TSTP Solution File: SEV521+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEV521+1 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n019.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 19:37:04 EDT 2023
% Result : Theorem 9.47s 2.07s
% Output : Proof 12.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEV521+1 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n019.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 03:44:58 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.63 ________ _____
% 0.20/0.63 ___ __ \_________(_)________________________________
% 0.20/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.63
% 0.20/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.63 (2023-06-19)
% 0.20/0.63
% 0.20/0.63 (c) Philipp Rümmer, 2009-2023
% 0.20/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.63 Amanda Stjerna.
% 0.20/0.63 Free software under BSD-3-Clause.
% 0.20/0.63
% 0.20/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.63
% 0.20/0.63 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.57/1.15 Prover 1: Preprocessing ...
% 2.57/1.15 Prover 4: Preprocessing ...
% 3.22/1.17 Prover 0: Preprocessing ...
% 3.22/1.17 Prover 5: Preprocessing ...
% 3.22/1.17 Prover 3: Preprocessing ...
% 3.22/1.17 Prover 6: Preprocessing ...
% 3.22/1.17 Prover 2: Preprocessing ...
% 7.23/1.76 Prover 5: Proving ...
% 7.23/1.76 Prover 2: Proving ...
% 7.82/1.80 Prover 3: Warning: ignoring some quantifiers
% 7.82/1.81 Prover 6: Proving ...
% 7.82/1.81 Prover 1: Warning: ignoring some quantifiers
% 7.82/1.83 Prover 3: Constructing countermodel ...
% 8.42/1.89 Prover 1: Constructing countermodel ...
% 9.17/2.00 Prover 4: Warning: ignoring some quantifiers
% 9.47/2.07 Prover 4: Constructing countermodel ...
% 9.47/2.07 Prover 3: proved (1423ms)
% 9.47/2.07
% 9.47/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 9.47/2.07
% 9.47/2.07 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.47/2.07 Prover 6: stopped
% 9.47/2.08 Prover 2: stopped
% 9.47/2.09 Prover 5: stopped
% 9.47/2.09 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.47/2.09 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.47/2.09 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.22/2.13 Prover 8: Preprocessing ...
% 10.22/2.13 Prover 10: Preprocessing ...
% 10.22/2.13 Prover 0: Proving ...
% 10.22/2.13 Prover 0: stopped
% 10.22/2.14 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.22/2.14 Prover 7: Preprocessing ...
% 10.22/2.19 Prover 11: Preprocessing ...
% 10.82/2.20 Prover 1: Found proof (size 40)
% 10.82/2.20 Prover 1: proved (1558ms)
% 10.82/2.21 Prover 4: stopped
% 10.82/2.21 Prover 13: Preprocessing ...
% 10.82/2.23 Prover 10: Warning: ignoring some quantifiers
% 10.82/2.25 Prover 10: Constructing countermodel ...
% 10.82/2.25 Prover 7: Warning: ignoring some quantifiers
% 10.82/2.28 Prover 10: stopped
% 10.82/2.29 Prover 13: stopped
% 10.82/2.29 Prover 7: Constructing countermodel ...
% 10.82/2.30 Prover 11: stopped
% 10.82/2.31 Prover 7: stopped
% 10.82/2.34 Prover 8: Warning: ignoring some quantifiers
% 10.82/2.35 Prover 8: Constructing countermodel ...
% 10.82/2.36 Prover 8: stopped
% 10.82/2.36
% 10.82/2.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.82/2.36
% 10.82/2.36 % SZS output start Proof for theBenchmark
% 10.82/2.36 Assumptions after simplification:
% 10.82/2.36 ---------------------------------
% 10.82/2.36
% 10.82/2.36 (partition)
% 11.97/2.39 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (partition(v0, v1) =
% 11.97/2.39 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ( ~ (v4 = v3) &
% 11.97/2.39 member(v4, v0) = 0 & member(v3, v0) = 0 & $i(v4) & $i(v3) & ? [v5: $i] :
% 11.97/2.39 (member(v5, v4) = 0 & member(v5, v3) = 0 & $i(v5))) | ? [v3: $i] : ?
% 11.97/2.39 [v4: int] : ( ~ (v4 = 0) & subset(v3, v1) = v4 & member(v3, v0) = 0 &
% 11.97/2.39 $i(v3)) | ? [v3: $i] : (member(v3, v1) = 0 & $i(v3) & ! [v4: $i] : ( ~
% 11.97/2.39 (member(v3, v4) = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) &
% 11.97/2.39 member(v4, v0) = v5)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 11.97/2.39 (partition(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ( ! [v2: $i] : ! [v3: $i]
% 11.97/2.39 : (v3 = v2 | ~ (member(v3, v0) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v3)
% 11.97/2.39 | ~ $i(v2) | ! [v4: $i] : ( ~ (member(v4, v2) = 0) | ~ $i(v4) | ?
% 11.97/2.39 [v5: int] : ( ~ (v5 = 0) & member(v4, v3) = v5))) & ! [v2: $i] : !
% 11.97/2.39 [v3: int] : (v3 = 0 | ~ (subset(v2, v1) = v3) | ~ $i(v2) | ? [v4: int]
% 11.97/2.39 : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v2: $i] : ( ~ (member(v2,
% 11.97/2.39 v1) = 0) | ~ $i(v2) | ? [v3: $i] : (member(v3, v0) = 0 &
% 11.97/2.40 member(v2, v3) = 0 & $i(v3)))))
% 11.97/2.40
% 11.97/2.40 (set_partitions_itself)
% 11.97/2.40 $i(empty_set) & ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & ~
% 11.97/2.40 (v0 = empty_set) & partition(v1, v0) = v2 & singleton(v0) = v1 & $i(v1) &
% 11.97/2.40 $i(v0))
% 11.97/2.40
% 11.97/2.40 (singleton)
% 11.97/2.40 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0) = v1) |
% 11.97/2.40 ~ (member(v0, v1) = v2) | ~ $i(v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 11.97/2.40 $i] : (v1 = v0 | ~ (singleton(v1) = v2) | ~ (member(v0, v2) = 0) | ~
% 11.97/2.40 $i(v1) | ~ $i(v0))
% 11.97/2.40
% 11.97/2.40 (subset)
% 11.97/2.40 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 11.97/2.40 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 11.97/2.40 member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : !
% 11.97/2.40 [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : (
% 11.97/2.40 ~ (member(v2, v0) = 0) | ~ $i(v2) | member(v2, v1) = 0))
% 11.97/2.40
% 11.97/2.40 (function-axioms)
% 11.97/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0
% 11.97/2.41 | ~ (insertIntoMember(v4, v3, v2) = v1) | ~ (insertIntoMember(v4, v3, v2)
% 11.97/2.41 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4:
% 11.97/2.41 $i] : (v1 = v0 | ~ (equivalence_class(v4, v3, v2) = v1) | ~
% 11.97/2.41 (equivalence_class(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.97/2.41 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 11.97/2.41 (apply(v4, v3, v2) = v1) | ~ (apply(v4, v3, v2) = v0)) & ! [v0:
% 11.97/2.41 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.97/2.41 : (v1 = v0 | ~ (pre_order(v3, v2) = v1) | ~ (pre_order(v3, v2) = v0)) & !
% 11.97/2.41 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 11.97/2.41 $i] : (v1 = v0 | ~ (equivalence(v3, v2) = v1) | ~ (equivalence(v3, v2) =
% 11.97/2.41 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 11.97/2.41 $i] : ! [v3: $i] : (v1 = v0 | ~ (partition(v3, v2) = v1) | ~
% 11.97/2.41 (partition(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.97/2.41 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (disjoint(v3,
% 11.97/2.41 v2) = v1) | ~ (disjoint(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 11.97/2.41 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (unordered_pair(v3, v2) = v1) | ~
% 11.97/2.41 (unordered_pair(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 11.97/2.41 ! [v3: $i] : (v1 = v0 | ~ (difference(v3, v2) = v1) | ~ (difference(v3, v2)
% 11.97/2.41 = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0
% 11.97/2.41 | ~ (union(v3, v2) = v1) | ~ (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 11.97/2.41 $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1)
% 11.97/2.41 | ~ (intersection(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.97/2.41 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.97/2.41 (equal_set(v3, v2) = v1) | ~ (equal_set(v3, v2) = v0)) & ! [v0:
% 11.97/2.41 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.97/2.41 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 11.97/2.41 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.97/2.41 : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0:
% 11.97/2.41 $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (unaryUnion(v2) = v1) | ~
% 11.97/2.41 (unaryUnion(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.97/2.41 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (non_overlapping(v2) = v1)
% 11.97/2.41 | ~ (non_overlapping(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 11.97/2.41 (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) = v0)) & ! [v0: $i] : !
% 11.97/2.41 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) = v1) | ~ (sum(v2) = v0)) &
% 11.97/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v2) = v1) |
% 11.97/2.41 ~ (singleton(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0
% 11.97/2.41 | ~ (power_set(v2) = v1) | ~ (power_set(v2) = v0))
% 11.97/2.41
% 11.97/2.41 Further assumptions not needed in the proof:
% 11.97/2.41 --------------------------------------------
% 11.97/2.41 d4_tarski, difference, disjoint, empty_set, equal_set, equivalence,
% 11.97/2.41 equivalence_class, insertIntoMember, intersection, non_overlapping, power_set,
% 11.97/2.41 pre_order, product, sum, union, unordered_pair
% 11.97/2.41
% 11.97/2.41 Those formulas are unsatisfiable:
% 11.97/2.41 ---------------------------------
% 11.97/2.41
% 11.97/2.41 Begin of proof
% 12.09/2.41 |
% 12.09/2.41 | ALPHA: (subset) implies:
% 12.09/2.41 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 12.09/2.41 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 12.09/2.41 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 12.09/2.41 |
% 12.09/2.41 | ALPHA: (singleton) implies:
% 12.09/2.41 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (singleton(v1)
% 12.09/2.41 | = v2) | ~ (member(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0))
% 12.09/2.41 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (singleton(v0)
% 12.09/2.41 | = v1) | ~ (member(v0, v1) = v2) | ~ $i(v0))
% 12.09/2.41 |
% 12.09/2.41 | ALPHA: (partition) implies:
% 12.09/2.41 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (partition(v0,
% 12.09/2.41 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : (
% 12.09/2.41 | ~ (v4 = v3) & member(v4, v0) = 0 & member(v3, v0) = 0 & $i(v4) &
% 12.09/2.41 | $i(v3) & ? [v5: $i] : (member(v5, v4) = 0 & member(v5, v3) = 0 &
% 12.09/2.41 | $i(v5))) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & subset(v3,
% 12.09/2.41 | v1) = v4 & member(v3, v0) = 0 & $i(v3)) | ? [v3: $i] :
% 12.09/2.41 | (member(v3, v1) = 0 & $i(v3) & ! [v4: $i] : ( ~ (member(v3, v4) = 0)
% 12.09/2.41 | | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & member(v4, v0) =
% 12.09/2.41 | v5))))
% 12.09/2.41 |
% 12.09/2.41 | ALPHA: (set_partitions_itself) implies:
% 12.09/2.42 | (5) ? [v0: $i] : ? [v1: $i] : ? [v2: int] : ( ~ (v2 = 0) & ~ (v0 =
% 12.09/2.42 | empty_set) & partition(v1, v0) = v2 & singleton(v0) = v1 & $i(v1) &
% 12.09/2.42 | $i(v0))
% 12.09/2.42 |
% 12.09/2.42 | ALPHA: (function-axioms) implies:
% 12.09/2.42 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.09/2.42 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 12.09/2.42 | = v0))
% 12.09/2.42 |
% 12.09/2.42 | DELTA: instantiating (5) with fresh symbols all_23_0, all_23_1, all_23_2
% 12.09/2.42 | gives:
% 12.09/2.42 | (7) ~ (all_23_0 = 0) & ~ (all_23_2 = empty_set) & partition(all_23_1,
% 12.09/2.42 | all_23_2) = all_23_0 & singleton(all_23_2) = all_23_1 & $i(all_23_1)
% 12.09/2.42 | & $i(all_23_2)
% 12.09/2.42 |
% 12.09/2.42 | ALPHA: (7) implies:
% 12.09/2.42 | (8) ~ (all_23_0 = 0)
% 12.09/2.42 | (9) $i(all_23_2)
% 12.09/2.42 | (10) $i(all_23_1)
% 12.09/2.42 | (11) singleton(all_23_2) = all_23_1
% 12.09/2.42 | (12) partition(all_23_1, all_23_2) = all_23_0
% 12.09/2.42 |
% 12.09/2.42 | GROUND_INST: instantiating (4) with all_23_1, all_23_2, all_23_0, simplifying
% 12.09/2.42 | with (9), (10), (12) gives:
% 12.15/2.42 | (13) all_23_0 = 0 | ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & member(v1,
% 12.15/2.42 | all_23_1) = 0 & member(v0, all_23_1) = 0 & $i(v1) & $i(v0) & ?
% 12.15/2.42 | [v2: $i] : (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2))) | ?
% 12.15/2.42 | [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0, all_23_2) = v1 &
% 12.15/2.42 | member(v0, all_23_1) = 0 & $i(v0)) | ? [v0: $i] : (member(v0,
% 12.15/2.42 | all_23_2) = 0 & $i(v0) & ! [v1: $i] : ( ~ (member(v0, v1) = 0) |
% 12.15/2.42 | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & member(v1, all_23_1) =
% 12.15/2.42 | v2)))
% 12.15/2.42 |
% 12.15/2.42 | BETA: splitting (13) gives:
% 12.15/2.42 |
% 12.15/2.42 | Case 1:
% 12.15/2.42 | |
% 12.15/2.42 | | (14) all_23_0 = 0
% 12.15/2.42 | |
% 12.15/2.42 | | REDUCE: (8), (14) imply:
% 12.15/2.42 | | (15) $false
% 12.15/2.42 | |
% 12.15/2.42 | | CLOSE: (15) is inconsistent.
% 12.15/2.42 | |
% 12.15/2.42 | Case 2:
% 12.15/2.42 | |
% 12.15/2.42 | | (16) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & member(v1, all_23_1) = 0
% 12.15/2.42 | | & member(v0, all_23_1) = 0 & $i(v1) & $i(v0) & ? [v2: $i] :
% 12.15/2.42 | | (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2))) | ? [v0: $i]
% 12.15/2.42 | | : ? [v1: int] : ( ~ (v1 = 0) & subset(v0, all_23_2) = v1 &
% 12.15/2.42 | | member(v0, all_23_1) = 0 & $i(v0)) | ? [v0: $i] : (member(v0,
% 12.15/2.42 | | all_23_2) = 0 & $i(v0) & ! [v1: $i] : ( ~ (member(v0, v1) = 0)
% 12.15/2.42 | | | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & member(v1, all_23_1)
% 12.15/2.42 | | = v2)))
% 12.15/2.42 | |
% 12.15/2.42 | | BETA: splitting (16) gives:
% 12.15/2.42 | |
% 12.15/2.42 | | Case 1:
% 12.15/2.42 | | |
% 12.15/2.43 | | | (17) ? [v0: $i] : ? [v1: $i] : ( ~ (v1 = v0) & member(v1, all_23_1) =
% 12.15/2.43 | | | 0 & member(v0, all_23_1) = 0 & $i(v1) & $i(v0) & ? [v2: $i] :
% 12.15/2.43 | | | (member(v2, v1) = 0 & member(v2, v0) = 0 & $i(v2)))
% 12.15/2.43 | | |
% 12.15/2.43 | | | DELTA: instantiating (17) with fresh symbols all_40_0, all_40_1 gives:
% 12.15/2.43 | | | (18) ~ (all_40_0 = all_40_1) & member(all_40_0, all_23_1) = 0 &
% 12.15/2.43 | | | member(all_40_1, all_23_1) = 0 & $i(all_40_0) & $i(all_40_1) & ?
% 12.15/2.43 | | | [v0: $i] : (member(v0, all_40_0) = 0 & member(v0, all_40_1) = 0 &
% 12.15/2.43 | | | $i(v0))
% 12.15/2.43 | | |
% 12.15/2.43 | | | ALPHA: (18) implies:
% 12.15/2.43 | | | (19) ~ (all_40_0 = all_40_1)
% 12.15/2.43 | | | (20) $i(all_40_1)
% 12.15/2.43 | | | (21) $i(all_40_0)
% 12.15/2.43 | | | (22) member(all_40_1, all_23_1) = 0
% 12.15/2.43 | | | (23) member(all_40_0, all_23_1) = 0
% 12.15/2.43 | | |
% 12.15/2.43 | | | GROUND_INST: instantiating (2) with all_40_1, all_23_2, all_23_1,
% 12.15/2.43 | | | simplifying with (9), (11), (20), (22) gives:
% 12.15/2.43 | | | (24) all_40_1 = all_23_2
% 12.15/2.43 | | |
% 12.15/2.43 | | | GROUND_INST: instantiating (2) with all_40_0, all_23_2, all_23_1,
% 12.15/2.43 | | | simplifying with (9), (11), (21), (23) gives:
% 12.15/2.43 | | | (25) all_40_0 = all_23_2
% 12.15/2.43 | | |
% 12.15/2.43 | | | REDUCE: (19), (24), (25) imply:
% 12.15/2.43 | | | (26) $false
% 12.15/2.43 | | |
% 12.15/2.43 | | | CLOSE: (26) is inconsistent.
% 12.15/2.43 | | |
% 12.15/2.43 | | Case 2:
% 12.15/2.43 | | |
% 12.15/2.43 | | | (27) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0, all_23_2) =
% 12.15/2.43 | | | v1 & member(v0, all_23_1) = 0 & $i(v0)) | ? [v0: $i] :
% 12.15/2.43 | | | (member(v0, all_23_2) = 0 & $i(v0) & ! [v1: $i] : ( ~ (member(v0,
% 12.15/2.43 | | | v1) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) &
% 12.15/2.43 | | | member(v1, all_23_1) = v2)))
% 12.15/2.43 | | |
% 12.15/2.43 | | | BETA: splitting (27) gives:
% 12.15/2.43 | | |
% 12.15/2.43 | | | Case 1:
% 12.15/2.43 | | | |
% 12.15/2.43 | | | | (28) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & subset(v0, all_23_2)
% 12.15/2.43 | | | | = v1 & member(v0, all_23_1) = 0 & $i(v0))
% 12.15/2.43 | | | |
% 12.15/2.43 | | | | DELTA: instantiating (28) with fresh symbols all_40_0, all_40_1 gives:
% 12.15/2.43 | | | | (29) ~ (all_40_0 = 0) & subset(all_40_1, all_23_2) = all_40_0 &
% 12.15/2.43 | | | | member(all_40_1, all_23_1) = 0 & $i(all_40_1)
% 12.15/2.43 | | | |
% 12.15/2.43 | | | | ALPHA: (29) implies:
% 12.15/2.43 | | | | (30) ~ (all_40_0 = 0)
% 12.15/2.43 | | | | (31) $i(all_40_1)
% 12.15/2.43 | | | | (32) member(all_40_1, all_23_1) = 0
% 12.15/2.43 | | | | (33) subset(all_40_1, all_23_2) = all_40_0
% 12.15/2.43 | | | |
% 12.15/2.43 | | | | GROUND_INST: instantiating (2) with all_40_1, all_23_2, all_23_1,
% 12.15/2.43 | | | | simplifying with (9), (11), (31), (32) gives:
% 12.15/2.43 | | | | (34) all_40_1 = all_23_2
% 12.15/2.43 | | | |
% 12.15/2.43 | | | | GROUND_INST: instantiating (1) with all_40_1, all_23_2, all_40_0,
% 12.15/2.43 | | | | simplifying with (9), (31), (33) gives:
% 12.15/2.43 | | | | (35) all_40_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 12.15/2.43 | | | | member(v0, all_40_1) = 0 & member(v0, all_23_2) = v1 & $i(v0))
% 12.15/2.43 | | | |
% 12.15/2.43 | | | | BETA: splitting (35) gives:
% 12.15/2.43 | | | |
% 12.15/2.43 | | | | Case 1:
% 12.15/2.43 | | | | |
% 12.15/2.43 | | | | | (36) all_40_0 = 0
% 12.15/2.43 | | | | |
% 12.15/2.43 | | | | | REDUCE: (30), (36) imply:
% 12.15/2.43 | | | | | (37) $false
% 12.15/2.43 | | | | |
% 12.15/2.43 | | | | | CLOSE: (37) is inconsistent.
% 12.15/2.43 | | | | |
% 12.15/2.43 | | | | Case 2:
% 12.15/2.43 | | | | |
% 12.15/2.44 | | | | | (38) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 12.15/2.44 | | | | | all_40_1) = 0 & member(v0, all_23_2) = v1 & $i(v0))
% 12.15/2.44 | | | | |
% 12.15/2.44 | | | | | DELTA: instantiating (38) with fresh symbols all_52_0, all_52_1 gives:
% 12.15/2.44 | | | | | (39) ~ (all_52_0 = 0) & member(all_52_1, all_40_1) = 0 &
% 12.15/2.44 | | | | | member(all_52_1, all_23_2) = all_52_0 & $i(all_52_1)
% 12.15/2.44 | | | | |
% 12.15/2.44 | | | | | ALPHA: (39) implies:
% 12.15/2.44 | | | | | (40) ~ (all_52_0 = 0)
% 12.15/2.44 | | | | | (41) member(all_52_1, all_23_2) = all_52_0
% 12.15/2.44 | | | | | (42) member(all_52_1, all_40_1) = 0
% 12.15/2.44 | | | | |
% 12.15/2.44 | | | | | REDUCE: (34), (42) imply:
% 12.15/2.44 | | | | | (43) member(all_52_1, all_23_2) = 0
% 12.15/2.44 | | | | |
% 12.15/2.44 | | | | | GROUND_INST: instantiating (6) with 0, all_52_0, all_23_2, all_52_1,
% 12.15/2.44 | | | | | simplifying with (41), (43) gives:
% 12.15/2.44 | | | | | (44) all_52_0 = 0
% 12.15/2.44 | | | | |
% 12.15/2.44 | | | | | REDUCE: (40), (44) imply:
% 12.15/2.44 | | | | | (45) $false
% 12.15/2.44 | | | | |
% 12.15/2.44 | | | | | CLOSE: (45) is inconsistent.
% 12.15/2.44 | | | | |
% 12.15/2.44 | | | | End of split
% 12.15/2.44 | | | |
% 12.15/2.44 | | | Case 2:
% 12.15/2.44 | | | |
% 12.15/2.44 | | | | (46) ? [v0: $i] : (member(v0, all_23_2) = 0 & $i(v0) & ! [v1: $i] :
% 12.15/2.44 | | | | ( ~ (member(v0, v1) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2
% 12.15/2.44 | | | | = 0) & member(v1, all_23_1) = v2)))
% 12.15/2.44 | | | |
% 12.15/2.44 | | | | DELTA: instantiating (46) with fresh symbol all_40_0 gives:
% 12.15/2.44 | | | | (47) member(all_40_0, all_23_2) = 0 & $i(all_40_0) & ! [v0: $i] : (
% 12.15/2.44 | | | | ~ (member(all_40_0, v0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 12.15/2.44 | | | | (v1 = 0) & member(v0, all_23_1) = v1))
% 12.15/2.44 | | | |
% 12.15/2.44 | | | | ALPHA: (47) implies:
% 12.15/2.44 | | | | (48) member(all_40_0, all_23_2) = 0
% 12.15/2.44 | | | | (49) ! [v0: $i] : ( ~ (member(all_40_0, v0) = 0) | ~ $i(v0) | ?
% 12.15/2.44 | | | | [v1: int] : ( ~ (v1 = 0) & member(v0, all_23_1) = v1))
% 12.15/2.44 | | | |
% 12.15/2.44 | | | | GROUND_INST: instantiating (49) with all_23_2, simplifying with (9),
% 12.15/2.44 | | | | (48) gives:
% 12.15/2.44 | | | | (50) ? [v0: int] : ( ~ (v0 = 0) & member(all_23_2, all_23_1) = v0)
% 12.15/2.44 | | | |
% 12.15/2.44 | | | | DELTA: instantiating (50) with fresh symbol all_48_0 gives:
% 12.15/2.44 | | | | (51) ~ (all_48_0 = 0) & member(all_23_2, all_23_1) = all_48_0
% 12.15/2.44 | | | |
% 12.15/2.44 | | | | ALPHA: (51) implies:
% 12.15/2.44 | | | | (52) ~ (all_48_0 = 0)
% 12.15/2.44 | | | | (53) member(all_23_2, all_23_1) = all_48_0
% 12.15/2.44 | | | |
% 12.15/2.44 | | | | GROUND_INST: instantiating (3) with all_23_2, all_23_1, all_48_0,
% 12.15/2.44 | | | | simplifying with (9), (11), (53) gives:
% 12.15/2.44 | | | | (54) all_48_0 = 0
% 12.15/2.44 | | | |
% 12.15/2.44 | | | | REDUCE: (52), (54) imply:
% 12.15/2.44 | | | | (55) $false
% 12.15/2.44 | | | |
% 12.15/2.44 | | | | CLOSE: (55) is inconsistent.
% 12.15/2.44 | | | |
% 12.15/2.44 | | | End of split
% 12.15/2.44 | | |
% 12.15/2.44 | | End of split
% 12.15/2.44 | |
% 12.15/2.44 | End of split
% 12.15/2.44 |
% 12.15/2.44 End of proof
% 12.15/2.44 % SZS output end Proof for theBenchmark
% 12.15/2.44
% 12.15/2.44 1813ms
%------------------------------------------------------------------------------