
% 22.84/3.84 End of proof
% 22.84/3.84 % SZS output end Proof for theBenchmark
% 22.84/3.84
% 22.84/3.84 3221ms
%------------------------------------------------------------------------------