TSTP Solution File: DAT038_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT038_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n022.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 : Wed Aug 30 22:18:58 EDT 2023
% Result : Theorem 11.26s 2.27s
% Output : Proof 17.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : DAT038_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.36 % Computer : n022.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Aug 24 14:33:11 EDT 2023
% 0.13/0.36 % 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 ...
% 0.22/0.64 Running up to 7 provers in parallel.
% 0.22/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.22/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.22/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.22/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.22/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.22/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.22/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.79/1.08 Prover 1: Preprocessing ...
% 2.79/1.08 Prover 4: Preprocessing ...
% 2.79/1.12 Prover 5: Preprocessing ...
% 2.79/1.12 Prover 3: Preprocessing ...
% 2.79/1.12 Prover 2: Preprocessing ...
% 2.79/1.12 Prover 0: Preprocessing ...
% 2.79/1.12 Prover 6: Preprocessing ...
% 4.86/1.42 Prover 5: Proving ...
% 4.86/1.42 Prover 3: Constructing countermodel ...
% 4.86/1.42 Prover 6: Constructing countermodel ...
% 4.86/1.42 Prover 1: Constructing countermodel ...
% 4.86/1.44 Prover 4: Constructing countermodel ...
% 4.86/1.47 Prover 2: Proving ...
% 4.86/1.50 Prover 0: Proving ...
% 4.86/1.54 Prover 1: gave up
% 4.86/1.54 Prover 6: gave up
% 4.86/1.54 Prover 3: gave up
% 4.86/1.56 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 4.86/1.56 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 4.86/1.56 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 4.86/1.57 Prover 8: Preprocessing ...
% 4.86/1.58 Prover 7: Preprocessing ...
% 4.86/1.60 Prover 9: Preprocessing ...
% 6.80/1.67 Prover 7: Constructing countermodel ...
% 7.02/1.71 Prover 7: gave up
% 7.02/1.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.40/1.73 Prover 8: Warning: ignoring some quantifiers
% 7.40/1.73 Prover 8: Constructing countermodel ...
% 7.40/1.74 Prover 10: Preprocessing ...
% 7.40/1.74 Prover 9: Constructing countermodel ...
% 7.61/1.81 Prover 8: gave up
% 7.61/1.82 Prover 10: Constructing countermodel ...
% 7.61/1.82 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.18/1.83 Prover 10: gave up
% 8.18/1.84 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 8.18/1.86 Prover 11: Preprocessing ...
% 8.51/1.89 Prover 12: Preprocessing ...
% 8.99/1.97 Prover 11: Constructing countermodel ...
% 9.20/2.01 Prover 12: Proving ...
% 11.26/2.27 Prover 0: proved (1627ms)
% 11.26/2.27
% 11.26/2.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.26/2.27
% 11.26/2.27 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.26/2.27 Prover 2: stopped
% 11.26/2.27 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 11.26/2.27 Prover 9: stopped
% 11.26/2.28 Prover 12: stopped
% 11.26/2.28 Prover 5: stopped
% 11.26/2.28 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 11.26/2.29 Prover 13: Preprocessing ...
% 11.26/2.30 Prover 16: Preprocessing ...
% 11.26/2.31 Prover 19: Preprocessing ...
% 11.73/2.36 Prover 16: Warning: ignoring some quantifiers
% 11.73/2.37 Prover 19: Warning: ignoring some quantifiers
% 11.73/2.37 Prover 13: Warning: ignoring some quantifiers
% 11.73/2.37 Prover 16: Constructing countermodel ...
% 11.73/2.37 Prover 19: Constructing countermodel ...
% 11.73/2.37 Prover 13: Constructing countermodel ...
% 12.26/2.44 Prover 13: gave up
% 12.26/2.45 Prover 19: gave up
% 13.26/2.56 Prover 16: gave up
% 16.05/3.01 Prover 11: Found proof (size 213)
% 16.05/3.01 Prover 11: proved (1196ms)
% 16.05/3.02 Prover 4: stopped
% 16.05/3.02
% 16.05/3.02 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 16.05/3.02
% 16.44/3.09 % SZS output start Proof for theBenchmark
% 16.44/3.10 Assumptions after simplification:
% 16.44/3.10 ---------------------------------
% 16.44/3.10
% 16.44/3.10 (ax1)
% 16.44/3.11 collection(empty) & ! [v0: collection] : ! [v1: int] : ( ~ ($lesseq(v1, -1))
% 16.44/3.11 | ~ (count(v0) = v1) | ~ collection(v0)) & ! [v0: int] : ~ (in(v0,
% 16.44/3.11 empty) = 0)
% 16.44/3.11
% 16.44/3.11 (ax2)
% 16.44/3.12 collection(empty) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] :
% 16.44/3.12 ( ~ (add(v0, v1) = v2) | ~ collection(v1) | in(v0, v2) = 0) & ! [v0:
% 16.44/3.12 collection] : (v0 = empty | ~ (count(v0) = 0) | ~ collection(v0)) & !
% 16.44/3.12 [v0: int] : (v0 = 0 | ~ (count(empty) = v0))
% 16.44/3.12
% 16.44/3.12 (ax3)
% 16.44/3.12 ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 16.44/3.12 v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int] : (add(v0,
% 16.44/3.12 v1) = v3 & count(v3) = v4 & count(v1) = $sum(v4, -1) & collection(v3)))
% 16.44/3.12 & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0,
% 16.44/3.12 v1) = v2) | ~ collection(v1) | ? [v3: int] : ( ~ (v3 = 0) & in(v0, v2)
% 16.44/3.12 = v3)) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~
% 16.44/3.13 (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ?
% 16.44/3.13 [v5: int] : (($difference(v5, v4) = -1 & count(v2) = v4 & count(v1) =
% 16.44/3.13 $sum(v4, -1)) | (v3 = 0 & in(v0, v1) = 0))) & ! [v0: int] : ! [v1:
% 16.44/3.13 collection] : ! [v2: collection] : ( ~ (add(v0, v1) = v2) | ~
% 16.44/3.13 collection(v1) | ? [v3: int] : ? [v4: int] : ? [v5: int] : (( ~ (v5 = 0)
% 16.44/3.13 & in(v0, v1) = v5) | ( ~ ($difference(v4, v3) = -1) & count(v2) = v3 &
% 16.44/3.13 count(v1) = v4))) & ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1)
% 16.44/3.13 = 0) | ~ collection(v1) | ? [v2: collection] : ? [v3: int] : ? [v4:
% 16.44/3.13 int] : ( ~ ($difference(v4, v3) = -1) & add(v0, v1) = v2 & count(v2) = v3
% 16.44/3.13 & count(v1) = v4 & collection(v2)))
% 16.44/3.13
% 16.44/3.13 (ax4)
% 16.44/3.13 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : !
% 16.44/3.13 [v4: int] : (v4 = 0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~
% 16.44/3.13 collection(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0:
% 16.44/3.13 int] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v3 = 0 |
% 16.44/3.13 ~ (add(v0, v1) = v2) | ~ (in(v0, v2) = v3) | ~ collection(v1)) & ! [v0:
% 16.44/3.13 int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : (v2 = v0 |
% 16.44/3.13 ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | in(v0, v1)
% 16.44/3.13 = 0) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~
% 16.44/3.13 (in(v0, v1) = v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int] :
% 16.44/3.13 ? [v5: int] : ( ~ (v5 = v4) & add(v0, v1) = v3 & count(v3) = v4 & count(v1)
% 16.44/3.13 = v5 & collection(v3))) & ! [v0: int] : ! [v1: collection] : ! [v2:
% 16.44/3.13 collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: int] : ?
% 16.44/3.13 [v4: int] : ? [v5: int] : ((v5 = v4 & count(v2) = v4 & count(v1) = v4) | (
% 16.44/3.13 ~ (v3 = 0) & in(v0, v1) = v3))) & ! [v0: int] : ! [v1: collection] :
% 16.44/3.13 ! [v2: collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: int]
% 16.44/3.13 : ? [v4: int] : ? [v5: int] : ((v5 = 0 & in(v0, v1) = 0) | ( ~ (v4 = v3) &
% 16.44/3.13 count(v2) = v3 & count(v1) = v4))) & ! [v0: int] : ! [v1: collection]
% 16.44/3.13 : ( ~ (in(v0, v1) = 0) | ~ collection(v1) | ? [v2: collection] : ? [v3:
% 16.44/3.13 int] : (add(v0, v1) = v2 & count(v2) = v3 & count(v1) = v3 &
% 16.44/3.13 collection(v2)))
% 16.44/3.13
% 16.44/3.13 (ax5)
% 16.44/3.14 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : !
% 16.44/3.14 [v4: int] : (v4 = 0 | v2 = v0 | ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) =
% 16.44/3.14 v4) | ~ collection(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 16.44/3.14 & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : (
% 16.44/3.14 ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | in(v0,
% 16.44/3.14 v1) = 0) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 |
% 16.44/3.14 ~ (in(v0, v1) = v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int]
% 16.44/3.14 : ? [v5: int] : ( ~ ($difference(v5, v4) = 1) & remove(v0, v1) = v3 &
% 16.44/3.14 count(v3) = v4 & count(v1) = v5 & collection(v3))) & ! [v0: int] : !
% 16.44/3.14 [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) = v2) | ~
% 16.44/3.14 (in(v0, v2) = 0) | ~ collection(v1)) & ! [v0: int] : ! [v1: collection] :
% 16.44/3.14 ! [v2: collection] : ( ~ (remove(v0, v1) = v2) | ~ collection(v1) | ? [v3:
% 16.44/3.14 int] : ? [v4: int] : ? [v5: int] : (($difference(v5, v4) = 1 & count(v2)
% 16.44/3.14 = v4 & count(v1) = $sum(v4, 1)) | ( ~ (v3 = 0) & in(v0, v1) = v3))) & !
% 16.44/3.14 [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) =
% 16.44/3.14 v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ? [v5: int] :
% 16.44/3.14 ((v5 = 0 & in(v0, v1) = 0) | ( ~ ($difference(v4, v3) = 1) & count(v2) = v3
% 16.44/3.14 & count(v1) = v4))) & ! [v0: int] : ! [v1: collection] : ( ~ (in(v0,
% 16.44/3.14 v1) = 0) | ~ collection(v1) | ? [v2: collection] : ? [v3: int] :
% 16.44/3.14 (remove(v0, v1) = v2 & count(v2) = v3 & count(v1) = $sum(v3, 1) &
% 16.44/3.14 collection(v2)))
% 16.44/3.14
% 16.44/3.14 (ax6)
% 16.44/3.14 ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 16.44/3.14 v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int] : (remove(v0,
% 16.44/3.14 v1) = v3 & count(v3) = v4 & count(v1) = v4 & collection(v3))) & ! [v0:
% 16.44/3.14 int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) = v2)
% 16.44/3.14 | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ? [v5: int] : ((v5 = v4
% 16.44/3.14 & count(v2) = v4 & count(v1) = v4) | (v3 = 0 & in(v0, v1) = 0))) & !
% 16.44/3.14 [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) =
% 16.44/3.14 v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ? [v5: int] : ((
% 16.44/3.14 ~ (v5 = 0) & in(v0, v1) = v5) | ( ~ (v4 = v3) & count(v2) = v3 &
% 16.44/3.14 count(v1) = v4))) & ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1)
% 16.44/3.14 = 0) | ~ collection(v1) | ? [v2: collection] : ? [v3: int] : ? [v4:
% 16.44/3.14 int] : ( ~ (v4 = v3) & remove(v0, v1) = v2 & count(v2) = v3 & count(v1) =
% 16.44/3.14 v4 & collection(v2)))
% 16.44/3.14
% 16.44/3.14 (ax7)
% 16.44/3.14 ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1)
% 16.44/3.14 = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: collection] : ((v4 = v1
% 16.44/3.14 & add(v0, v2) = v1) | ( ~ (v3 = 0) & in(v0, v1) = v3))) & ! [v0: int] :
% 16.44/3.14 ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~ collection(v1) | ? [v2:
% 16.44/3.14 collection] : (remove(v0, v1) = v2 & add(v0, v2) = v1 & collection(v2)))
% 16.44/3.14
% 16.44/3.14 (co1)
% 16.44/3.15 ? [v0: collection] : (count(v0) = 2 & in(5, v0) = 0 & in(3, v0) = 0 & in(2,
% 16.44/3.15 v0) = 0 & collection(v0))
% 16.44/3.15
% 16.44/3.15 (function-axioms)
% 16.44/3.15 ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int]
% 16.44/3.15 : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) = v0)) & ! [v0:
% 16.44/3.15 collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v1
% 16.44/3.15 = v0 | ~ (add(v3, v2) = v1) | ~ (add(v3, v2) = v0)) & ! [v0:
% 16.44/3.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: collection] : !
% 16.44/3.15 [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 16.44/3.15 int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~ (count(v2) = v1) |
% 16.44/3.15 ~ (count(v2) = v0))
% 16.44/3.15
% 16.44/3.15 Those formulas are unsatisfiable:
% 16.44/3.15 ---------------------------------
% 16.44/3.15
% 16.44/3.15 Begin of proof
% 16.44/3.15 |
% 16.44/3.15 | ALPHA: (ax1) implies:
% 16.44/3.15 | (1) ! [v0: int] : ~ (in(v0, empty) = 0)
% 16.44/3.15 |
% 16.44/3.15 | ALPHA: (ax2) implies:
% 16.44/3.15 | (2) ! [v0: collection] : (v0 = empty | ~ (count(v0) = 0) | ~
% 16.44/3.15 | collection(v0))
% 16.44/3.15 |
% 16.44/3.15 | ALPHA: (ax3) implies:
% 16.44/3.15 | (3) ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~
% 16.44/3.15 | collection(v1) | ? [v2: collection] : ? [v3: int] : ? [v4: int] :
% 16.44/3.15 | ( ~ ($difference(v4, v3) = -1) & add(v0, v1) = v2 & count(v2) = v3 &
% 16.44/3.15 | count(v1) = v4 & collection(v2)))
% 16.44/3.15 | (4) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0,
% 16.44/3.15 | v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ?
% 16.44/3.15 | [v5: int] : (( ~ (v5 = 0) & in(v0, v1) = v5) | ( ~ ($difference(v4,
% 16.44/3.15 | v3) = -1) & count(v2) = v3 & count(v1) = v4)))
% 16.44/3.16 | (5) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~
% 16.44/3.16 | (remove(v0, v1) = v2) | ~ collection(v1) | ? [v3: int] : ( ~ (v3 =
% 16.44/3.16 | 0) & in(v0, v2) = v3))
% 16.44/3.16 |
% 16.44/3.16 | ALPHA: (ax4) implies:
% 16.44/3.16 | (6) ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~
% 16.44/3.16 | collection(v1) | ? [v2: collection] : ? [v3: int] : (add(v0, v1) =
% 16.44/3.16 | v2 & count(v2) = v3 & count(v1) = v3 & collection(v2)))
% 16.44/3.16 | (7) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0,
% 16.44/3.16 | v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ?
% 16.44/3.16 | [v5: int] : ((v5 = v4 & count(v2) = v4 & count(v1) = v4) | ( ~ (v3 =
% 16.44/3.16 | 0) & in(v0, v1) = v3)))
% 16.44/3.16 | (8) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection]
% 16.44/3.16 | : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~
% 16.44/3.16 | collection(v1) | in(v0, v1) = 0)
% 16.44/3.16 |
% 16.44/3.16 | ALPHA: (ax5) implies:
% 16.44/3.16 | (9) ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~
% 16.44/3.16 | collection(v1) | ? [v2: collection] : ? [v3: int] : (remove(v0, v1)
% 16.44/3.16 | = v2 & count(v2) = v3 & count(v1) = $sum(v3, 1) & collection(v2)))
% 16.44/3.16 | (10) ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~
% 16.44/3.16 | (in(v0, v1) = v2) | ~ collection(v1) | ? [v3: collection] : ?
% 16.44/3.16 | [v4: int] : ? [v5: int] : ( ~ ($difference(v5, v4) = 1) &
% 16.44/3.16 | remove(v0, v1) = v3 & count(v3) = v4 & count(v1) = v5 &
% 16.44/3.16 | collection(v3)))
% 16.44/3.16 |
% 16.44/3.16 | ALPHA: (ax6) implies:
% 16.44/3.16 | (11) ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~
% 16.44/3.16 | collection(v1) | ? [v2: collection] : ? [v3: int] : ? [v4: int] :
% 16.44/3.16 | ( ~ (v4 = v3) & remove(v0, v1) = v2 & count(v2) = v3 & count(v1) =
% 16.44/3.16 | v4 & collection(v2)))
% 16.44/3.16 | (12) ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~
% 16.44/3.16 | (in(v0, v1) = v2) | ~ collection(v1) | ? [v3: collection] : ?
% 16.44/3.16 | [v4: int] : (remove(v0, v1) = v3 & count(v3) = v4 & count(v1) = v4 &
% 16.44/3.16 | collection(v3)))
% 16.44/3.16 |
% 16.44/3.16 | ALPHA: (ax7) implies:
% 16.44/3.16 | (13) ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~
% 16.44/3.16 | collection(v1) | ? [v2: collection] : (remove(v0, v1) = v2 &
% 16.44/3.16 | add(v0, v2) = v1 & collection(v2)))
% 16.44/3.16 |
% 16.44/3.16 | ALPHA: (function-axioms) implies:
% 16.44/3.16 | (14) ! [v0: int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~
% 16.44/3.16 | (count(v2) = v1) | ~ (count(v2) = v0))
% 16.44/3.16 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 16.44/3.16 | collection] : ! [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~
% 16.44/3.16 | (in(v3, v2) = v0))
% 16.44/3.16 | (16) ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : !
% 16.44/3.16 | [v3: int] : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) =
% 16.44/3.16 | v0))
% 16.44/3.16 |
% 16.44/3.16 | DELTA: instantiating (co1) with fresh symbol all_13_0 gives:
% 16.44/3.17 | (17) count(all_13_0) = 2 & in(5, all_13_0) = 0 & in(3, all_13_0) = 0 &
% 16.44/3.17 | in(2, all_13_0) = 0 & collection(all_13_0)
% 16.44/3.17 |
% 16.44/3.17 | ALPHA: (17) implies:
% 16.44/3.17 | (18) collection(all_13_0)
% 16.44/3.17 | (19) in(2, all_13_0) = 0
% 16.44/3.17 | (20) in(3, all_13_0) = 0
% 16.44/3.17 | (21) in(5, all_13_0) = 0
% 16.44/3.17 | (22) count(all_13_0) = 2
% 16.44/3.17 |
% 16.44/3.17 | GROUND_INST: instantiating (3) with 2, all_13_0, simplifying with (18), (19)
% 16.44/3.17 | gives:
% 16.44/3.17 | (23) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~
% 16.44/3.17 | ($difference(v2, v1) = -1) & add(2, all_13_0) = v0 & count(v0) = v1
% 16.44/3.17 | & count(all_13_0) = v2 & collection(v0))
% 16.44/3.17 |
% 16.44/3.17 | GROUND_INST: instantiating (11) with 2, all_13_0, simplifying with (18), (19)
% 16.44/3.17 | gives:
% 16.44/3.17 | (24) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) &
% 16.44/3.17 | remove(2, all_13_0) = v0 & count(v0) = v1 & count(all_13_0) = v2 &
% 16.44/3.17 | collection(v0))
% 16.44/3.17 |
% 16.44/3.17 | GROUND_INST: instantiating (9) with 2, all_13_0, simplifying with (18), (19)
% 16.44/3.17 | gives:
% 16.44/3.17 | (25) ? [v0: collection] : ? [v1: int] : (remove(2, all_13_0) = v0 &
% 16.44/3.17 | count(v0) = v1 & count(all_13_0) = $sum(v1, 1) & collection(v0))
% 16.44/3.17 |
% 16.44/3.17 | GROUND_INST: instantiating (6) with 2, all_13_0, simplifying with (18), (19)
% 16.44/3.17 | gives:
% 16.44/3.17 | (26) ? [v0: collection] : ? [v1: int] : (add(2, all_13_0) = v0 &
% 16.44/3.17 | count(v0) = v1 & count(all_13_0) = v1 & collection(v0))
% 16.44/3.17 |
% 16.44/3.17 | GROUND_INST: instantiating (13) with 2, all_13_0, simplifying with (18), (19)
% 16.44/3.17 | gives:
% 16.44/3.17 | (27) ? [v0: collection] : (remove(2, all_13_0) = v0 & add(2, v0) =
% 16.44/3.17 | all_13_0 & collection(v0))
% 16.44/3.17 |
% 16.44/3.17 | GROUND_INST: instantiating (3) with 3, all_13_0, simplifying with (18), (20)
% 16.44/3.17 | gives:
% 16.44/3.17 | (28) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~
% 16.44/3.17 | ($difference(v2, v1) = -1) & add(3, all_13_0) = v0 & count(v0) = v1
% 16.44/3.17 | & count(all_13_0) = v2 & collection(v0))
% 16.44/3.17 |
% 16.44/3.17 | GROUND_INST: instantiating (11) with 3, all_13_0, simplifying with (18), (20)
% 16.44/3.17 | gives:
% 16.44/3.17 | (29) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) &
% 16.44/3.17 | remove(3, all_13_0) = v0 & count(v0) = v1 & count(all_13_0) = v2 &
% 16.44/3.17 | collection(v0))
% 16.44/3.17 |
% 16.44/3.17 | GROUND_INST: instantiating (9) with 3, all_13_0, simplifying with (18), (20)
% 16.44/3.17 | gives:
% 16.44/3.17 | (30) ? [v0: collection] : ? [v1: int] : (remove(3, all_13_0) = v0 &
% 16.44/3.17 | count(v0) = v1 & count(all_13_0) = $sum(v1, 1) & collection(v0))
% 16.44/3.17 |
% 16.44/3.17 | GROUND_INST: instantiating (6) with 3, all_13_0, simplifying with (18), (20)
% 16.44/3.17 | gives:
% 16.86/3.17 | (31) ? [v0: collection] : ? [v1: int] : (add(3, all_13_0) = v0 &
% 16.86/3.17 | count(v0) = v1 & count(all_13_0) = v1 & collection(v0))
% 16.86/3.17 |
% 16.86/3.17 | GROUND_INST: instantiating (3) with 5, all_13_0, simplifying with (18), (21)
% 16.86/3.17 | gives:
% 16.86/3.18 | (32) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~
% 16.86/3.18 | ($difference(v2, v1) = -1) & add(5, all_13_0) = v0 & count(v0) = v1
% 16.86/3.18 | & count(all_13_0) = v2 & collection(v0))
% 16.86/3.18 |
% 16.86/3.18 | GROUND_INST: instantiating (11) with 5, all_13_0, simplifying with (18), (21)
% 16.86/3.18 | gives:
% 16.86/3.18 | (33) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) &
% 16.86/3.18 | remove(5, all_13_0) = v0 & count(v0) = v1 & count(all_13_0) = v2 &
% 16.86/3.18 | collection(v0))
% 16.86/3.18 |
% 16.86/3.18 | GROUND_INST: instantiating (9) with 5, all_13_0, simplifying with (18), (21)
% 16.86/3.18 | gives:
% 16.86/3.18 | (34) ? [v0: collection] : ? [v1: int] : (remove(5, all_13_0) = v0 &
% 16.86/3.18 | count(v0) = v1 & count(all_13_0) = $sum(v1, 1) & collection(v0))
% 16.86/3.18 |
% 16.86/3.18 | GROUND_INST: instantiating (6) with 5, all_13_0, simplifying with (18), (21)
% 16.86/3.18 | gives:
% 16.86/3.18 | (35) ? [v0: collection] : ? [v1: int] : (add(5, all_13_0) = v0 &
% 16.86/3.18 | count(v0) = v1 & count(all_13_0) = v1 & collection(v0))
% 16.86/3.18 |
% 16.86/3.18 | DELTA: instantiating (27) with fresh symbol all_22_0 gives:
% 16.86/3.18 | (36) remove(2, all_13_0) = all_22_0 & add(2, all_22_0) = all_13_0 &
% 16.86/3.18 | collection(all_22_0)
% 16.86/3.18 |
% 16.86/3.18 | ALPHA: (36) implies:
% 16.86/3.18 | (37) add(2, all_22_0) = all_13_0
% 16.86/3.18 | (38) remove(2, all_13_0) = all_22_0
% 16.86/3.18 |
% 16.86/3.18 | DELTA: instantiating (35) with fresh symbols all_26_0, all_26_1 gives:
% 16.86/3.18 | (39) add(5, all_13_0) = all_26_1 & count(all_26_1) = all_26_0 &
% 16.86/3.18 | count(all_13_0) = all_26_0 & collection(all_26_1)
% 16.86/3.18 |
% 16.86/3.18 | ALPHA: (39) implies:
% 16.86/3.18 | (40) count(all_13_0) = all_26_0
% 16.86/3.18 |
% 16.86/3.18 | DELTA: instantiating (34) with fresh symbols all_28_0, all_28_1 gives:
% 16.86/3.18 | (41) remove(5, all_13_0) = all_28_1 & count(all_28_1) = all_28_0 &
% 16.86/3.18 | count(all_13_0) = $sum(all_28_0, 1) & collection(all_28_1)
% 16.86/3.18 |
% 16.86/3.18 | ALPHA: (41) implies:
% 16.86/3.18 | (42) count(all_13_0) = $sum(all_28_0, 1)
% 16.86/3.18 |
% 16.86/3.18 | DELTA: instantiating (30) with fresh symbols all_30_0, all_30_1 gives:
% 16.86/3.18 | (43) remove(3, all_13_0) = all_30_1 & count(all_30_1) = all_30_0 &
% 16.86/3.18 | count(all_13_0) = $sum(all_30_0, 1) & collection(all_30_1)
% 16.86/3.18 |
% 16.86/3.18 | ALPHA: (43) implies:
% 16.86/3.18 | (44) count(all_13_0) = $sum(all_30_0, 1)
% 16.86/3.18 |
% 16.86/3.18 | DELTA: instantiating (26) with fresh symbols all_32_0, all_32_1 gives:
% 16.86/3.18 | (45) add(2, all_13_0) = all_32_1 & count(all_32_1) = all_32_0 &
% 16.86/3.18 | count(all_13_0) = all_32_0 & collection(all_32_1)
% 16.86/3.18 |
% 16.86/3.18 | ALPHA: (45) implies:
% 16.86/3.18 | (46) count(all_13_0) = all_32_0
% 16.86/3.18 |
% 16.86/3.18 | DELTA: instantiating (31) with fresh symbols all_34_0, all_34_1 gives:
% 16.86/3.18 | (47) add(3, all_13_0) = all_34_1 & count(all_34_1) = all_34_0 &
% 16.86/3.18 | count(all_13_0) = all_34_0 & collection(all_34_1)
% 16.86/3.18 |
% 16.86/3.18 | ALPHA: (47) implies:
% 16.86/3.18 | (48) count(all_13_0) = all_34_0
% 16.86/3.18 |
% 16.86/3.18 | DELTA: instantiating (25) with fresh symbols all_36_0, all_36_1 gives:
% 16.86/3.18 | (49) remove(2, all_13_0) = all_36_1 & count(all_36_1) = all_36_0 &
% 16.86/3.18 | count(all_13_0) = $sum(all_36_0, 1) & collection(all_36_1)
% 16.86/3.18 |
% 16.86/3.18 | ALPHA: (49) implies:
% 16.86/3.18 | (50) collection(all_36_1)
% 16.86/3.18 | (51) count(all_13_0) = $sum(all_36_0, 1)
% 16.86/3.18 | (52) count(all_36_1) = all_36_0
% 16.86/3.18 | (53) remove(2, all_13_0) = all_36_1
% 16.86/3.18 |
% 16.86/3.18 | DELTA: instantiating (33) with fresh symbols all_38_0, all_38_1, all_38_2
% 16.86/3.18 | gives:
% 16.86/3.18 | (54) ~ (all_38_0 = all_38_1) & remove(5, all_13_0) = all_38_2 &
% 16.86/3.18 | count(all_38_2) = all_38_1 & count(all_13_0) = all_38_0 &
% 16.86/3.18 | collection(all_38_2)
% 16.86/3.18 |
% 16.86/3.18 | ALPHA: (54) implies:
% 16.86/3.18 | (55) count(all_13_0) = all_38_0
% 16.86/3.18 |
% 16.86/3.18 | DELTA: instantiating (32) with fresh symbols all_40_0, all_40_1, all_40_2
% 16.86/3.18 | gives:
% 16.91/3.19 | (56) ~ ($difference(all_40_0, all_40_1) = -1) & add(5, all_13_0) =
% 16.91/3.19 | all_40_2 & count(all_40_2) = all_40_1 & count(all_13_0) = all_40_0 &
% 16.91/3.19 | collection(all_40_2)
% 16.91/3.19 |
% 16.91/3.19 | ALPHA: (56) implies:
% 16.91/3.19 | (57) count(all_13_0) = all_40_0
% 16.91/3.19 |
% 16.91/3.19 | DELTA: instantiating (24) with fresh symbols all_42_0, all_42_1, all_42_2
% 16.91/3.19 | gives:
% 16.91/3.19 | (58) ~ (all_42_0 = all_42_1) & remove(2, all_13_0) = all_42_2 &
% 16.91/3.19 | count(all_42_2) = all_42_1 & count(all_13_0) = all_42_0 &
% 16.91/3.19 | collection(all_42_2)
% 16.91/3.19 |
% 16.91/3.19 | ALPHA: (58) implies:
% 16.91/3.19 | (59) count(all_13_0) = all_42_0
% 16.91/3.19 | (60) count(all_42_2) = all_42_1
% 16.91/3.19 | (61) remove(2, all_13_0) = all_42_2
% 16.91/3.19 |
% 16.91/3.19 | DELTA: instantiating (23) with fresh symbols all_44_0, all_44_1, all_44_2
% 16.91/3.19 | gives:
% 16.91/3.19 | (62) ~ ($difference(all_44_0, all_44_1) = -1) & add(2, all_13_0) =
% 16.91/3.19 | all_44_2 & count(all_44_2) = all_44_1 & count(all_13_0) = all_44_0 &
% 16.91/3.19 | collection(all_44_2)
% 16.91/3.19 |
% 16.91/3.19 | ALPHA: (62) implies:
% 16.91/3.19 | (63) count(all_13_0) = all_44_0
% 16.91/3.19 |
% 16.91/3.19 | DELTA: instantiating (28) with fresh symbols all_46_0, all_46_1, all_46_2
% 16.91/3.19 | gives:
% 16.91/3.19 | (64) ~ ($difference(all_46_0, all_46_1) = -1) & add(3, all_13_0) =
% 16.91/3.19 | all_46_2 & count(all_46_2) = all_46_1 & count(all_13_0) = all_46_0 &
% 16.91/3.19 | collection(all_46_2)
% 16.91/3.19 |
% 16.91/3.19 | ALPHA: (64) implies:
% 16.91/3.19 | (65) count(all_13_0) = all_46_0
% 16.91/3.19 |
% 16.91/3.19 | DELTA: instantiating (29) with fresh symbols all_48_0, all_48_1, all_48_2
% 16.91/3.19 | gives:
% 16.91/3.19 | (66) ~ (all_48_0 = all_48_1) & remove(3, all_13_0) = all_48_2 &
% 16.91/3.19 | count(all_48_2) = all_48_1 & count(all_13_0) = all_48_0 &
% 16.91/3.19 | collection(all_48_2)
% 16.91/3.19 |
% 16.91/3.19 | ALPHA: (66) implies:
% 16.91/3.19 | (67) count(all_13_0) = all_48_0
% 16.91/3.19 |
% 16.91/3.19 | GROUND_INST: instantiating (14) with $sum(all_28_0, 1), all_32_0, all_13_0,
% 16.91/3.19 | simplifying with (42), (46) gives:
% 16.91/3.19 | (68) $difference(all_32_0, all_28_0) = 1
% 16.91/3.19 |
% 16.91/3.19 | GROUND_INST: instantiating (14) with all_32_0, $sum(all_36_0, 1), all_13_0,
% 16.91/3.19 | simplifying with (46), (51) gives:
% 16.91/3.19 | (69) $difference(all_36_0, all_32_0) = -1
% 16.91/3.19 |
% 16.91/3.19 | GROUND_INST: instantiating (14) with all_38_0, all_40_0, all_13_0, simplifying
% 16.91/3.19 | with (55), (57) gives:
% 16.91/3.19 | (70) all_40_0 = all_38_0
% 16.91/3.19 |
% 16.91/3.19 | GROUND_INST: instantiating (14) with all_34_0, all_40_0, all_13_0, simplifying
% 16.91/3.19 | with (48), (57) gives:
% 16.91/3.19 | (71) all_40_0 = all_34_0
% 16.91/3.19 |
% 16.91/3.19 | GROUND_INST: instantiating (14) with all_32_0, all_40_0, all_13_0, simplifying
% 16.91/3.19 | with (46), (57) gives:
% 16.91/3.19 | (72) all_40_0 = all_32_0
% 16.91/3.19 |
% 16.91/3.19 | GROUND_INST: instantiating (14) with all_42_0, all_44_0, all_13_0, simplifying
% 16.91/3.19 | with (59), (63) gives:
% 16.91/3.19 | (73) all_44_0 = all_42_0
% 16.91/3.19 |
% 16.91/3.19 | GROUND_INST: instantiating (14) with $sum(all_36_0, 1), all_44_0, all_13_0,
% 16.91/3.19 | simplifying with (51), (63) gives:
% 16.91/3.19 | (74) $difference(all_44_0, all_36_0) = 1
% 16.91/3.19 |
% 16.91/3.19 | GROUND_INST: instantiating (14) with $sum(all_30_0, 1), all_44_0, all_13_0,
% 16.91/3.19 | simplifying with (44), (63) gives:
% 16.91/3.19 | (75) $difference(all_44_0, all_30_0) = 1
% 16.91/3.19 |
% 16.91/3.19 | GROUND_INST: instantiating (14) with 2, all_46_0, all_13_0, simplifying with
% 16.91/3.19 | (22), (65) gives:
% 16.91/3.19 | (76) all_46_0 = 2
% 16.91/3.19 |
% 16.91/3.19 | GROUND_INST: instantiating (14) with $sum(all_28_0, 1), all_46_0, all_13_0,
% 16.91/3.19 | simplifying with (42), (65) gives:
% 16.91/3.19 | (77) $difference(all_46_0, all_28_0) = 1
% 16.91/3.19 |
% 16.91/3.19 | GROUND_INST: instantiating (14) with all_38_0, all_48_0, all_13_0, simplifying
% 16.91/3.19 | with (55), (67) gives:
% 16.91/3.19 | (78) all_48_0 = all_38_0
% 16.91/3.19 |
% 16.91/3.19 | GROUND_INST: instantiating (14) with all_26_0, all_48_0, all_13_0, simplifying
% 16.91/3.19 | with (40), (67) gives:
% 16.91/3.19 | (79) all_48_0 = all_26_0
% 16.91/3.19 |
% 16.91/3.19 | GROUND_INST: instantiating (16) with all_36_1, all_42_2, all_13_0, 2,
% 16.91/3.19 | simplifying with (53), (61) gives:
% 16.91/3.19 | (80) all_42_2 = all_36_1
% 16.91/3.19 |
% 16.91/3.20 | GROUND_INST: instantiating (16) with all_22_0, all_42_2, all_13_0, 2,
% 16.91/3.20 | simplifying with (38), (61) gives:
% 16.91/3.20 | (81) all_42_2 = all_22_0
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (78), (79) imply:
% 16.91/3.20 | (82) all_38_0 = all_26_0
% 16.91/3.20 |
% 16.91/3.20 | SIMP: (82) implies:
% 16.91/3.20 | (83) all_38_0 = all_26_0
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (76), (77) imply:
% 16.91/3.20 | (84) all_28_0 = 1
% 16.91/3.20 |
% 16.91/3.20 | SIMP: (84) implies:
% 16.91/3.20 | (85) all_28_0 = 1
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (73), (74) imply:
% 16.91/3.20 | (86) $difference(all_42_0, all_36_0) = 1
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (73), (75) imply:
% 16.91/3.20 | (87) $difference(all_42_0, all_30_0) = 1
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (86), (87) imply:
% 16.91/3.20 | (88) all_36_0 = all_30_0
% 16.91/3.20 |
% 16.91/3.20 | SIMP: (88) implies:
% 16.91/3.20 | (89) all_36_0 = all_30_0
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (80), (81) imply:
% 16.91/3.20 | (90) all_36_1 = all_22_0
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (70), (71) imply:
% 16.91/3.20 | (91) all_38_0 = all_34_0
% 16.91/3.20 |
% 16.91/3.20 | SIMP: (91) implies:
% 16.91/3.20 | (92) all_38_0 = all_34_0
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (71), (72) imply:
% 16.91/3.20 | (93) all_34_0 = all_32_0
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (83), (92) imply:
% 16.91/3.20 | (94) all_34_0 = all_26_0
% 16.91/3.20 |
% 16.91/3.20 | SIMP: (94) implies:
% 16.91/3.20 | (95) all_34_0 = all_26_0
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (69), (89) imply:
% 16.91/3.20 | (96) $difference(all_32_0, all_30_0) = 1
% 16.91/3.20 |
% 16.91/3.20 | SIMP: (96) implies:
% 16.91/3.20 | (97) $difference(all_32_0, all_30_0) = 1
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (93), (95) imply:
% 16.91/3.20 | (98) all_32_0 = all_26_0
% 16.91/3.20 |
% 16.91/3.20 | SIMP: (98) implies:
% 16.91/3.20 | (99) all_32_0 = all_26_0
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (68), (97) imply:
% 16.91/3.20 | (100) all_30_0 = all_28_0
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (97), (99) imply:
% 16.91/3.20 | (101) $difference(all_30_0, all_26_0) = -1
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (100), (101) imply:
% 16.91/3.20 | (102) $difference(all_28_0, all_26_0) = -1
% 16.91/3.20 |
% 16.91/3.20 | SIMP: (102) implies:
% 16.91/3.20 | (103) $difference(all_28_0, all_26_0) = -1
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (85), (103) imply:
% 16.91/3.20 | (104) all_26_0 = 2
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (101), (104) imply:
% 16.91/3.20 | (105) all_30_0 = 1
% 16.91/3.20 |
% 16.91/3.20 | COMBINE_EQS: (89), (105) imply:
% 16.91/3.20 | (106) all_36_0 = 1
% 16.91/3.20 |
% 16.91/3.20 | REDUCE: (60), (81) imply:
% 16.91/3.20 | (107) count(all_22_0) = all_42_1
% 16.91/3.20 |
% 16.91/3.20 | REDUCE: (52), (90), (106) imply:
% 16.91/3.20 | (108) count(all_22_0) = 1
% 16.91/3.20 |
% 16.91/3.20 | REDUCE: (50), (90) imply:
% 16.91/3.20 | (109) collection(all_22_0)
% 16.91/3.20 |
% 16.91/3.20 | GROUND_INST: instantiating (14) with 1, all_42_1, all_22_0, simplifying with
% 16.91/3.20 | (107), (108) gives:
% 16.91/3.20 | (110) all_42_1 = 1
% 16.91/3.20 |
% 16.91/3.20 | GROUND_INST: instantiating (8) with 5, all_22_0, 2, all_13_0, simplifying with
% 16.91/3.20 | (21), (37), (109) gives:
% 16.91/3.20 | (111) in(5, all_22_0) = 0
% 16.91/3.20 |
% 16.91/3.20 | GROUND_INST: instantiating (8) with 3, all_22_0, 2, all_13_0, simplifying with
% 16.91/3.20 | (20), (37), (109) gives:
% 16.91/3.20 | (112) in(3, all_22_0) = 0
% 16.91/3.20 |
% 16.91/3.20 | GROUND_INST: instantiating (7) with 2, all_22_0, all_13_0, simplifying with
% 16.91/3.20 | (37), (109) gives:
% 16.91/3.20 | (113) ? [v0: int] : ? [v1: int] : ? [v2: int] : ((v2 = v1 &
% 16.91/3.20 | count(all_22_0) = v1 & count(all_13_0) = v1) | ( ~ (v0 = 0) &
% 16.91/3.20 | in(2, all_22_0) = v0))
% 16.91/3.20 |
% 16.91/3.20 | GROUND_INST: instantiating (4) with 2, all_22_0, all_13_0, simplifying with
% 16.91/3.20 | (37), (109) gives:
% 16.91/3.20 | (114) ? [v0: int] : ? [v1: int] : ? [v2: int] : (( ~ (v2 = 0) & in(2,
% 16.91/3.20 | all_22_0) = v2) | ( ~ ($difference(v1, v0) = -1) &
% 16.91/3.20 | count(all_22_0) = v1 & count(all_13_0) = v0))
% 16.91/3.20 |
% 16.91/3.20 | GROUND_INST: instantiating (5) with 2, all_13_0, all_22_0, simplifying with
% 16.91/3.20 | (18), (38) gives:
% 16.91/3.20 | (115) ? [v0: int] : ( ~ (v0 = 0) & in(2, all_22_0) = v0)
% 16.91/3.20 |
% 16.91/3.20 | DELTA: instantiating (115) with fresh symbol all_68_0 gives:
% 16.91/3.20 | (116) ~ (all_68_0 = 0) & in(2, all_22_0) = all_68_0
% 16.91/3.20 |
% 16.91/3.20 | ALPHA: (116) implies:
% 16.91/3.20 | (117) in(2, all_22_0) = all_68_0
% 16.91/3.20 |
% 16.91/3.20 | DELTA: instantiating (114) with fresh symbols all_75_0, all_75_1, all_75_2
% 16.91/3.20 | gives:
% 16.91/3.21 | (118) ( ~ (all_75_0 = 0) & in(2, all_22_0) = all_75_0) | ( ~
% 16.91/3.21 | ($difference(all_75_1, all_75_2) = -1) & count(all_22_0) = all_75_1
% 16.91/3.21 | & count(all_13_0) = all_75_2)
% 16.91/3.21 |
% 16.91/3.21 | DELTA: instantiating (113) with fresh symbols all_81_0, all_81_1, all_81_2
% 16.91/3.21 | gives:
% 16.91/3.21 | (119) (all_81_0 = all_81_1 & count(all_22_0) = all_81_1 & count(all_13_0) =
% 16.91/3.21 | all_81_1) | ( ~ (all_81_2 = 0) & in(2, all_22_0) = all_81_2)
% 16.91/3.21 |
% 16.91/3.21 | BETA: splitting (118) gives:
% 16.91/3.21 |
% 16.91/3.21 | Case 1:
% 16.91/3.21 | |
% 16.91/3.21 | | (120) ~ (all_75_0 = 0) & in(2, all_22_0) = all_75_0
% 16.91/3.21 | |
% 16.91/3.21 | | ALPHA: (120) implies:
% 16.91/3.21 | | (121) ~ (all_75_0 = 0)
% 16.91/3.21 | | (122) in(2, all_22_0) = all_75_0
% 16.91/3.21 | |
% 16.91/3.21 | | BETA: splitting (119) gives:
% 16.91/3.21 | |
% 16.91/3.21 | | Case 1:
% 16.91/3.21 | | |
% 16.91/3.21 | | | (123) all_81_0 = all_81_1 & count(all_22_0) = all_81_1 &
% 16.91/3.21 | | | count(all_13_0) = all_81_1
% 16.91/3.21 | | |
% 16.91/3.21 | | | ALPHA: (123) implies:
% 16.91/3.21 | | | (124) count(all_13_0) = all_81_1
% 16.91/3.21 | | | (125) count(all_22_0) = all_81_1
% 16.91/3.21 | | |
% 17.03/3.21 | | | GROUND_INST: instantiating (14) with 2, all_81_1, all_13_0, simplifying
% 17.03/3.21 | | | with (22), (124) gives:
% 17.03/3.21 | | | (126) all_81_1 = 2
% 17.03/3.21 | | |
% 17.03/3.21 | | | GROUND_INST: instantiating (14) with 1, all_81_1, all_22_0, simplifying
% 17.03/3.21 | | | with (108), (125) gives:
% 17.03/3.21 | | | (127) all_81_1 = 1
% 17.03/3.21 | | |
% 17.03/3.21 | | | COMBINE_EQS: (126), (127) imply:
% 17.03/3.21 | | | (128) $false
% 17.03/3.21 | | |
% 17.03/3.21 | | | CLOSE: (128) is inconsistent.
% 17.03/3.21 | | |
% 17.03/3.21 | | Case 2:
% 17.03/3.21 | | |
% 17.03/3.21 | | | (129) ~ (all_81_2 = 0) & in(2, all_22_0) = all_81_2
% 17.03/3.21 | | |
% 17.03/3.21 | | | ALPHA: (129) implies:
% 17.03/3.21 | | | (130) in(2, all_22_0) = all_81_2
% 17.03/3.21 | | |
% 17.03/3.21 | | | GROUND_INST: instantiating (15) with all_68_0, all_81_2, all_22_0, 2,
% 17.03/3.21 | | | simplifying with (117), (130) gives:
% 17.03/3.21 | | | (131) all_81_2 = all_68_0
% 17.03/3.21 | | |
% 17.03/3.21 | | | GROUND_INST: instantiating (15) with all_75_0, all_81_2, all_22_0, 2,
% 17.03/3.21 | | | simplifying with (122), (130) gives:
% 17.03/3.21 | | | (132) all_81_2 = all_75_0
% 17.03/3.21 | | |
% 17.03/3.21 | | | COMBINE_EQS: (131), (132) imply:
% 17.03/3.21 | | | (133) all_75_0 = all_68_0
% 17.03/3.21 | | |
% 17.03/3.21 | | | REDUCE: (121), (133) imply:
% 17.03/3.21 | | | (134) ~ (all_68_0 = 0)
% 17.03/3.21 | | |
% 17.03/3.21 | | | GROUND_INST: instantiating (10) with 2, all_22_0, all_68_0, simplifying
% 17.03/3.21 | | | with (109), (117) gives:
% 17.03/3.21 | | | (135) all_68_0 = 0 | ? [v0: collection] : ? [v1: int] : ? [v2: int]
% 17.03/3.21 | | | : ( ~ ($difference(v2, v1) = 1) & remove(2, all_22_0) = v0 &
% 17.03/3.21 | | | count(v0) = v1 & count(all_22_0) = v2 & collection(v0))
% 17.03/3.21 | | |
% 17.03/3.21 | | | GROUND_INST: instantiating (12) with 2, all_22_0, all_68_0, simplifying
% 17.03/3.21 | | | with (109), (117) gives:
% 17.03/3.21 | | | (136) all_68_0 = 0 | ? [v0: collection] : ? [v1: int] : (remove(2,
% 17.03/3.21 | | | all_22_0) = v0 & count(v0) = v1 & count(all_22_0) = v1 &
% 17.03/3.21 | | | collection(v0))
% 17.03/3.21 | | |
% 17.03/3.21 | | | GROUND_INST: instantiating (3) with 3, all_22_0, simplifying with (109),
% 17.03/3.21 | | | (112) gives:
% 17.03/3.21 | | | (137) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~
% 17.03/3.21 | | | ($difference(v2, v1) = -1) & add(3, all_22_0) = v0 & count(v0)
% 17.03/3.21 | | | = v1 & count(all_22_0) = v2 & collection(v0))
% 17.03/3.21 | | |
% 17.03/3.21 | | | GROUND_INST: instantiating (11) with 3, all_22_0, simplifying with (109),
% 17.03/3.21 | | | (112) gives:
% 17.03/3.21 | | | (138) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1)
% 17.03/3.21 | | | & remove(3, all_22_0) = v0 & count(v0) = v1 & count(all_22_0) =
% 17.03/3.21 | | | v2 & collection(v0))
% 17.03/3.21 | | |
% 17.03/3.21 | | | GROUND_INST: instantiating (9) with 3, all_22_0, simplifying with (109),
% 17.03/3.21 | | | (112) gives:
% 17.03/3.21 | | | (139) ? [v0: collection] : ? [v1: int] : (remove(3, all_22_0) = v0 &
% 17.03/3.21 | | | count(v0) = v1 & count(all_22_0) = $sum(v1, 1) &
% 17.03/3.21 | | | collection(v0))
% 17.03/3.21 | | |
% 17.03/3.22 | | | GROUND_INST: instantiating (6) with 3, all_22_0, simplifying with (109),
% 17.03/3.22 | | | (112) gives:
% 17.03/3.22 | | | (140) ? [v0: collection] : ? [v1: int] : (add(3, all_22_0) = v0 &
% 17.03/3.22 | | | count(v0) = v1 & count(all_22_0) = v1 & collection(v0))
% 17.03/3.22 | | |
% 17.03/3.22 | | | GROUND_INST: instantiating (13) with 3, all_22_0, simplifying with (109),
% 17.03/3.22 | | | (112) gives:
% 17.03/3.22 | | | (141) ? [v0: collection] : (remove(3, all_22_0) = v0 & add(3, v0) =
% 17.03/3.22 | | | all_22_0 & collection(v0))
% 17.03/3.22 | | |
% 17.03/3.22 | | | GROUND_INST: instantiating (3) with 5, all_22_0, simplifying with (109),
% 17.03/3.22 | | | (111) gives:
% 17.03/3.22 | | | (142) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~
% 17.03/3.22 | | | ($difference(v2, v1) = -1) & add(5, all_22_0) = v0 & count(v0)
% 17.03/3.22 | | | = v1 & count(all_22_0) = v2 & collection(v0))
% 17.03/3.22 | | |
% 17.03/3.22 | | | GROUND_INST: instantiating (11) with 5, all_22_0, simplifying with (109),
% 17.03/3.22 | | | (111) gives:
% 17.03/3.22 | | | (143) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1)
% 17.03/3.22 | | | & remove(5, all_22_0) = v0 & count(v0) = v1 & count(all_22_0) =
% 17.03/3.22 | | | v2 & collection(v0))
% 17.03/3.22 | | |
% 17.03/3.22 | | | GROUND_INST: instantiating (9) with 5, all_22_0, simplifying with (109),
% 17.03/3.22 | | | (111) gives:
% 17.03/3.22 | | | (144) ? [v0: collection] : ? [v1: int] : (remove(5, all_22_0) = v0 &
% 17.03/3.22 | | | count(v0) = v1 & count(all_22_0) = $sum(v1, 1) &
% 17.03/3.22 | | | collection(v0))
% 17.03/3.22 | | |
% 17.03/3.22 | | | GROUND_INST: instantiating (6) with 5, all_22_0, simplifying with (109),
% 17.03/3.22 | | | (111) gives:
% 17.03/3.22 | | | (145) ? [v0: collection] : ? [v1: int] : (add(5, all_22_0) = v0 &
% 17.03/3.22 | | | count(v0) = v1 & count(all_22_0) = v1 & collection(v0))
% 17.03/3.22 | | |
% 17.03/3.22 | | | DELTA: instantiating (141) with fresh symbol all_145_0 gives:
% 17.03/3.22 | | | (146) remove(3, all_22_0) = all_145_0 & add(3, all_145_0) = all_22_0 &
% 17.03/3.22 | | | collection(all_145_0)
% 17.03/3.22 | | |
% 17.03/3.22 | | | ALPHA: (146) implies:
% 17.03/3.22 | | | (147) add(3, all_145_0) = all_22_0
% 17.03/3.22 | | | (148) remove(3, all_22_0) = all_145_0
% 17.03/3.22 | | |
% 17.03/3.22 | | | DELTA: instantiating (145) with fresh symbols all_187_0, all_187_1 gives:
% 17.03/3.22 | | | (149) add(5, all_22_0) = all_187_1 & count(all_187_1) = all_187_0 &
% 17.03/3.22 | | | count(all_22_0) = all_187_0 & collection(all_187_1)
% 17.03/3.22 | | |
% 17.03/3.22 | | | ALPHA: (149) implies:
% 17.03/3.22 | | | (150) count(all_22_0) = all_187_0
% 17.03/3.22 | | |
% 17.03/3.22 | | | DELTA: instantiating (140) with fresh symbols all_189_0, all_189_1 gives:
% 17.03/3.22 | | | (151) add(3, all_22_0) = all_189_1 & count(all_189_1) = all_189_0 &
% 17.03/3.22 | | | count(all_22_0) = all_189_0 & collection(all_189_1)
% 17.03/3.22 | | |
% 17.03/3.22 | | | ALPHA: (151) implies:
% 17.09/3.22 | | | (152) count(all_22_0) = all_189_0
% 17.09/3.22 | | |
% 17.09/3.22 | | | DELTA: instantiating (144) with fresh symbols all_191_0, all_191_1 gives:
% 17.09/3.22 | | | (153) remove(5, all_22_0) = all_191_1 & count(all_191_1) = all_191_0 &
% 17.09/3.22 | | | count(all_22_0) = $sum(all_191_0, 1) & collection(all_191_1)
% 17.09/3.22 | | |
% 17.09/3.22 | | | ALPHA: (153) implies:
% 17.09/3.22 | | | (154) count(all_22_0) = $sum(all_191_0, 1)
% 17.09/3.22 | | |
% 17.09/3.22 | | | DELTA: instantiating (139) with fresh symbols all_195_0, all_195_1 gives:
% 17.09/3.22 | | | (155) remove(3, all_22_0) = all_195_1 & count(all_195_1) = all_195_0 &
% 17.09/3.22 | | | count(all_22_0) = $sum(all_195_0, 1) & collection(all_195_1)
% 17.09/3.22 | | |
% 17.09/3.22 | | | ALPHA: (155) implies:
% 17.09/3.22 | | | (156) collection(all_195_1)
% 17.09/3.22 | | | (157) count(all_22_0) = $sum(all_195_0, 1)
% 17.09/3.22 | | | (158) count(all_195_1) = all_195_0
% 17.09/3.22 | | | (159) remove(3, all_22_0) = all_195_1
% 17.09/3.22 | | |
% 17.09/3.22 | | | DELTA: instantiating (143) with fresh symbols all_197_0, all_197_1,
% 17.09/3.22 | | | all_197_2 gives:
% 17.09/3.22 | | | (160) ~ (all_197_0 = all_197_1) & remove(5, all_22_0) = all_197_2 &
% 17.09/3.22 | | | count(all_197_2) = all_197_1 & count(all_22_0) = all_197_0 &
% 17.09/3.22 | | | collection(all_197_2)
% 17.09/3.22 | | |
% 17.09/3.22 | | | ALPHA: (160) implies:
% 17.09/3.22 | | | (161) count(all_22_0) = all_197_0
% 17.09/3.22 | | |
% 17.09/3.22 | | | DELTA: instantiating (142) with fresh symbols all_199_0, all_199_1,
% 17.09/3.22 | | | all_199_2 gives:
% 17.09/3.22 | | | (162) ~ ($difference(all_199_0, all_199_1) = -1) & add(5, all_22_0) =
% 17.09/3.22 | | | all_199_2 & count(all_199_2) = all_199_1 & count(all_22_0) =
% 17.09/3.22 | | | all_199_0 & collection(all_199_2)
% 17.09/3.22 | | |
% 17.09/3.22 | | | ALPHA: (162) implies:
% 17.09/3.22 | | | (163) count(all_22_0) = all_199_0
% 17.09/3.22 | | |
% 17.09/3.22 | | | DELTA: instantiating (138) with fresh symbols all_209_0, all_209_1,
% 17.09/3.22 | | | all_209_2 gives:
% 17.09/3.22 | | | (164) ~ (all_209_0 = all_209_1) & remove(3, all_22_0) = all_209_2 &
% 17.09/3.22 | | | count(all_209_2) = all_209_1 & count(all_22_0) = all_209_0 &
% 17.09/3.22 | | | collection(all_209_2)
% 17.09/3.22 | | |
% 17.09/3.22 | | | ALPHA: (164) implies:
% 17.09/3.22 | | | (165) count(all_22_0) = all_209_0
% 17.09/3.22 | | | (166) count(all_209_2) = all_209_1
% 17.09/3.22 | | | (167) remove(3, all_22_0) = all_209_2
% 17.09/3.22 | | |
% 17.09/3.22 | | | DELTA: instantiating (137) with fresh symbols all_229_0, all_229_1,
% 17.09/3.22 | | | all_229_2 gives:
% 17.09/3.22 | | | (168) ~ ($difference(all_229_0, all_229_1) = -1) & add(3, all_22_0) =
% 17.09/3.22 | | | all_229_2 & count(all_229_2) = all_229_1 & count(all_22_0) =
% 17.09/3.22 | | | all_229_0 & collection(all_229_2)
% 17.09/3.22 | | |
% 17.09/3.22 | | | ALPHA: (168) implies:
% 17.09/3.22 | | | (169) count(all_22_0) = all_229_0
% 17.09/3.22 | | |
% 17.09/3.22 | | | BETA: splitting (136) gives:
% 17.09/3.22 | | |
% 17.09/3.22 | | | Case 1:
% 17.09/3.22 | | | |
% 17.09/3.22 | | | | (170) all_68_0 = 0
% 17.09/3.22 | | | |
% 17.09/3.22 | | | | REDUCE: (134), (170) imply:
% 17.09/3.22 | | | | (171) $false
% 17.09/3.22 | | | |
% 17.09/3.22 | | | | CLOSE: (171) is inconsistent.
% 17.09/3.22 | | | |
% 17.09/3.22 | | | Case 2:
% 17.09/3.22 | | | |
% 17.09/3.22 | | | | (172) ? [v0: collection] : ? [v1: int] : (remove(2, all_22_0) = v0
% 17.09/3.22 | | | | & count(v0) = v1 & count(all_22_0) = v1 & collection(v0))
% 17.09/3.22 | | | |
% 17.09/3.22 | | | | DELTA: instantiating (172) with fresh symbols all_242_0, all_242_1
% 17.09/3.22 | | | | gives:
% 17.09/3.22 | | | | (173) remove(2, all_22_0) = all_242_1 & count(all_242_1) = all_242_0
% 17.09/3.22 | | | | & count(all_22_0) = all_242_0 & collection(all_242_1)
% 17.09/3.22 | | | |
% 17.09/3.22 | | | | ALPHA: (173) implies:
% 17.09/3.22 | | | | (174) count(all_22_0) = all_242_0
% 17.09/3.22 | | | |
% 17.09/3.22 | | | | BETA: splitting (135) gives:
% 17.09/3.22 | | | |
% 17.09/3.22 | | | | Case 1:
% 17.09/3.22 | | | | |
% 17.09/3.22 | | | | | (175) all_68_0 = 0
% 17.09/3.22 | | | | |
% 17.09/3.22 | | | | | REDUCE: (134), (175) imply:
% 17.09/3.23 | | | | | (176) $false
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | CLOSE: (176) is inconsistent.
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | Case 2:
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | (177) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~
% 17.09/3.23 | | | | | ($difference(v2, v1) = 1) & remove(2, all_22_0) = v0 &
% 17.09/3.23 | | | | | count(v0) = v1 & count(all_22_0) = v2 & collection(v0))
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | DELTA: instantiating (177) with fresh symbols all_262_0, all_262_1,
% 17.09/3.23 | | | | | all_262_2 gives:
% 17.09/3.23 | | | | | (178) ~ ($difference(all_262_0, all_262_1) = 1) & remove(2,
% 17.09/3.23 | | | | | all_22_0) = all_262_2 & count(all_262_2) = all_262_1 &
% 17.09/3.23 | | | | | count(all_22_0) = all_262_0 & collection(all_262_2)
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | ALPHA: (178) implies:
% 17.09/3.23 | | | | | (179) count(all_22_0) = all_262_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (14) with 1, all_189_0, all_22_0,
% 17.09/3.23 | | | | | simplifying with (108), (152) gives:
% 17.09/3.23 | | | | | (180) all_189_0 = 1
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (14) with all_199_0, all_209_0, all_22_0,
% 17.09/3.23 | | | | | simplifying with (163), (165) gives:
% 17.09/3.23 | | | | | (181) all_209_0 = all_199_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (14) with $sum(all_195_0, 1), all_209_0,
% 17.09/3.23 | | | | | all_22_0, simplifying with (157), (165) gives:
% 17.09/3.23 | | | | | (182) $difference(all_209_0, all_195_0) = 1
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (14) with $sum(all_191_0, 1), all_209_0,
% 17.09/3.23 | | | | | all_22_0, simplifying with (154), (165) gives:
% 17.09/3.23 | | | | | (183) $difference(all_209_0, all_191_0) = 1
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (14) with all_189_0, all_209_0, all_22_0,
% 17.09/3.23 | | | | | simplifying with (152), (165) gives:
% 17.09/3.23 | | | | | (184) all_209_0 = all_189_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (14) with all_197_0, all_229_0, all_22_0,
% 17.09/3.23 | | | | | simplifying with (161), (169) gives:
% 17.09/3.23 | | | | | (185) all_229_0 = all_197_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (14) with $sum(all_195_0, 1), all_229_0,
% 17.09/3.23 | | | | | all_22_0, simplifying with (157), (169) gives:
% 17.09/3.23 | | | | | (186) $difference(all_229_0, all_195_0) = 1
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (14) with all_229_0, all_242_0, all_22_0,
% 17.09/3.23 | | | | | simplifying with (169), (174) gives:
% 17.09/3.23 | | | | | (187) all_242_0 = all_229_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (14) with all_242_0, all_262_0, all_22_0,
% 17.09/3.23 | | | | | simplifying with (174), (179) gives:
% 17.09/3.23 | | | | | (188) all_262_0 = all_242_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (14) with all_187_0, all_262_0, all_22_0,
% 17.09/3.23 | | | | | simplifying with (150), (179) gives:
% 17.09/3.23 | | | | | (189) all_262_0 = all_187_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (16) with all_195_1, all_209_2, all_22_0,
% 17.09/3.23 | | | | | 3, simplifying with (159), (167) gives:
% 17.09/3.23 | | | | | (190) all_209_2 = all_195_1
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (16) with all_145_0, all_209_2, all_22_0,
% 17.09/3.23 | | | | | 3, simplifying with (148), (167) gives:
% 17.09/3.23 | | | | | (191) all_209_2 = all_145_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | COMBINE_EQS: (188), (189) imply:
% 17.09/3.23 | | | | | (192) all_242_0 = all_187_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | SIMP: (192) implies:
% 17.09/3.23 | | | | | (193) all_242_0 = all_187_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | COMBINE_EQS: (187), (193) imply:
% 17.09/3.23 | | | | | (194) all_229_0 = all_187_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | SIMP: (194) implies:
% 17.09/3.23 | | | | | (195) all_229_0 = all_187_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | COMBINE_EQS: (185), (195) imply:
% 17.09/3.23 | | | | | (196) all_197_0 = all_187_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | COMBINE_EQS: (185), (186) imply:
% 17.09/3.23 | | | | | (197) $difference(all_197_0, all_195_0) = 1
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | COMBINE_EQS: (181), (183) imply:
% 17.09/3.23 | | | | | (198) $difference(all_199_0, all_191_0) = 1
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | COMBINE_EQS: (181), (182) imply:
% 17.09/3.23 | | | | | (199) $difference(all_199_0, all_195_0) = 1
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | COMBINE_EQS: (181), (184) imply:
% 17.09/3.23 | | | | | (200) all_199_0 = all_189_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | COMBINE_EQS: (190), (191) imply:
% 17.09/3.23 | | | | | (201) all_195_1 = all_145_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | COMBINE_EQS: (198), (200) imply:
% 17.09/3.23 | | | | | (202) $difference(all_191_0, all_189_0) = -1
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | COMBINE_EQS: (198), (199) imply:
% 17.09/3.23 | | | | | (203) all_195_0 = all_191_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | SIMP: (203) implies:
% 17.09/3.23 | | | | | (204) all_195_0 = all_191_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | COMBINE_EQS: (196), (197) imply:
% 17.09/3.23 | | | | | (205) $difference(all_195_0, all_187_0) = -1
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | SIMP: (205) implies:
% 17.09/3.23 | | | | | (206) $difference(all_195_0, all_187_0) = -1
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | COMBINE_EQS: (204), (206) imply:
% 17.09/3.23 | | | | | (207) $difference(all_191_0, all_187_0) = -1
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | SIMP: (207) implies:
% 17.09/3.23 | | | | | (208) $difference(all_191_0, all_187_0) = -1
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | COMBINE_EQS: (202), (208) imply:
% 17.09/3.23 | | | | | (209) all_189_0 = all_187_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | SIMP: (209) implies:
% 17.09/3.23 | | | | | (210) all_189_0 = all_187_0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | COMBINE_EQS: (180), (210) imply:
% 17.09/3.23 | | | | | (211) all_187_0 = 1
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | COMBINE_EQS: (206), (211) imply:
% 17.09/3.23 | | | | | (212) all_195_0 = 0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | REDUCE: (166), (191) imply:
% 17.09/3.23 | | | | | (213) count(all_145_0) = all_209_1
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | REDUCE: (158), (201), (212) imply:
% 17.09/3.23 | | | | | (214) count(all_145_0) = 0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | REDUCE: (156), (201) imply:
% 17.09/3.23 | | | | | (215) collection(all_145_0)
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (14) with 0, all_209_1, all_145_0,
% 17.09/3.23 | | | | | simplifying with (213), (214) gives:
% 17.09/3.23 | | | | | (216) all_209_1 = 0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (2) with all_145_0, simplifying with (214),
% 17.09/3.23 | | | | | (215) gives:
% 17.09/3.23 | | | | | (217) all_145_0 = empty
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (8) with 5, all_145_0, 3, all_22_0,
% 17.09/3.23 | | | | | simplifying with (111), (147), (215) gives:
% 17.09/3.23 | | | | | (218) in(5, all_145_0) = 0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | REDUCE: (217), (218) imply:
% 17.09/3.23 | | | | | (219) in(5, empty) = 0
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | GROUND_INST: instantiating (1) with 5, simplifying with (219) gives:
% 17.09/3.23 | | | | | (220) $false
% 17.09/3.23 | | | | |
% 17.09/3.23 | | | | | CLOSE: (220) is inconsistent.
% 17.09/3.23 | | | | |
% 17.09/3.24 | | | | End of split
% 17.09/3.24 | | | |
% 17.09/3.24 | | | End of split
% 17.09/3.24 | | |
% 17.09/3.24 | | End of split
% 17.09/3.24 | |
% 17.09/3.24 | Case 2:
% 17.09/3.24 | |
% 17.09/3.24 | | (221) ~ ($difference(all_75_1, all_75_2) = -1) & count(all_22_0) =
% 17.09/3.24 | | all_75_1 & count(all_13_0) = all_75_2
% 17.09/3.24 | |
% 17.09/3.24 | | ALPHA: (221) implies:
% 17.09/3.24 | | (222) ~ ($difference(all_75_1, all_75_2) = -1)
% 17.09/3.24 | | (223) count(all_13_0) = all_75_2
% 17.09/3.24 | | (224) count(all_22_0) = all_75_1
% 17.09/3.24 | |
% 17.09/3.24 | | GROUND_INST: instantiating (14) with 2, all_75_2, all_13_0, simplifying with
% 17.09/3.24 | | (22), (223) gives:
% 17.09/3.24 | | (225) all_75_2 = 2
% 17.09/3.24 | |
% 17.09/3.24 | | GROUND_INST: instantiating (14) with 1, all_75_1, all_22_0, simplifying with
% 17.09/3.24 | | (108), (224) gives:
% 17.09/3.24 | | (226) all_75_1 = 1
% 17.09/3.24 | |
% 17.09/3.24 | | REDUCE: (222), (225), (226) imply:
% 17.09/3.24 | | (227) $false
% 17.09/3.24 | |
% 17.09/3.24 | | CLOSE: (227) is inconsistent.
% 17.09/3.24 | |
% 17.09/3.24 | End of split
% 17.09/3.24 |
% 17.09/3.24 End of proof
% 17.09/3.24 % SZS output end Proof for theBenchmark
% 17.09/3.24
% 17.09/3.24 2612ms
%------------------------------------------------------------------------------