TSTP Solution File: SET700+4 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET700+4 : TPTP v8.1.2. Released v2.2.0.
% 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 15:26:03 EDT 2023
% Result : Theorem 8.64s 1.90s
% Output : Proof 12.53s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET700+4 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sat Aug 26 10:07:28 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.61 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 1.90/1.01 Prover 4: Preprocessing ...
% 1.90/1.02 Prover 1: Preprocessing ...
% 2.52/1.08 Prover 3: Preprocessing ...
% 2.52/1.08 Prover 2: Preprocessing ...
% 2.52/1.08 Prover 0: Preprocessing ...
% 2.52/1.08 Prover 6: Preprocessing ...
% 2.52/1.08 Prover 5: Preprocessing ...
% 4.59/1.47 Prover 6: Proving ...
% 4.59/1.48 Prover 1: Constructing countermodel ...
% 4.59/1.48 Prover 5: Proving ...
% 4.59/1.50 Prover 3: Constructing countermodel ...
% 4.59/1.50 Prover 2: Proving ...
% 4.59/1.51 Prover 4: Constructing countermodel ...
% 4.59/1.52 Prover 0: Proving ...
% 7.23/1.74 Prover 3: gave up
% 7.23/1.75 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 7.86/1.80 Prover 1: gave up
% 7.86/1.81 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.86/1.81 Prover 7: Preprocessing ...
% 7.86/1.86 Prover 8: Preprocessing ...
% 8.51/1.89 Prover 7: Warning: ignoring some quantifiers
% 8.51/1.89 Prover 7: Constructing countermodel ...
% 8.64/1.90 Prover 0: proved (1288ms)
% 8.64/1.90
% 8.64/1.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.64/1.90
% 8.64/1.90 Prover 5: stopped
% 8.64/1.90 Prover 2: stopped
% 8.64/1.91 Prover 6: stopped
% 8.64/1.91 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.64/1.91 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 8.64/1.91 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 8.64/1.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.76/1.94 Prover 11: Preprocessing ...
% 8.76/1.94 Prover 16: Preprocessing ...
% 8.76/1.94 Prover 10: Preprocessing ...
% 8.76/1.96 Prover 13: Preprocessing ...
% 8.76/1.99 Prover 7: gave up
% 9.34/2.00 Prover 8: Warning: ignoring some quantifiers
% 9.34/2.00 Prover 8: Constructing countermodel ...
% 9.34/2.01 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 9.34/2.02 Prover 16: Warning: ignoring some quantifiers
% 9.34/2.03 Prover 16: Constructing countermodel ...
% 9.34/2.03 Prover 10: Warning: ignoring some quantifiers
% 9.34/2.04 Prover 19: Preprocessing ...
% 9.34/2.04 Prover 10: Constructing countermodel ...
% 9.97/2.09 Prover 8: gave up
% 9.97/2.09 Prover 11: Constructing countermodel ...
% 9.97/2.10 Prover 10: gave up
% 9.97/2.11 Prover 13: Warning: ignoring some quantifiers
% 9.97/2.12 Prover 13: Constructing countermodel ...
% 9.97/2.16 Prover 19: Warning: ignoring some quantifiers
% 9.97/2.17 Prover 19: Constructing countermodel ...
% 11.72/2.34 Prover 4: Found proof (size 140)
% 11.72/2.34 Prover 4: proved (1726ms)
% 11.72/2.34 Prover 16: stopped
% 11.72/2.34 Prover 19: stopped
% 11.72/2.34 Prover 13: stopped
% 11.88/2.34 Prover 11: stopped
% 11.88/2.34
% 11.88/2.34 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.88/2.34
% 11.88/2.37 % SZS output start Proof for theBenchmark
% 11.88/2.37 Assumptions after simplification:
% 11.88/2.37 ---------------------------------
% 11.88/2.37
% 11.88/2.37 (difference)
% 11.88/2.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 11.88/2.40 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~
% 11.88/2.40 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v5 &
% 11.88/2.40 member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 = 0))) & ! [v0: $i] : ! [v1: $i]
% 11.88/2.40 : ! [v2: $i] : ! [v3: $i] : ( ~ (difference(v2, v1) = v3) | ~ (member(v0,
% 11.88/2.40 v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 =
% 11.88/2.40 0) & member(v0, v2) = 0 & member(v0, v1) = v4))
% 11.88/2.40
% 11.88/2.40 (equal_set)
% 11.88/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (equal_set(v0, v1) =
% 11.88/2.41 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (subset(v1,
% 11.88/2.41 v0) = v4 & subset(v0, v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0:
% 11.88/2.41 $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) | ~ $i(v1) |
% 11.88/2.41 ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 &
% 11.88/2.41 subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] :
% 11.88/2.41 ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0)
% 11.88/2.41 | ? [v3: any] : ? [v4: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) =
% 11.88/2.41 v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 = 0)))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 11.88/2.41 (equal_set(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | (subset(v1, v0) = 0 &
% 11.88/2.41 subset(v0, v1) = 0)) & ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v1, v0) =
% 11.88/2.41 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0,
% 11.88/2.41 v1) = v3 & subset(v0, v1) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0: $i]
% 11.88/2.41 : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2:
% 11.88/2.41 any] : ? [v3: any] : (equal_set(v0, v1) = v3 & subset(v1, v0) = v2 & ( ~
% 11.88/2.41 (v2 = 0) | v3 = 0)))
% 11.88/2.41
% 11.88/2.41 (intersection)
% 11.88/2.41 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 11.88/2.41 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) | ~ $i(v2) | ~
% 11.88/2.41 $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (member(v0, v2) = v6 &
% 11.88/2.41 member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 11.88/2.41 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (intersection(v1, v2) = v3) | ~
% 11.88/2.41 (member(v0, v3) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) =
% 11.88/2.41 0 & member(v0, v1) = 0))
% 11.88/2.41
% 11.88/2.41 (subset)
% 11.88/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 11.88/2.42 (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~
% 11.88/2.42 $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) = v4)) & ! [v0: $i] :
% 11.88/2.42 ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2) | ~ $i(v1) |
% 11.88/2.42 ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & member(v3, v1) = v4 &
% 11.88/2.42 member(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 11.88/2.42 ( ~ (subset(v0, v1) = 0) | ~ (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) |
% 11.88/2.42 ~ $i(v0) | member(v2, v1) = 0)
% 11.88/2.42
% 11.88/2.42 (thI34)
% 12.25/2.42 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: $i] : ? [v5:
% 12.25/2.42 $i] : ? [v6: any] : (difference(v2, v1) = v4 & intersection(v0, v4) = v5 &
% 12.25/2.42 subset(v5, v1) = v6 & subset(v1, v2) = 0 & subset(v0, v2) = 0 & subset(v0,
% 12.25/2.42 v1) = v3 & $i(v5) & $i(v4) & $i(v2) & $i(v1) & $i(v0) & ((v6 = 0 & ~ (v3
% 12.25/2.42 = 0)) | (v3 = 0 & ~ (v6 = 0))))
% 12.25/2.42
% 12.25/2.42 (function-axioms)
% 12.25/2.42 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.25/2.42 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 12.25/2.42 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.25/2.42 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 12.25/2.42 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 12.25/2.42 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 12.25/2.42 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 12.25/2.42 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 12.25/2.42 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 12.25/2.42 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 12.25/2.42 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 12.25/2.42 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 12.25/2.42 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.25/2.42 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 12.25/2.42 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 12.25/2.42 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 12.25/2.42 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 12.25/2.42 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 12.25/2.42 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 12.25/2.42 (power_set(v2) = v0))
% 12.25/2.42
% 12.25/2.42 Further assumptions not needed in the proof:
% 12.25/2.42 --------------------------------------------
% 12.25/2.43 empty_set, power_set, product, singleton, sum, union, unordered_pair
% 12.25/2.43
% 12.25/2.43 Those formulas are unsatisfiable:
% 12.25/2.43 ---------------------------------
% 12.25/2.43
% 12.25/2.43 Begin of proof
% 12.25/2.43 |
% 12.25/2.43 | ALPHA: (subset) implies:
% 12.25/2.43 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (subset(v0, v1) = 0) | ~
% 12.25/2.43 | (member(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | member(v2,
% 12.25/2.43 | v1) = 0)
% 12.25/2.43 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1)
% 12.25/2.43 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~
% 12.25/2.43 | (v4 = 0) & member(v3, v1) = v4 & member(v3, v0) = 0 & $i(v3)))
% 12.25/2.43 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 12.25/2.43 | (subset(v0, v1) = 0) | ~ (member(v2, v1) = v3) | ~ $i(v2) | ~
% 12.25/2.43 | $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v0) =
% 12.25/2.43 | v4))
% 12.25/2.43 |
% 12.25/2.43 | ALPHA: (equal_set) implies:
% 12.25/2.43 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 12.25/2.43 | $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0, v1) = v3 &
% 12.25/2.43 | subset(v1, v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 12.25/2.43 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v1, v0) = 0) | ~ $i(v1) | ~
% 12.25/2.43 | $i(v0) | ? [v2: any] : ? [v3: any] : (equal_set(v0, v1) = v3 &
% 12.25/2.43 | subset(v0, v1) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 12.25/2.43 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v0, v1) = v2) |
% 12.25/2.43 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0,
% 12.25/2.43 | v1) = v3 & subset(v1, v0) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 =
% 12.25/2.43 | 0))))
% 12.25/2.43 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~ (subset(v1, v0) = v2) |
% 12.25/2.43 | ~ $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (equal_set(v0,
% 12.25/2.43 | v1) = v3 & subset(v0, v1) = v4 & ( ~ (v3 = 0) | (v4 = 0 & v2 =
% 12.25/2.43 | 0))))
% 12.25/2.43 |
% 12.25/2.43 | ALPHA: (intersection) implies:
% 12.25/2.44 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 12.25/2.44 | (intersection(v1, v2) = v3) | ~ (member(v0, v3) = 0) | ~ $i(v2) |
% 12.25/2.44 | ~ $i(v1) | ~ $i(v0) | (member(v0, v2) = 0 & member(v0, v1) = 0))
% 12.25/2.44 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 12.25/2.44 | (v4 = 0 | ~ (intersection(v1, v2) = v3) | ~ (member(v0, v3) = v4) |
% 12.25/2.44 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 12.25/2.44 | (member(v0, v2) = v6 & member(v0, v1) = v5 & ( ~ (v6 = 0) | ~ (v5 =
% 12.25/2.44 | 0))))
% 12.25/2.44 |
% 12.25/2.44 | ALPHA: (difference) implies:
% 12.25/2.44 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 12.25/2.44 | (v4 = 0 | ~ (difference(v2, v1) = v3) | ~ (member(v0, v3) = v4) | ~
% 12.25/2.44 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 12.25/2.44 | (member(v0, v2) = v5 & member(v0, v1) = v6 & ( ~ (v5 = 0) | v6 =
% 12.25/2.44 | 0)))
% 12.25/2.44 |
% 12.25/2.44 | ALPHA: (function-axioms) implies:
% 12.25/2.44 | (11) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 12.25/2.44 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3,
% 12.25/2.44 | v2) = v0))
% 12.25/2.44 | (12) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 12.25/2.44 | : ! [v3: $i] : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3,
% 12.25/2.44 | v2) = v0))
% 12.25/2.44 |
% 12.25/2.44 | DELTA: instantiating (thI34) with fresh symbols all_15_0, all_15_1, all_15_2,
% 12.25/2.44 | all_15_3, all_15_4, all_15_5, all_15_6 gives:
% 12.25/2.44 | (13) difference(all_15_4, all_15_5) = all_15_2 & intersection(all_15_6,
% 12.25/2.44 | all_15_2) = all_15_1 & subset(all_15_1, all_15_5) = all_15_0 &
% 12.25/2.44 | subset(all_15_5, all_15_4) = 0 & subset(all_15_6, all_15_4) = 0 &
% 12.25/2.44 | subset(all_15_6, all_15_5) = all_15_3 & $i(all_15_1) & $i(all_15_2) &
% 12.25/2.44 | $i(all_15_4) & $i(all_15_5) & $i(all_15_6) & ((all_15_0 = 0 & ~
% 12.25/2.44 | (all_15_3 = 0)) | (all_15_3 = 0 & ~ (all_15_0 = 0)))
% 12.25/2.44 |
% 12.25/2.44 | ALPHA: (13) implies:
% 12.25/2.44 | (14) $i(all_15_6)
% 12.25/2.44 | (15) $i(all_15_5)
% 12.25/2.44 | (16) $i(all_15_4)
% 12.25/2.44 | (17) $i(all_15_2)
% 12.25/2.44 | (18) $i(all_15_1)
% 12.25/2.44 | (19) subset(all_15_6, all_15_5) = all_15_3
% 12.25/2.44 | (20) subset(all_15_6, all_15_4) = 0
% 12.25/2.44 | (21) subset(all_15_1, all_15_5) = all_15_0
% 12.25/2.44 | (22) intersection(all_15_6, all_15_2) = all_15_1
% 12.25/2.44 | (23) difference(all_15_4, all_15_5) = all_15_2
% 12.25/2.44 | (24) (all_15_0 = 0 & ~ (all_15_3 = 0)) | (all_15_3 = 0 & ~ (all_15_0 =
% 12.25/2.44 | 0))
% 12.25/2.44 |
% 12.25/2.44 | GROUND_INST: instantiating (2) with all_15_6, all_15_5, all_15_3, simplifying
% 12.25/2.45 | with (14), (15), (19) gives:
% 12.25/2.45 | (25) all_15_3 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 12.25/2.45 | all_15_5) = v1 & member(v0, all_15_6) = 0 & $i(v0))
% 12.25/2.45 |
% 12.25/2.45 | GROUND_INST: instantiating (7) with all_15_5, all_15_6, all_15_3, simplifying
% 12.25/2.45 | with (14), (15), (19) gives:
% 12.25/2.45 | (26) ? [v0: any] : ? [v1: any] : (equal_set(all_15_5, all_15_6) = v0 &
% 12.25/2.45 | subset(all_15_5, all_15_6) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_3
% 12.25/2.45 | = 0)))
% 12.25/2.45 |
% 12.25/2.45 | GROUND_INST: instantiating (6) with all_15_6, all_15_5, all_15_3, simplifying
% 12.25/2.45 | with (14), (15), (19) gives:
% 12.25/2.45 | (27) ? [v0: any] : ? [v1: any] : (equal_set(all_15_6, all_15_5) = v0 &
% 12.25/2.45 | subset(all_15_5, all_15_6) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_3
% 12.25/2.45 | = 0)))
% 12.25/2.45 |
% 12.25/2.45 | GROUND_INST: instantiating (5) with all_15_4, all_15_6, simplifying with (14),
% 12.25/2.45 | (16), (20) gives:
% 12.25/2.45 | (28) ? [v0: any] : ? [v1: any] : (equal_set(all_15_4, all_15_6) = v1 &
% 12.25/2.45 | subset(all_15_4, all_15_6) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 12.25/2.45 |
% 12.25/2.45 | GROUND_INST: instantiating (4) with all_15_6, all_15_4, simplifying with (14),
% 12.25/2.45 | (16), (20) gives:
% 12.25/2.45 | (29) ? [v0: any] : ? [v1: any] : (equal_set(all_15_6, all_15_4) = v1 &
% 12.25/2.45 | subset(all_15_4, all_15_6) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 12.25/2.45 |
% 12.25/2.45 | GROUND_INST: instantiating (7) with all_15_4, all_15_6, 0, simplifying with
% 12.25/2.45 | (14), (16), (20) gives:
% 12.25/2.45 | (30) ? [v0: any] : ? [v1: any] : (equal_set(all_15_4, all_15_6) = v0 &
% 12.25/2.45 | subset(all_15_4, all_15_6) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 12.25/2.45 |
% 12.25/2.45 | GROUND_INST: instantiating (6) with all_15_6, all_15_4, 0, simplifying with
% 12.25/2.45 | (14), (16), (20) gives:
% 12.25/2.45 | (31) ? [v0: any] : ? [v1: any] : (equal_set(all_15_6, all_15_4) = v0 &
% 12.25/2.45 | subset(all_15_4, all_15_6) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 12.25/2.45 |
% 12.25/2.45 | GROUND_INST: instantiating (2) with all_15_1, all_15_5, all_15_0, simplifying
% 12.25/2.45 | with (15), (18), (21) gives:
% 12.25/2.45 | (32) all_15_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0,
% 12.25/2.45 | all_15_1) = 0 & member(v0, all_15_5) = v1 & $i(v0))
% 12.25/2.45 |
% 12.25/2.45 | GROUND_INST: instantiating (7) with all_15_5, all_15_1, all_15_0, simplifying
% 12.25/2.45 | with (15), (18), (21) gives:
% 12.25/2.45 | (33) ? [v0: any] : ? [v1: any] : (equal_set(all_15_5, all_15_1) = v0 &
% 12.25/2.45 | subset(all_15_5, all_15_1) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_0
% 12.25/2.45 | = 0)))
% 12.25/2.45 |
% 12.25/2.45 | GROUND_INST: instantiating (6) with all_15_1, all_15_5, all_15_0, simplifying
% 12.25/2.45 | with (15), (18), (21) gives:
% 12.25/2.45 | (34) ? [v0: any] : ? [v1: any] : (equal_set(all_15_1, all_15_5) = v0 &
% 12.25/2.45 | subset(all_15_5, all_15_1) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_15_0
% 12.25/2.45 | = 0)))
% 12.25/2.45 |
% 12.25/2.45 | DELTA: instantiating (31) with fresh symbols all_34_0, all_34_1 gives:
% 12.25/2.46 | (35) equal_set(all_15_6, all_15_4) = all_34_1 & subset(all_15_4, all_15_6)
% 12.25/2.46 | = all_34_0 & ( ~ (all_34_1 = 0) | all_34_0 = 0)
% 12.25/2.46 |
% 12.25/2.46 | ALPHA: (35) implies:
% 12.25/2.46 | (36) subset(all_15_4, all_15_6) = all_34_0
% 12.25/2.46 |
% 12.25/2.46 | DELTA: instantiating (29) with fresh symbols all_36_0, all_36_1 gives:
% 12.25/2.46 | (37) equal_set(all_15_6, all_15_4) = all_36_0 & subset(all_15_4, all_15_6)
% 12.25/2.46 | = all_36_1 & ( ~ (all_36_1 = 0) | all_36_0 = 0)
% 12.25/2.46 |
% 12.25/2.46 | ALPHA: (37) implies:
% 12.25/2.46 | (38) subset(all_15_4, all_15_6) = all_36_1
% 12.25/2.46 |
% 12.25/2.46 | DELTA: instantiating (28) with fresh symbols all_38_0, all_38_1 gives:
% 12.25/2.46 | (39) equal_set(all_15_4, all_15_6) = all_38_0 & subset(all_15_4, all_15_6)
% 12.25/2.46 | = all_38_1 & ( ~ (all_38_1 = 0) | all_38_0 = 0)
% 12.25/2.46 |
% 12.25/2.46 | ALPHA: (39) implies:
% 12.25/2.46 | (40) subset(all_15_4, all_15_6) = all_38_1
% 12.25/2.46 |
% 12.25/2.46 | DELTA: instantiating (30) with fresh symbols all_40_0, all_40_1 gives:
% 12.25/2.46 | (41) equal_set(all_15_4, all_15_6) = all_40_1 & subset(all_15_4, all_15_6)
% 12.25/2.46 | = all_40_0 & ( ~ (all_40_1 = 0) | all_40_0 = 0)
% 12.25/2.46 |
% 12.25/2.46 | ALPHA: (41) implies:
% 12.25/2.46 | (42) subset(all_15_4, all_15_6) = all_40_0
% 12.25/2.46 |
% 12.25/2.46 | DELTA: instantiating (26) with fresh symbols all_42_0, all_42_1 gives:
% 12.25/2.46 | (43) equal_set(all_15_5, all_15_6) = all_42_1 & subset(all_15_5, all_15_6)
% 12.25/2.46 | = all_42_0 & ( ~ (all_42_1 = 0) | (all_42_0 = 0 & all_15_3 = 0))
% 12.25/2.46 |
% 12.25/2.46 | ALPHA: (43) implies:
% 12.25/2.46 | (44) subset(all_15_5, all_15_6) = all_42_0
% 12.25/2.46 |
% 12.25/2.46 | DELTA: instantiating (27) with fresh symbols all_44_0, all_44_1 gives:
% 12.25/2.46 | (45) equal_set(all_15_6, all_15_5) = all_44_1 & subset(all_15_5, all_15_6)
% 12.25/2.46 | = all_44_0 & ( ~ (all_44_1 = 0) | (all_44_0 = 0 & all_15_3 = 0))
% 12.25/2.46 |
% 12.25/2.46 | ALPHA: (45) implies:
% 12.25/2.46 | (46) subset(all_15_5, all_15_6) = all_44_0
% 12.25/2.46 |
% 12.25/2.46 | DELTA: instantiating (34) with fresh symbols all_46_0, all_46_1 gives:
% 12.25/2.46 | (47) equal_set(all_15_1, all_15_5) = all_46_1 & subset(all_15_5, all_15_1)
% 12.25/2.46 | = all_46_0 & ( ~ (all_46_1 = 0) | (all_46_0 = 0 & all_15_0 = 0))
% 12.25/2.46 |
% 12.25/2.46 | ALPHA: (47) implies:
% 12.25/2.46 | (48) subset(all_15_5, all_15_1) = all_46_0
% 12.25/2.46 |
% 12.25/2.46 | DELTA: instantiating (33) with fresh symbols all_48_0, all_48_1 gives:
% 12.25/2.46 | (49) equal_set(all_15_5, all_15_1) = all_48_1 & subset(all_15_5, all_15_1)
% 12.25/2.46 | = all_48_0 & ( ~ (all_48_1 = 0) | (all_48_0 = 0 & all_15_0 = 0))
% 12.25/2.46 |
% 12.25/2.46 | ALPHA: (49) implies:
% 12.25/2.46 | (50) subset(all_15_5, all_15_1) = all_48_0
% 12.25/2.46 |
% 12.25/2.46 | GROUND_INST: instantiating (12) with all_42_0, all_44_0, all_15_6, all_15_5,
% 12.25/2.46 | simplifying with (44), (46) gives:
% 12.25/2.46 | (51) all_44_0 = all_42_0
% 12.25/2.46 |
% 12.25/2.46 | GROUND_INST: instantiating (12) with all_46_0, all_48_0, all_15_1, all_15_5,
% 12.25/2.46 | simplifying with (48), (50) gives:
% 12.25/2.46 | (52) all_48_0 = all_46_0
% 12.25/2.46 |
% 12.25/2.46 | GROUND_INST: instantiating (12) with all_36_1, all_38_1, all_15_6, all_15_4,
% 12.25/2.46 | simplifying with (38), (40) gives:
% 12.25/2.46 | (53) all_38_1 = all_36_1
% 12.25/2.46 |
% 12.25/2.46 | GROUND_INST: instantiating (12) with all_38_1, all_40_0, all_15_6, all_15_4,
% 12.25/2.46 | simplifying with (40), (42) gives:
% 12.25/2.46 | (54) all_40_0 = all_38_1
% 12.25/2.46 |
% 12.25/2.46 | GROUND_INST: instantiating (12) with all_34_0, all_40_0, all_15_6, all_15_4,
% 12.25/2.46 | simplifying with (36), (42) gives:
% 12.25/2.46 | (55) all_40_0 = all_34_0
% 12.25/2.46 |
% 12.25/2.46 | COMBINE_EQS: (54), (55) imply:
% 12.25/2.46 | (56) all_38_1 = all_34_0
% 12.25/2.46 |
% 12.25/2.46 | SIMP: (56) implies:
% 12.25/2.46 | (57) all_38_1 = all_34_0
% 12.25/2.46 |
% 12.25/2.46 | COMBINE_EQS: (53), (57) imply:
% 12.25/2.46 | (58) all_36_1 = all_34_0
% 12.25/2.46 |
% 12.25/2.46 | GROUND_INST: instantiating (7) with all_15_6, all_15_5, all_42_0, simplifying
% 12.25/2.46 | with (14), (15), (44) gives:
% 12.25/2.47 | (59) ? [v0: any] : ? [v1: any] : (equal_set(all_15_6, all_15_5) = v0 &
% 12.25/2.47 | subset(all_15_6, all_15_5) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_42_0
% 12.25/2.47 | = 0)))
% 12.25/2.47 |
% 12.25/2.47 | GROUND_INST: instantiating (6) with all_15_5, all_15_6, all_42_0, simplifying
% 12.25/2.47 | with (14), (15), (44) gives:
% 12.25/2.47 | (60) ? [v0: any] : ? [v1: any] : (equal_set(all_15_5, all_15_6) = v0 &
% 12.25/2.47 | subset(all_15_6, all_15_5) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_42_0
% 12.25/2.47 | = 0)))
% 12.25/2.47 |
% 12.25/2.47 | GROUND_INST: instantiating (7) with all_15_1, all_15_5, all_46_0, simplifying
% 12.25/2.47 | with (15), (18), (48) gives:
% 12.25/2.47 | (61) ? [v0: any] : ? [v1: any] : (equal_set(all_15_1, all_15_5) = v0 &
% 12.25/2.47 | subset(all_15_1, all_15_5) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_46_0
% 12.25/2.47 | = 0)))
% 12.25/2.47 |
% 12.25/2.47 | GROUND_INST: instantiating (6) with all_15_5, all_15_1, all_46_0, simplifying
% 12.25/2.47 | with (15), (18), (48) gives:
% 12.25/2.47 | (62) ? [v0: any] : ? [v1: any] : (equal_set(all_15_5, all_15_1) = v0 &
% 12.25/2.47 | subset(all_15_1, all_15_5) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_46_0
% 12.25/2.47 | = 0)))
% 12.25/2.47 |
% 12.25/2.47 | GROUND_INST: instantiating (7) with all_15_6, all_15_4, all_34_0, simplifying
% 12.25/2.47 | with (14), (16), (36) gives:
% 12.25/2.47 | (63) ? [v0: any] : ? [v1: any] : (equal_set(all_15_6, all_15_4) = v0 &
% 12.25/2.47 | subset(all_15_6, all_15_4) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_34_0
% 12.25/2.47 | = 0)))
% 12.25/2.47 |
% 12.25/2.47 | GROUND_INST: instantiating (6) with all_15_4, all_15_6, all_34_0, simplifying
% 12.25/2.47 | with (14), (16), (36) gives:
% 12.25/2.47 | (64) ? [v0: any] : ? [v1: any] : (equal_set(all_15_4, all_15_6) = v0 &
% 12.25/2.47 | subset(all_15_6, all_15_4) = v1 & ( ~ (v0 = 0) | (v1 = 0 & all_34_0
% 12.25/2.47 | = 0)))
% 12.25/2.47 |
% 12.25/2.47 | DELTA: instantiating (62) with fresh symbols all_61_0, all_61_1 gives:
% 12.25/2.47 | (65) equal_set(all_15_5, all_15_1) = all_61_1 & subset(all_15_1, all_15_5)
% 12.25/2.47 | = all_61_0 & ( ~ (all_61_1 = 0) | (all_61_0 = 0 & all_46_0 = 0))
% 12.25/2.47 |
% 12.25/2.47 | ALPHA: (65) implies:
% 12.25/2.47 | (66) subset(all_15_1, all_15_5) = all_61_0
% 12.25/2.47 |
% 12.25/2.47 | DELTA: instantiating (61) with fresh symbols all_63_0, all_63_1 gives:
% 12.25/2.47 | (67) equal_set(all_15_1, all_15_5) = all_63_1 & subset(all_15_1, all_15_5)
% 12.25/2.47 | = all_63_0 & ( ~ (all_63_1 = 0) | (all_63_0 = 0 & all_46_0 = 0))
% 12.25/2.47 |
% 12.25/2.47 | ALPHA: (67) implies:
% 12.25/2.47 | (68) subset(all_15_1, all_15_5) = all_63_0
% 12.25/2.47 |
% 12.25/2.47 | DELTA: instantiating (64) with fresh symbols all_67_0, all_67_1 gives:
% 12.25/2.47 | (69) equal_set(all_15_4, all_15_6) = all_67_1 & subset(all_15_6, all_15_4)
% 12.25/2.47 | = all_67_0 & ( ~ (all_67_1 = 0) | (all_67_0 = 0 & all_34_0 = 0))
% 12.25/2.47 |
% 12.25/2.47 | ALPHA: (69) implies:
% 12.25/2.47 | (70) subset(all_15_6, all_15_4) = all_67_0
% 12.25/2.47 |
% 12.25/2.47 | DELTA: instantiating (60) with fresh symbols all_69_0, all_69_1 gives:
% 12.53/2.47 | (71) equal_set(all_15_5, all_15_6) = all_69_1 & subset(all_15_6, all_15_5)
% 12.53/2.47 | = all_69_0 & ( ~ (all_69_1 = 0) | (all_69_0 = 0 & all_42_0 = 0))
% 12.53/2.47 |
% 12.53/2.47 | ALPHA: (71) implies:
% 12.53/2.47 | (72) subset(all_15_6, all_15_5) = all_69_0
% 12.53/2.47 |
% 12.53/2.47 | DELTA: instantiating (59) with fresh symbols all_71_0, all_71_1 gives:
% 12.53/2.47 | (73) equal_set(all_15_6, all_15_5) = all_71_1 & subset(all_15_6, all_15_5)
% 12.53/2.47 | = all_71_0 & ( ~ (all_71_1 = 0) | (all_71_0 = 0 & all_42_0 = 0))
% 12.53/2.47 |
% 12.53/2.47 | ALPHA: (73) implies:
% 12.53/2.47 | (74) subset(all_15_6, all_15_5) = all_71_0
% 12.53/2.47 |
% 12.53/2.47 | DELTA: instantiating (63) with fresh symbols all_73_0, all_73_1 gives:
% 12.53/2.48 | (75) equal_set(all_15_6, all_15_4) = all_73_1 & subset(all_15_6, all_15_4)
% 12.53/2.48 | = all_73_0 & ( ~ (all_73_1 = 0) | (all_73_0 = 0 & all_34_0 = 0))
% 12.53/2.48 |
% 12.53/2.48 | ALPHA: (75) implies:
% 12.53/2.48 | (76) subset(all_15_6, all_15_4) = all_73_0
% 12.53/2.48 |
% 12.53/2.48 | GROUND_INST: instantiating (12) with all_15_3, all_71_0, all_15_5, all_15_6,
% 12.53/2.48 | simplifying with (19), (74) gives:
% 12.53/2.48 | (77) all_71_0 = all_15_3
% 12.53/2.48 |
% 12.53/2.48 | GROUND_INST: instantiating (12) with all_69_0, all_71_0, all_15_5, all_15_6,
% 12.53/2.48 | simplifying with (72), (74) gives:
% 12.53/2.48 | (78) all_71_0 = all_69_0
% 12.53/2.48 |
% 12.53/2.48 | GROUND_INST: instantiating (12) with 0, all_73_0, all_15_4, all_15_6,
% 12.53/2.48 | simplifying with (20), (76) gives:
% 12.53/2.48 | (79) all_73_0 = 0
% 12.53/2.48 |
% 12.53/2.48 | GROUND_INST: instantiating (12) with all_67_0, all_73_0, all_15_4, all_15_6,
% 12.53/2.48 | simplifying with (70), (76) gives:
% 12.53/2.48 | (80) all_73_0 = all_67_0
% 12.53/2.48 |
% 12.53/2.48 | GROUND_INST: instantiating (12) with all_15_0, all_63_0, all_15_5, all_15_1,
% 12.53/2.48 | simplifying with (21), (68) gives:
% 12.53/2.48 | (81) all_63_0 = all_15_0
% 12.53/2.48 |
% 12.53/2.48 | GROUND_INST: instantiating (12) with all_61_0, all_63_0, all_15_5, all_15_1,
% 12.53/2.48 | simplifying with (66), (68) gives:
% 12.53/2.48 | (82) all_63_0 = all_61_0
% 12.53/2.48 |
% 12.53/2.48 | COMBINE_EQS: (79), (80) imply:
% 12.53/2.48 | (83) all_67_0 = 0
% 12.53/2.48 |
% 12.53/2.48 | COMBINE_EQS: (77), (78) imply:
% 12.53/2.48 | (84) all_69_0 = all_15_3
% 12.53/2.48 |
% 12.53/2.48 | SIMP: (84) implies:
% 12.53/2.48 | (85) all_69_0 = all_15_3
% 12.53/2.48 |
% 12.53/2.48 | COMBINE_EQS: (81), (82) imply:
% 12.53/2.48 | (86) all_61_0 = all_15_0
% 12.53/2.48 |
% 12.53/2.48 | BETA: splitting (24) gives:
% 12.53/2.48 |
% 12.53/2.48 | Case 1:
% 12.53/2.48 | |
% 12.53/2.48 | | (87) all_15_0 = 0 & ~ (all_15_3 = 0)
% 12.53/2.48 | |
% 12.53/2.48 | | ALPHA: (87) implies:
% 12.53/2.48 | | (88) all_15_0 = 0
% 12.53/2.48 | | (89) ~ (all_15_3 = 0)
% 12.53/2.48 | |
% 12.53/2.48 | | REDUCE: (21), (88) imply:
% 12.53/2.48 | | (90) subset(all_15_1, all_15_5) = 0
% 12.53/2.48 | |
% 12.53/2.48 | | BETA: splitting (25) gives:
% 12.53/2.48 | |
% 12.53/2.48 | | Case 1:
% 12.53/2.48 | | |
% 12.53/2.48 | | | (91) all_15_3 = 0
% 12.53/2.48 | | |
% 12.53/2.48 | | | REDUCE: (89), (91) imply:
% 12.53/2.48 | | | (92) $false
% 12.53/2.48 | | |
% 12.53/2.48 | | | CLOSE: (92) is inconsistent.
% 12.53/2.48 | | |
% 12.53/2.48 | | Case 2:
% 12.53/2.48 | | |
% 12.53/2.48 | | | (93) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_5) =
% 12.53/2.48 | | | v1 & member(v0, all_15_6) = 0 & $i(v0))
% 12.53/2.48 | | |
% 12.53/2.48 | | | DELTA: instantiating (93) with fresh symbols all_93_0, all_93_1 gives:
% 12.53/2.48 | | | (94) ~ (all_93_0 = 0) & member(all_93_1, all_15_5) = all_93_0 &
% 12.53/2.48 | | | member(all_93_1, all_15_6) = 0 & $i(all_93_1)
% 12.53/2.48 | | |
% 12.53/2.48 | | | ALPHA: (94) implies:
% 12.53/2.48 | | | (95) ~ (all_93_0 = 0)
% 12.53/2.48 | | | (96) $i(all_93_1)
% 12.53/2.48 | | | (97) member(all_93_1, all_15_6) = 0
% 12.53/2.48 | | | (98) member(all_93_1, all_15_5) = all_93_0
% 12.53/2.48 | | |
% 12.53/2.48 | | | GROUND_INST: instantiating (1) with all_15_6, all_15_4, all_93_1,
% 12.53/2.48 | | | simplifying with (14), (16), (20), (96), (97) gives:
% 12.53/2.48 | | | (99) member(all_93_1, all_15_4) = 0
% 12.53/2.48 | | |
% 12.53/2.48 | | | GROUND_INST: instantiating (3) with all_15_1, all_15_5, all_93_1,
% 12.53/2.49 | | | all_93_0, simplifying with (15), (18), (90), (96), (98)
% 12.53/2.49 | | | gives:
% 12.53/2.49 | | | (100) all_93_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_93_1,
% 12.53/2.49 | | | all_15_1) = v0)
% 12.53/2.49 | | |
% 12.53/2.49 | | | BETA: splitting (100) gives:
% 12.53/2.49 | | |
% 12.53/2.49 | | | Case 1:
% 12.53/2.49 | | | |
% 12.53/2.49 | | | | (101) all_93_0 = 0
% 12.53/2.49 | | | |
% 12.53/2.49 | | | | REDUCE: (95), (101) imply:
% 12.53/2.49 | | | | (102) $false
% 12.53/2.49 | | | |
% 12.53/2.49 | | | | CLOSE: (102) is inconsistent.
% 12.53/2.49 | | | |
% 12.53/2.49 | | | Case 2:
% 12.53/2.49 | | | |
% 12.53/2.49 | | | | (103) ? [v0: int] : ( ~ (v0 = 0) & member(all_93_1, all_15_1) = v0)
% 12.53/2.49 | | | |
% 12.53/2.49 | | | | DELTA: instantiating (103) with fresh symbol all_121_0 gives:
% 12.53/2.49 | | | | (104) ~ (all_121_0 = 0) & member(all_93_1, all_15_1) = all_121_0
% 12.53/2.49 | | | |
% 12.53/2.49 | | | | ALPHA: (104) implies:
% 12.53/2.49 | | | | (105) ~ (all_121_0 = 0)
% 12.53/2.49 | | | | (106) member(all_93_1, all_15_1) = all_121_0
% 12.53/2.49 | | | |
% 12.53/2.49 | | | | GROUND_INST: instantiating (9) with all_93_1, all_15_6, all_15_2,
% 12.53/2.49 | | | | all_15_1, all_121_0, simplifying with (14), (17), (22),
% 12.53/2.49 | | | | (96), (106) gives:
% 12.53/2.49 | | | | (107) all_121_0 = 0 | ? [v0: any] : ? [v1: any] : (member(all_93_1,
% 12.53/2.49 | | | | all_15_2) = v1 & member(all_93_1, all_15_6) = v0 & ( ~ (v1
% 12.53/2.49 | | | | = 0) | ~ (v0 = 0)))
% 12.53/2.49 | | | |
% 12.53/2.49 | | | | BETA: splitting (107) gives:
% 12.53/2.49 | | | |
% 12.53/2.49 | | | | Case 1:
% 12.53/2.49 | | | | |
% 12.53/2.49 | | | | | (108) all_121_0 = 0
% 12.53/2.49 | | | | |
% 12.53/2.49 | | | | | REDUCE: (105), (108) imply:
% 12.53/2.49 | | | | | (109) $false
% 12.53/2.49 | | | | |
% 12.53/2.49 | | | | | CLOSE: (109) is inconsistent.
% 12.53/2.49 | | | | |
% 12.53/2.49 | | | | Case 2:
% 12.53/2.49 | | | | |
% 12.53/2.49 | | | | | (110) ? [v0: any] : ? [v1: any] : (member(all_93_1, all_15_2) =
% 12.53/2.49 | | | | | v1 & member(all_93_1, all_15_6) = v0 & ( ~ (v1 = 0) | ~
% 12.53/2.49 | | | | | (v0 = 0)))
% 12.53/2.49 | | | | |
% 12.53/2.49 | | | | | DELTA: instantiating (110) with fresh symbols all_145_0, all_145_1
% 12.53/2.49 | | | | | gives:
% 12.53/2.49 | | | | | (111) member(all_93_1, all_15_2) = all_145_0 & member(all_93_1,
% 12.53/2.49 | | | | | all_15_6) = all_145_1 & ( ~ (all_145_0 = 0) | ~ (all_145_1
% 12.53/2.49 | | | | | = 0))
% 12.53/2.49 | | | | |
% 12.53/2.49 | | | | | ALPHA: (111) implies:
% 12.53/2.49 | | | | | (112) member(all_93_1, all_15_6) = all_145_1
% 12.53/2.49 | | | | | (113) member(all_93_1, all_15_2) = all_145_0
% 12.53/2.49 | | | | | (114) ~ (all_145_0 = 0) | ~ (all_145_1 = 0)
% 12.53/2.49 | | | | |
% 12.53/2.49 | | | | | GROUND_INST: instantiating (11) with 0, all_145_1, all_15_6, all_93_1,
% 12.53/2.49 | | | | | simplifying with (97), (112) gives:
% 12.53/2.49 | | | | | (115) all_145_1 = 0
% 12.53/2.49 | | | | |
% 12.53/2.49 | | | | | BETA: splitting (114) gives:
% 12.53/2.49 | | | | |
% 12.53/2.49 | | | | | Case 1:
% 12.53/2.49 | | | | | |
% 12.53/2.49 | | | | | | (116) ~ (all_145_0 = 0)
% 12.53/2.49 | | | | | |
% 12.53/2.49 | | | | | | GROUND_INST: instantiating (10) with all_93_1, all_15_5, all_15_4,
% 12.53/2.49 | | | | | | all_15_2, all_145_0, simplifying with (15), (16), (23),
% 12.53/2.49 | | | | | | (96), (113) gives:
% 12.53/2.49 | | | | | | (117) all_145_0 = 0 | ? [v0: any] : ? [v1: any] :
% 12.53/2.49 | | | | | | (member(all_93_1, all_15_4) = v0 & member(all_93_1,
% 12.53/2.49 | | | | | | all_15_5) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 12.53/2.49 | | | | | |
% 12.53/2.49 | | | | | | BETA: splitting (117) gives:
% 12.53/2.49 | | | | | |
% 12.53/2.49 | | | | | | Case 1:
% 12.53/2.49 | | | | | | |
% 12.53/2.49 | | | | | | | (118) all_145_0 = 0
% 12.53/2.49 | | | | | | |
% 12.53/2.49 | | | | | | | REDUCE: (116), (118) imply:
% 12.53/2.49 | | | | | | | (119) $false
% 12.53/2.49 | | | | | | |
% 12.53/2.49 | | | | | | | CLOSE: (119) is inconsistent.
% 12.53/2.49 | | | | | | |
% 12.53/2.49 | | | | | | Case 2:
% 12.53/2.49 | | | | | | |
% 12.53/2.49 | | | | | | | (120) ? [v0: any] : ? [v1: any] : (member(all_93_1, all_15_4)
% 12.53/2.49 | | | | | | | = v0 & member(all_93_1, all_15_5) = v1 & ( ~ (v0 = 0) |
% 12.53/2.49 | | | | | | | v1 = 0))
% 12.53/2.49 | | | | | | |
% 12.53/2.49 | | | | | | | DELTA: instantiating (120) with fresh symbols all_181_0, all_181_1
% 12.53/2.49 | | | | | | | gives:
% 12.53/2.49 | | | | | | | (121) member(all_93_1, all_15_4) = all_181_1 & member(all_93_1,
% 12.53/2.49 | | | | | | | all_15_5) = all_181_0 & ( ~ (all_181_1 = 0) | all_181_0
% 12.53/2.49 | | | | | | | = 0)
% 12.53/2.49 | | | | | | |
% 12.53/2.49 | | | | | | | ALPHA: (121) implies:
% 12.53/2.49 | | | | | | | (122) member(all_93_1, all_15_5) = all_181_0
% 12.53/2.49 | | | | | | | (123) member(all_93_1, all_15_4) = all_181_1
% 12.53/2.49 | | | | | | | (124) ~ (all_181_1 = 0) | all_181_0 = 0
% 12.53/2.49 | | | | | | |
% 12.53/2.49 | | | | | | | GROUND_INST: instantiating (11) with all_93_0, all_181_0,
% 12.53/2.49 | | | | | | | all_15_5, all_93_1, simplifying with (98), (122)
% 12.53/2.49 | | | | | | | gives:
% 12.53/2.49 | | | | | | | (125) all_181_0 = all_93_0
% 12.53/2.49 | | | | | | |
% 12.53/2.49 | | | | | | | GROUND_INST: instantiating (11) with 0, all_181_1, all_15_4,
% 12.53/2.49 | | | | | | | all_93_1, simplifying with (99), (123) gives:
% 12.53/2.49 | | | | | | | (126) all_181_1 = 0
% 12.53/2.49 | | | | | | |
% 12.53/2.49 | | | | | | | BETA: splitting (124) gives:
% 12.53/2.49 | | | | | | |
% 12.53/2.49 | | | | | | | Case 1:
% 12.53/2.49 | | | | | | | |
% 12.53/2.49 | | | | | | | | (127) ~ (all_181_1 = 0)
% 12.53/2.50 | | | | | | | |
% 12.53/2.50 | | | | | | | | REDUCE: (126), (127) imply:
% 12.53/2.50 | | | | | | | | (128) $false
% 12.53/2.50 | | | | | | | |
% 12.53/2.50 | | | | | | | | CLOSE: (128) is inconsistent.
% 12.53/2.50 | | | | | | | |
% 12.53/2.50 | | | | | | | Case 2:
% 12.53/2.50 | | | | | | | |
% 12.53/2.50 | | | | | | | | (129) all_181_0 = 0
% 12.53/2.50 | | | | | | | |
% 12.53/2.50 | | | | | | | | COMBINE_EQS: (125), (129) imply:
% 12.53/2.50 | | | | | | | | (130) all_93_0 = 0
% 12.53/2.50 | | | | | | | |
% 12.53/2.50 | | | | | | | | REDUCE: (95), (130) imply:
% 12.53/2.50 | | | | | | | | (131) $false
% 12.53/2.50 | | | | | | | |
% 12.53/2.50 | | | | | | | | CLOSE: (131) is inconsistent.
% 12.53/2.50 | | | | | | | |
% 12.53/2.50 | | | | | | | End of split
% 12.53/2.50 | | | | | | |
% 12.53/2.50 | | | | | | End of split
% 12.53/2.50 | | | | | |
% 12.53/2.50 | | | | | Case 2:
% 12.53/2.50 | | | | | |
% 12.53/2.50 | | | | | | (132) ~ (all_145_1 = 0)
% 12.53/2.50 | | | | | |
% 12.53/2.50 | | | | | | REDUCE: (115), (132) imply:
% 12.53/2.50 | | | | | | (133) $false
% 12.53/2.50 | | | | | |
% 12.53/2.50 | | | | | | CLOSE: (133) is inconsistent.
% 12.53/2.50 | | | | | |
% 12.53/2.50 | | | | | End of split
% 12.53/2.50 | | | | |
% 12.53/2.50 | | | | End of split
% 12.53/2.50 | | | |
% 12.53/2.50 | | | End of split
% 12.53/2.50 | | |
% 12.53/2.50 | | End of split
% 12.53/2.50 | |
% 12.53/2.50 | Case 2:
% 12.53/2.50 | |
% 12.53/2.50 | | (134) all_15_3 = 0 & ~ (all_15_0 = 0)
% 12.53/2.50 | |
% 12.53/2.50 | | ALPHA: (134) implies:
% 12.53/2.50 | | (135) all_15_3 = 0
% 12.53/2.50 | | (136) ~ (all_15_0 = 0)
% 12.53/2.50 | |
% 12.53/2.50 | | REDUCE: (19), (135) imply:
% 12.53/2.50 | | (137) subset(all_15_6, all_15_5) = 0
% 12.53/2.50 | |
% 12.53/2.50 | | BETA: splitting (32) gives:
% 12.53/2.50 | |
% 12.53/2.50 | | Case 1:
% 12.53/2.50 | | |
% 12.53/2.50 | | | (138) all_15_0 = 0
% 12.53/2.50 | | |
% 12.53/2.50 | | | REDUCE: (136), (138) imply:
% 12.53/2.50 | | | (139) $false
% 12.53/2.50 | | |
% 12.53/2.50 | | | CLOSE: (139) is inconsistent.
% 12.53/2.50 | | |
% 12.53/2.50 | | Case 2:
% 12.53/2.50 | | |
% 12.53/2.50 | | | (140) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & member(v0, all_15_1)
% 12.53/2.50 | | | = 0 & member(v0, all_15_5) = v1 & $i(v0))
% 12.53/2.50 | | |
% 12.53/2.50 | | | DELTA: instantiating (140) with fresh symbols all_98_0, all_98_1 gives:
% 12.53/2.50 | | | (141) ~ (all_98_0 = 0) & member(all_98_1, all_15_1) = 0 &
% 12.53/2.50 | | | member(all_98_1, all_15_5) = all_98_0 & $i(all_98_1)
% 12.53/2.50 | | |
% 12.53/2.50 | | | ALPHA: (141) implies:
% 12.53/2.50 | | | (142) ~ (all_98_0 = 0)
% 12.53/2.50 | | | (143) $i(all_98_1)
% 12.53/2.50 | | | (144) member(all_98_1, all_15_5) = all_98_0
% 12.53/2.50 | | | (145) member(all_98_1, all_15_1) = 0
% 12.53/2.50 | | |
% 12.53/2.50 | | | GROUND_INST: instantiating (8) with all_98_1, all_15_6, all_15_2,
% 12.53/2.50 | | | all_15_1, simplifying with (14), (17), (22), (143), (145)
% 12.53/2.50 | | | gives:
% 12.53/2.50 | | | (146) member(all_98_1, all_15_2) = 0 & member(all_98_1, all_15_6) = 0
% 12.53/2.50 | | |
% 12.53/2.50 | | | ALPHA: (146) implies:
% 12.53/2.50 | | | (147) member(all_98_1, all_15_6) = 0
% 12.53/2.50 | | |
% 12.53/2.50 | | | GROUND_INST: instantiating (3) with all_15_6, all_15_5, all_98_1,
% 12.53/2.50 | | | all_98_0, simplifying with (14), (15), (137), (143), (144)
% 12.53/2.50 | | | gives:
% 12.53/2.50 | | | (148) all_98_0 = 0 | ? [v0: int] : ( ~ (v0 = 0) & member(all_98_1,
% 12.53/2.50 | | | all_15_6) = v0)
% 12.53/2.50 | | |
% 12.53/2.50 | | | BETA: splitting (148) gives:
% 12.53/2.50 | | |
% 12.53/2.50 | | | Case 1:
% 12.53/2.50 | | | |
% 12.53/2.50 | | | | (149) all_98_0 = 0
% 12.53/2.50 | | | |
% 12.53/2.50 | | | | REDUCE: (142), (149) imply:
% 12.53/2.50 | | | | (150) $false
% 12.53/2.50 | | | |
% 12.53/2.50 | | | | CLOSE: (150) is inconsistent.
% 12.53/2.50 | | | |
% 12.53/2.50 | | | Case 2:
% 12.53/2.50 | | | |
% 12.53/2.50 | | | | (151) ? [v0: int] : ( ~ (v0 = 0) & member(all_98_1, all_15_6) = v0)
% 12.53/2.50 | | | |
% 12.53/2.50 | | | | DELTA: instantiating (151) with fresh symbol all_121_0 gives:
% 12.53/2.50 | | | | (152) ~ (all_121_0 = 0) & member(all_98_1, all_15_6) = all_121_0
% 12.53/2.50 | | | |
% 12.53/2.50 | | | | ALPHA: (152) implies:
% 12.53/2.50 | | | | (153) ~ (all_121_0 = 0)
% 12.53/2.50 | | | | (154) member(all_98_1, all_15_6) = all_121_0
% 12.53/2.50 | | | |
% 12.53/2.50 | | | | GROUND_INST: instantiating (11) with 0, all_121_0, all_15_6, all_98_1,
% 12.53/2.50 | | | | simplifying with (147), (154) gives:
% 12.53/2.50 | | | | (155) all_121_0 = 0
% 12.53/2.50 | | | |
% 12.53/2.50 | | | | REDUCE: (153), (155) imply:
% 12.53/2.50 | | | | (156) $false
% 12.53/2.50 | | | |
% 12.53/2.50 | | | | CLOSE: (156) is inconsistent.
% 12.53/2.50 | | | |
% 12.53/2.50 | | | End of split
% 12.53/2.50 | | |
% 12.53/2.50 | | End of split
% 12.53/2.50 | |
% 12.53/2.50 | End of split
% 12.53/2.50 |
% 12.53/2.50 End of proof
% 12.53/2.50 % SZS output end Proof for theBenchmark
% 12.53/2.50
% 12.53/2.50 1912ms
%------------------------------------------------------------------------------