TSTP Solution File: DAT039_1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : DAT039_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 : n026.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 11.69s 2.43s
% Output : Proof 17.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT039_1 : TPTP v8.1.2. Released v5.0.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Thu Aug 24 14:18:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.62 ________ _____
% 0.20/0.62 ___ __ \_________(_)________________________________
% 0.20/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.62
% 0.20/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.62 (2023-06-19)
% 0.20/0.62
% 0.20/0.62 (c) Philipp Rümmer, 2009-2023
% 0.20/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.62 Amanda Stjerna.
% 0.20/0.62 Free software under BSD-3-Clause.
% 0.20/0.62
% 0.20/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.62
% 0.20/0.62 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.63 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 2.43/1.13 Prover 1: Preprocessing ...
% 2.43/1.14 Prover 4: Preprocessing ...
% 3.04/1.17 Prover 0: Preprocessing ...
% 3.04/1.17 Prover 3: Preprocessing ...
% 3.04/1.17 Prover 5: Preprocessing ...
% 3.04/1.17 Prover 2: Preprocessing ...
% 3.04/1.18 Prover 6: Preprocessing ...
% 3.97/1.51 Prover 3: Constructing countermodel ...
% 3.97/1.52 Prover 1: Constructing countermodel ...
% 3.97/1.53 Prover 5: Proving ...
% 3.97/1.53 Prover 6: Constructing countermodel ...
% 5.05/1.56 Prover 4: Constructing countermodel ...
% 5.05/1.57 Prover 2: Proving ...
% 5.05/1.57 Prover 0: Proving ...
% 5.05/1.62 Prover 3: gave up
% 5.05/1.62 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.15/1.64 Prover 6: gave up
% 6.15/1.64 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 6.15/1.64 Prover 1: gave up
% 6.15/1.65 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 6.27/1.66 Prover 7: Preprocessing ...
% 6.27/1.68 Prover 8: Preprocessing ...
% 6.27/1.69 Prover 9: Preprocessing ...
% 7.12/1.78 Prover 7: Constructing countermodel ...
% 7.12/1.78 Prover 8: Warning: ignoring some quantifiers
% 7.12/1.79 Prover 8: Constructing countermodel ...
% 7.12/1.83 Prover 7: gave up
% 7.12/1.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 7.75/1.85 Prover 9: Constructing countermodel ...
% 7.75/1.87 Prover 10: Preprocessing ...
% 7.98/1.90 Prover 8: gave up
% 7.98/1.91 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 8.46/1.95 Prover 11: Preprocessing ...
% 8.46/1.97 Prover 10: Constructing countermodel ...
% 8.46/2.01 Prover 10: gave up
% 9.00/2.02 Prover 12: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=2024365391
% 9.00/2.04 Prover 11: Constructing countermodel ...
% 9.32/2.08 Prover 12: Preprocessing ...
% 9.32/2.19 Prover 12: Proving ...
% 11.69/2.43 Prover 0: proved (1795ms)
% 11.69/2.43
% 11.69/2.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 11.69/2.43
% 11.69/2.44 Prover 9: stopped
% 11.69/2.44 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 11.69/2.44 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 11.69/2.44 Prover 5: stopped
% 11.69/2.44 Prover 12: stopped
% 11.69/2.44 Prover 2: stopped
% 11.69/2.44 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 12.06/2.45 Prover 13: Preprocessing ...
% 12.06/2.45 Prover 16: Preprocessing ...
% 12.06/2.46 Prover 19: Preprocessing ...
% 12.06/2.49 Prover 16: Warning: ignoring some quantifiers
% 12.06/2.49 Prover 13: Warning: ignoring some quantifiers
% 12.06/2.50 Prover 16: Constructing countermodel ...
% 12.06/2.50 Prover 13: Constructing countermodel ...
% 12.06/2.50 Prover 19: Warning: ignoring some quantifiers
% 12.06/2.51 Prover 19: Constructing countermodel ...
% 12.82/2.58 Prover 13: gave up
% 12.82/2.58 Prover 19: gave up
% 13.86/2.75 Prover 16: gave up
% 16.97/3.29 Prover 11: Found proof (size 213)
% 16.97/3.29 Prover 11: proved (1383ms)
% 17.22/3.30 Prover 4: stopped
% 17.22/3.30
% 17.22/3.30 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 17.22/3.30
% 17.43/3.34 % SZS output start Proof for theBenchmark
% 17.44/3.34 Assumptions after simplification:
% 17.44/3.34 ---------------------------------
% 17.44/3.34
% 17.44/3.34 (ax1)
% 17.44/3.36 collection(empty) & ! [v0: collection] : ! [v1: int] : ( ~ ($lesseq(v1, -1))
% 17.44/3.36 | ~ (count(v0) = v1) | ~ collection(v0)) & ! [v0: int] : ~ (in(v0,
% 17.44/3.36 empty) = 0)
% 17.44/3.36
% 17.44/3.36 (ax2)
% 17.44/3.37 collection(empty) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] :
% 17.44/3.37 ( ~ (add(v0, v1) = v2) | ~ collection(v1) | in(v0, v2) = 0) & ! [v0:
% 17.44/3.37 collection] : (v0 = empty | ~ (count(v0) = 0) | ~ collection(v0)) & !
% 17.44/3.37 [v0: int] : (v0 = 0 | ~ (count(empty) = v0))
% 17.44/3.37
% 17.44/3.37 (ax3)
% 17.44/3.37 ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 17.44/3.37 v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int] : (add(v0,
% 17.44/3.37 v1) = v3 & count(v3) = v4 & count(v1) = $sum(v4, -1) & collection(v3)))
% 17.44/3.37 & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0,
% 17.44/3.37 v1) = v2) | ~ collection(v1) | ? [v3: int] : ( ~ (v3 = 0) & in(v0, v2)
% 17.44/3.37 = v3)) & ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~
% 17.44/3.38 (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ?
% 17.44/3.38 [v5: int] : (($difference(v5, v4) = -1 & count(v2) = v4 & count(v1) =
% 17.44/3.38 $sum(v4, -1)) | (v3 = 0 & in(v0, v1) = 0))) & ! [v0: int] : ! [v1:
% 17.44/3.38 collection] : ! [v2: collection] : ( ~ (add(v0, v1) = v2) | ~
% 17.44/3.38 collection(v1) | ? [v3: int] : ? [v4: int] : ? [v5: int] : (( ~ (v5 = 0)
% 17.44/3.38 & in(v0, v1) = v5) | ( ~ ($difference(v4, v3) = -1) & count(v2) = v3 &
% 17.44/3.38 count(v1) = v4))) & ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1)
% 17.44/3.38 = 0) | ~ collection(v1) | ? [v2: collection] : ? [v3: int] : ? [v4:
% 17.44/3.38 int] : ( ~ ($difference(v4, v3) = -1) & add(v0, v1) = v2 & count(v2) = v3
% 17.44/3.38 & count(v1) = v4 & collection(v2)))
% 17.44/3.38
% 17.44/3.38 (ax4)
% 17.44/3.39 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : !
% 17.44/3.39 [v4: int] : (v4 = 0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = v4) | ~
% 17.44/3.39 collection(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5)) & ! [v0:
% 17.44/3.39 int] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v3 = 0 |
% 17.44/3.39 ~ (add(v0, v1) = v2) | ~ (in(v0, v2) = v3) | ~ collection(v1)) & ! [v0:
% 17.44/3.39 int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : (v2 = v0 |
% 17.44/3.39 ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | in(v0, v1)
% 17.44/3.39 = 0) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~
% 17.44/3.39 (in(v0, v1) = v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int] :
% 17.44/3.39 ? [v5: int] : ( ~ (v5 = v4) & add(v0, v1) = v3 & count(v3) = v4 & count(v1)
% 17.44/3.39 = v5 & collection(v3))) & ! [v0: int] : ! [v1: collection] : ! [v2:
% 17.44/3.39 collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: int] : ?
% 17.44/3.39 [v4: int] : ? [v5: int] : ((v5 = v4 & count(v2) = v4 & count(v1) = v4) | (
% 17.44/3.39 ~ (v3 = 0) & in(v0, v1) = v3))) & ! [v0: int] : ! [v1: collection] :
% 17.44/3.39 ! [v2: collection] : ( ~ (add(v0, v1) = v2) | ~ collection(v1) | ? [v3: int]
% 17.44/3.39 : ? [v4: int] : ? [v5: int] : ((v5 = 0 & in(v0, v1) = 0) | ( ~ (v4 = v3) &
% 17.44/3.39 count(v2) = v3 & count(v1) = v4))) & ! [v0: int] : ! [v1: collection]
% 17.44/3.39 : ( ~ (in(v0, v1) = 0) | ~ collection(v1) | ? [v2: collection] : ? [v3:
% 17.44/3.39 int] : (add(v0, v1) = v2 & count(v2) = v3 & count(v1) = v3 &
% 17.44/3.39 collection(v2)))
% 17.44/3.39
% 17.44/3.39 (ax5)
% 17.44/3.39 ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : !
% 17.44/3.39 [v4: int] : (v4 = 0 | v2 = v0 | ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) =
% 17.44/3.39 v4) | ~ collection(v1) | ? [v5: int] : ( ~ (v5 = 0) & in(v0, v1) = v5))
% 17.44/3.39 & ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection] : (
% 17.44/3.39 ~ (remove(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~ collection(v1) | in(v0,
% 17.44/3.39 v1) = 0) & ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 |
% 17.44/3.39 ~ (in(v0, v1) = v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int]
% 17.44/3.39 : ? [v5: int] : ( ~ ($difference(v5, v4) = 1) & remove(v0, v1) = v3 &
% 17.44/3.39 count(v3) = v4 & count(v1) = v5 & collection(v3))) & ! [v0: int] : !
% 17.44/3.39 [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) = v2) | ~
% 17.44/3.39 (in(v0, v2) = 0) | ~ collection(v1)) & ! [v0: int] : ! [v1: collection] :
% 17.44/3.39 ! [v2: collection] : ( ~ (remove(v0, v1) = v2) | ~ collection(v1) | ? [v3:
% 17.44/3.39 int] : ? [v4: int] : ? [v5: int] : (($difference(v5, v4) = 1 & count(v2)
% 17.44/3.40 = v4 & count(v1) = $sum(v4, 1)) | ( ~ (v3 = 0) & in(v0, v1) = v3))) & !
% 17.44/3.40 [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) =
% 17.44/3.40 v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ? [v5: int] :
% 17.44/3.40 ((v5 = 0 & in(v0, v1) = 0) | ( ~ ($difference(v4, v3) = 1) & count(v2) = v3
% 17.44/3.40 & count(v1) = v4))) & ! [v0: int] : ! [v1: collection] : ( ~ (in(v0,
% 17.44/3.40 v1) = 0) | ~ collection(v1) | ? [v2: collection] : ? [v3: int] :
% 17.44/3.40 (remove(v0, v1) = v2 & count(v2) = v3 & count(v1) = $sum(v3, 1) &
% 17.44/3.40 collection(v2)))
% 17.44/3.40
% 17.44/3.40 (ax6)
% 17.44/3.40 ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~ (in(v0, v1) =
% 17.44/3.40 v2) | ~ collection(v1) | ? [v3: collection] : ? [v4: int] : (remove(v0,
% 17.44/3.40 v1) = v3 & count(v3) = v4 & count(v1) = v4 & collection(v3))) & ! [v0:
% 17.44/3.40 int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) = v2)
% 17.44/3.40 | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ? [v5: int] : ((v5 = v4
% 17.44/3.40 & count(v2) = v4 & count(v1) = v4) | (v3 = 0 & in(v0, v1) = 0))) & !
% 17.44/3.40 [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1) =
% 17.44/3.40 v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ? [v5: int] : ((
% 17.44/3.40 ~ (v5 = 0) & in(v0, v1) = v5) | ( ~ (v4 = v3) & count(v2) = v3 &
% 17.44/3.40 count(v1) = v4))) & ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1)
% 17.44/3.40 = 0) | ~ collection(v1) | ? [v2: collection] : ? [v3: int] : ? [v4:
% 17.44/3.40 int] : ( ~ (v4 = v3) & remove(v0, v1) = v2 & count(v2) = v3 & count(v1) =
% 17.44/3.40 v4 & collection(v2)))
% 17.44/3.40
% 17.44/3.40 (ax7)
% 17.71/3.40 ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (remove(v0, v1)
% 17.71/3.40 = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: collection] : ((v4 = v1
% 17.71/3.40 & add(v0, v2) = v1) | ( ~ (v3 = 0) & in(v0, v1) = v3))) & ! [v0: int] :
% 17.71/3.40 ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~ collection(v1) | ? [v2:
% 17.71/3.40 collection] : (remove(v0, v1) = v2 & add(v0, v2) = v1 & collection(v2)))
% 17.71/3.40
% 17.71/3.40 (co1)
% 17.71/3.40 ? [v0: collection] : ? [v1: int] : ($lesseq(4, v1) & count(v0) = 2 & in(v1,
% 17.71/3.40 v0) = 0 & in(3, v0) = 0 & in(2, v0) = 0 & collection(v0))
% 17.71/3.40
% 17.71/3.40 (function-axioms)
% 17.71/3.41 ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int]
% 17.71/3.41 : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) = v0)) & ! [v0:
% 17.71/3.41 collection] : ! [v1: collection] : ! [v2: collection] : ! [v3: int] : (v1
% 17.71/3.41 = v0 | ~ (add(v3, v2) = v1) | ~ (add(v3, v2) = v0)) & ! [v0:
% 17.71/3.41 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: collection] : !
% 17.71/3.41 [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0)) & ! [v0:
% 17.71/3.41 int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~ (count(v2) = v1) |
% 17.71/3.41 ~ (count(v2) = v0))
% 17.71/3.41
% 17.71/3.41 Those formulas are unsatisfiable:
% 17.71/3.41 ---------------------------------
% 17.71/3.41
% 17.71/3.41 Begin of proof
% 17.71/3.41 |
% 17.71/3.41 | ALPHA: (ax1) implies:
% 17.71/3.41 | (1) ! [v0: int] : ~ (in(v0, empty) = 0)
% 17.71/3.41 |
% 17.71/3.41 | ALPHA: (ax2) implies:
% 17.71/3.41 | (2) ! [v0: collection] : (v0 = empty | ~ (count(v0) = 0) | ~
% 17.71/3.41 | collection(v0))
% 17.71/3.41 |
% 17.71/3.41 | ALPHA: (ax3) implies:
% 17.71/3.41 | (3) ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~
% 17.71/3.41 | collection(v1) | ? [v2: collection] : ? [v3: int] : ? [v4: int] :
% 17.71/3.41 | ( ~ ($difference(v4, v3) = -1) & add(v0, v1) = v2 & count(v2) = v3 &
% 17.71/3.41 | count(v1) = v4 & collection(v2)))
% 17.71/3.41 | (4) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~ (add(v0,
% 17.71/3.41 | v1) = v2) | ~ collection(v1) | ? [v3: int] : ? [v4: int] : ?
% 17.71/3.41 | [v5: int] : (( ~ (v5 = 0) & in(v0, v1) = v5) | ( ~ ($difference(v4,
% 17.71/3.41 | v3) = -1) & count(v2) = v3 & count(v1) = v4)))
% 17.71/3.41 | (5) ! [v0: int] : ! [v1: collection] : ! [v2: collection] : ( ~
% 17.71/3.41 | (remove(v0, v1) = v2) | ~ collection(v1) | ? [v3: int] : ( ~ (v3 =
% 17.71/3.41 | 0) & in(v0, v2) = v3))
% 17.71/3.41 |
% 17.71/3.41 | ALPHA: (ax4) implies:
% 17.71/3.42 | (6) ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~
% 17.71/3.42 | collection(v1) | ? [v2: collection] : ? [v3: int] : (add(v0, v1) =
% 17.71/3.42 | v2 & count(v2) = v3 & count(v1) = v3 & collection(v2)))
% 17.71/3.42 | (7) ! [v0: int] : ! [v1: collection] : ! [v2: int] : ! [v3: collection]
% 17.71/3.42 | : (v2 = v0 | ~ (add(v2, v1) = v3) | ~ (in(v0, v3) = 0) | ~
% 17.71/3.42 | collection(v1) | in(v0, v1) = 0)
% 17.71/3.42 |
% 17.71/3.42 | ALPHA: (ax5) implies:
% 17.71/3.42 | (8) ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~
% 17.71/3.42 | collection(v1) | ? [v2: collection] : ? [v3: int] : (remove(v0, v1)
% 17.71/3.42 | = v2 & count(v2) = v3 & count(v1) = $sum(v3, 1) & collection(v2)))
% 17.71/3.42 | (9) ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~
% 17.71/3.42 | (in(v0, v1) = v2) | ~ collection(v1) | ? [v3: collection] : ? [v4:
% 17.71/3.42 | int] : ? [v5: int] : ( ~ ($difference(v5, v4) = 1) & remove(v0,
% 17.71/3.42 | v1) = v3 & count(v3) = v4 & count(v1) = v5 & collection(v3)))
% 17.71/3.42 |
% 17.71/3.42 | ALPHA: (ax6) implies:
% 17.71/3.42 | (10) ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~
% 17.71/3.42 | collection(v1) | ? [v2: collection] : ? [v3: int] : ? [v4: int] :
% 17.71/3.42 | ( ~ (v4 = v3) & remove(v0, v1) = v2 & count(v2) = v3 & count(v1) =
% 17.71/3.42 | v4 & collection(v2)))
% 17.71/3.42 | (11) ! [v0: int] : ! [v1: collection] : ! [v2: int] : (v2 = 0 | ~
% 17.71/3.42 | (in(v0, v1) = v2) | ~ collection(v1) | ? [v3: collection] : ?
% 17.71/3.42 | [v4: int] : (remove(v0, v1) = v3 & count(v3) = v4 & count(v1) = v4 &
% 17.71/3.42 | collection(v3)))
% 17.71/3.42 |
% 17.71/3.42 | ALPHA: (ax7) implies:
% 17.71/3.42 | (12) ! [v0: int] : ! [v1: collection] : ( ~ (in(v0, v1) = 0) | ~
% 17.71/3.42 | collection(v1) | ? [v2: collection] : (remove(v0, v1) = v2 &
% 17.71/3.42 | add(v0, v2) = v1 & collection(v2)))
% 17.71/3.42 |
% 17.71/3.42 | ALPHA: (function-axioms) implies:
% 17.71/3.42 | (13) ! [v0: int] : ! [v1: int] : ! [v2: collection] : (v1 = v0 | ~
% 17.71/3.42 | (count(v2) = v1) | ~ (count(v2) = v0))
% 17.71/3.42 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 17.71/3.42 | collection] : ! [v3: int] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~
% 17.71/3.42 | (in(v3, v2) = v0))
% 17.71/3.43 | (15) ! [v0: collection] : ! [v1: collection] : ! [v2: collection] : !
% 17.71/3.43 | [v3: int] : (v1 = v0 | ~ (remove(v3, v2) = v1) | ~ (remove(v3, v2) =
% 17.71/3.43 | v0))
% 17.71/3.43 |
% 17.71/3.43 | DELTA: instantiating (co1) with fresh symbols all_13_0, all_13_1 gives:
% 17.71/3.43 | (16) $lesseq(4, all_13_0) & count(all_13_1) = 2 & in(all_13_0, all_13_1) =
% 17.71/3.43 | 0 & in(3, all_13_1) = 0 & in(2, all_13_1) = 0 & collection(all_13_1)
% 17.71/3.43 |
% 17.71/3.43 | ALPHA: (16) implies:
% 17.71/3.43 | (17) $lesseq(4, all_13_0)
% 17.71/3.43 | (18) collection(all_13_1)
% 17.71/3.43 | (19) in(2, all_13_1) = 0
% 17.71/3.43 | (20) in(3, all_13_1) = 0
% 17.71/3.43 | (21) in(all_13_0, all_13_1) = 0
% 17.71/3.43 | (22) count(all_13_1) = 2
% 17.71/3.43 |
% 17.71/3.43 | GROUND_INST: instantiating (3) with 2, all_13_1, simplifying with (18), (19)
% 17.71/3.43 | gives:
% 17.71/3.43 | (23) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~
% 17.71/3.43 | ($difference(v2, v1) = -1) & add(2, all_13_1) = v0 & count(v0) = v1
% 17.71/3.43 | & count(all_13_1) = v2 & collection(v0))
% 17.71/3.43 |
% 17.71/3.43 | GROUND_INST: instantiating (10) with 2, all_13_1, simplifying with (18), (19)
% 17.71/3.43 | gives:
% 17.71/3.43 | (24) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) &
% 17.71/3.43 | remove(2, all_13_1) = v0 & count(v0) = v1 & count(all_13_1) = v2 &
% 17.71/3.43 | collection(v0))
% 17.71/3.43 |
% 17.71/3.43 | GROUND_INST: instantiating (8) with 2, all_13_1, simplifying with (18), (19)
% 17.71/3.43 | gives:
% 17.71/3.43 | (25) ? [v0: collection] : ? [v1: int] : (remove(2, all_13_1) = v0 &
% 17.71/3.43 | count(v0) = v1 & count(all_13_1) = $sum(v1, 1) & collection(v0))
% 17.71/3.43 |
% 17.71/3.43 | GROUND_INST: instantiating (6) with 2, all_13_1, simplifying with (18), (19)
% 17.71/3.43 | gives:
% 17.71/3.43 | (26) ? [v0: collection] : ? [v1: int] : (add(2, all_13_1) = v0 &
% 17.71/3.43 | count(v0) = v1 & count(all_13_1) = v1 & collection(v0))
% 17.71/3.43 |
% 17.71/3.43 | GROUND_INST: instantiating (3) with 3, all_13_1, simplifying with (18), (20)
% 17.71/3.43 | gives:
% 17.71/3.43 | (27) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~
% 17.71/3.43 | ($difference(v2, v1) = -1) & add(3, all_13_1) = v0 & count(v0) = v1
% 17.71/3.44 | & count(all_13_1) = v2 & collection(v0))
% 17.71/3.44 |
% 17.71/3.44 | GROUND_INST: instantiating (10) with 3, all_13_1, simplifying with (18), (20)
% 17.71/3.44 | gives:
% 17.71/3.44 | (28) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) &
% 17.71/3.44 | remove(3, all_13_1) = v0 & count(v0) = v1 & count(all_13_1) = v2 &
% 17.71/3.44 | collection(v0))
% 17.71/3.44 |
% 17.71/3.44 | GROUND_INST: instantiating (8) with 3, all_13_1, simplifying with (18), (20)
% 17.71/3.44 | gives:
% 17.71/3.44 | (29) ? [v0: collection] : ? [v1: int] : (remove(3, all_13_1) = v0 &
% 17.71/3.44 | count(v0) = v1 & count(all_13_1) = $sum(v1, 1) & collection(v0))
% 17.71/3.44 |
% 17.71/3.44 | GROUND_INST: instantiating (6) with 3, all_13_1, simplifying with (18), (20)
% 17.71/3.44 | gives:
% 17.71/3.44 | (30) ? [v0: collection] : ? [v1: int] : (add(3, all_13_1) = v0 &
% 17.71/3.44 | count(v0) = v1 & count(all_13_1) = v1 & collection(v0))
% 17.71/3.44 |
% 17.71/3.44 | GROUND_INST: instantiating (12) with 3, all_13_1, simplifying with (18), (20)
% 17.71/3.44 | gives:
% 17.71/3.44 | (31) ? [v0: collection] : (remove(3, all_13_1) = v0 & add(3, v0) =
% 17.71/3.44 | all_13_1 & collection(v0))
% 17.71/3.44 |
% 17.71/3.44 | GROUND_INST: instantiating (3) with all_13_0, all_13_1, simplifying with (18),
% 17.71/3.44 | (21) gives:
% 17.71/3.44 | (32) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~
% 17.71/3.44 | ($difference(v2, v1) = -1) & add(all_13_0, all_13_1) = v0 &
% 17.71/3.44 | count(v0) = v1 & count(all_13_1) = v2 & collection(v0))
% 17.71/3.44 |
% 17.71/3.44 | GROUND_INST: instantiating (10) with all_13_0, all_13_1, simplifying with
% 17.71/3.44 | (18), (21) gives:
% 17.71/3.44 | (33) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1) &
% 17.71/3.44 | remove(all_13_0, all_13_1) = v0 & count(v0) = v1 & count(all_13_1) =
% 17.71/3.44 | v2 & collection(v0))
% 17.71/3.44 |
% 17.71/3.44 | GROUND_INST: instantiating (8) with all_13_0, all_13_1, simplifying with (18),
% 17.71/3.44 | (21) gives:
% 17.71/3.44 | (34) ? [v0: collection] : ? [v1: int] : (remove(all_13_0, all_13_1) = v0
% 17.71/3.44 | & count(v0) = v1 & count(all_13_1) = $sum(v1, 1) & collection(v0))
% 17.71/3.44 |
% 17.71/3.44 | GROUND_INST: instantiating (6) with all_13_0, all_13_1, simplifying with (18),
% 17.71/3.44 | (21) gives:
% 17.71/3.44 | (35) ? [v0: collection] : ? [v1: int] : (add(all_13_0, all_13_1) = v0 &
% 17.71/3.44 | count(v0) = v1 & count(all_13_1) = v1 & collection(v0))
% 17.71/3.44 |
% 17.71/3.44 | DELTA: instantiating (31) with fresh symbol all_28_0 gives:
% 17.71/3.44 | (36) remove(3, all_13_1) = all_28_0 & add(3, all_28_0) = all_13_1 &
% 17.71/3.44 | collection(all_28_0)
% 17.71/3.44 |
% 17.71/3.44 | ALPHA: (36) implies:
% 17.71/3.44 | (37) add(3, all_28_0) = all_13_1
% 17.71/3.44 | (38) remove(3, all_13_1) = all_28_0
% 17.71/3.44 |
% 17.71/3.44 | DELTA: instantiating (35) with fresh symbols all_30_0, all_30_1 gives:
% 17.71/3.44 | (39) add(all_13_0, all_13_1) = all_30_1 & count(all_30_1) = all_30_0 &
% 17.71/3.44 | count(all_13_1) = all_30_0 & collection(all_30_1)
% 17.71/3.44 |
% 17.71/3.44 | ALPHA: (39) implies:
% 17.71/3.44 | (40) count(all_13_1) = all_30_0
% 17.71/3.45 |
% 17.71/3.45 | DELTA: instantiating (34) with fresh symbols all_32_0, all_32_1 gives:
% 17.71/3.45 | (41) remove(all_13_0, all_13_1) = all_32_1 & count(all_32_1) = all_32_0 &
% 17.71/3.45 | count(all_13_1) = $sum(all_32_0, 1) & collection(all_32_1)
% 17.71/3.45 |
% 17.71/3.45 | ALPHA: (41) implies:
% 17.71/3.45 | (42) count(all_13_1) = $sum(all_32_0, 1)
% 17.71/3.45 |
% 17.71/3.45 | DELTA: instantiating (29) with fresh symbols all_34_0, all_34_1 gives:
% 17.71/3.45 | (43) remove(3, all_13_1) = all_34_1 & count(all_34_1) = all_34_0 &
% 17.71/3.45 | count(all_13_1) = $sum(all_34_0, 1) & collection(all_34_1)
% 17.71/3.45 |
% 17.71/3.45 | ALPHA: (43) implies:
% 17.71/3.45 | (44) collection(all_34_1)
% 17.71/3.45 | (45) count(all_13_1) = $sum(all_34_0, 1)
% 17.71/3.45 | (46) count(all_34_1) = all_34_0
% 17.71/3.45 | (47) remove(3, all_13_1) = all_34_1
% 17.71/3.45 |
% 17.71/3.45 | DELTA: instantiating (26) with fresh symbols all_36_0, all_36_1 gives:
% 17.71/3.45 | (48) add(2, all_13_1) = all_36_1 & count(all_36_1) = all_36_0 &
% 17.71/3.45 | count(all_13_1) = all_36_0 & collection(all_36_1)
% 17.71/3.45 |
% 17.71/3.45 | ALPHA: (48) implies:
% 17.71/3.45 | (49) count(all_13_1) = all_36_0
% 17.71/3.45 |
% 17.71/3.45 | DELTA: instantiating (30) with fresh symbols all_38_0, all_38_1 gives:
% 17.71/3.45 | (50) add(3, all_13_1) = all_38_1 & count(all_38_1) = all_38_0 &
% 17.71/3.45 | count(all_13_1) = all_38_0 & collection(all_38_1)
% 17.71/3.45 |
% 17.71/3.45 | ALPHA: (50) implies:
% 17.71/3.45 | (51) count(all_13_1) = all_38_0
% 17.71/3.45 |
% 17.71/3.45 | DELTA: instantiating (25) with fresh symbols all_40_0, all_40_1 gives:
% 17.71/3.45 | (52) remove(2, all_13_1) = all_40_1 & count(all_40_1) = all_40_0 &
% 17.71/3.45 | count(all_13_1) = $sum(all_40_0, 1) & collection(all_40_1)
% 17.71/3.45 |
% 17.71/3.45 | ALPHA: (52) implies:
% 17.71/3.45 | (53) count(all_13_1) = $sum(all_40_0, 1)
% 17.71/3.45 |
% 17.71/3.45 | DELTA: instantiating (33) with fresh symbols all_42_0, all_42_1, all_42_2
% 17.71/3.45 | gives:
% 17.71/3.45 | (54) ~ (all_42_0 = all_42_1) & remove(all_13_0, all_13_1) = all_42_2 &
% 17.71/3.45 | count(all_42_2) = all_42_1 & count(all_13_1) = all_42_0 &
% 17.71/3.45 | collection(all_42_2)
% 17.71/3.45 |
% 17.71/3.45 | ALPHA: (54) implies:
% 17.71/3.45 | (55) count(all_13_1) = all_42_0
% 17.71/3.45 |
% 17.71/3.45 | DELTA: instantiating (32) with fresh symbols all_44_0, all_44_1, all_44_2
% 17.71/3.45 | gives:
% 17.71/3.45 | (56) ~ ($difference(all_44_0, all_44_1) = -1) & add(all_13_0, all_13_1) =
% 17.71/3.45 | all_44_2 & count(all_44_2) = all_44_1 & count(all_13_1) = all_44_0 &
% 17.71/3.45 | collection(all_44_2)
% 17.71/3.45 |
% 17.71/3.45 | ALPHA: (56) implies:
% 17.71/3.45 | (57) count(all_13_1) = all_44_0
% 17.71/3.45 |
% 17.71/3.45 | DELTA: instantiating (24) with fresh symbols all_46_0, all_46_1, all_46_2
% 17.71/3.45 | gives:
% 17.71/3.45 | (58) ~ (all_46_0 = all_46_1) & remove(2, all_13_1) = all_46_2 &
% 17.71/3.45 | count(all_46_2) = all_46_1 & count(all_13_1) = all_46_0 &
% 17.71/3.45 | collection(all_46_2)
% 17.71/3.45 |
% 17.71/3.45 | ALPHA: (58) implies:
% 17.71/3.45 | (59) count(all_13_1) = all_46_0
% 17.71/3.45 |
% 17.71/3.45 | DELTA: instantiating (23) with fresh symbols all_48_0, all_48_1, all_48_2
% 17.71/3.45 | gives:
% 17.71/3.45 | (60) ~ ($difference(all_48_0, all_48_1) = -1) & add(2, all_13_1) =
% 17.71/3.45 | all_48_2 & count(all_48_2) = all_48_1 & count(all_13_1) = all_48_0 &
% 17.71/3.45 | collection(all_48_2)
% 17.71/3.45 |
% 17.71/3.45 | ALPHA: (60) implies:
% 17.71/3.45 | (61) count(all_13_1) = all_48_0
% 17.71/3.45 |
% 17.71/3.45 | DELTA: instantiating (27) with fresh symbols all_50_0, all_50_1, all_50_2
% 17.71/3.45 | gives:
% 17.71/3.45 | (62) ~ ($difference(all_50_0, all_50_1) = -1) & add(3, all_13_1) =
% 17.71/3.45 | all_50_2 & count(all_50_2) = all_50_1 & count(all_13_1) = all_50_0 &
% 17.71/3.45 | collection(all_50_2)
% 17.71/3.45 |
% 17.71/3.45 | ALPHA: (62) implies:
% 17.71/3.45 | (63) count(all_13_1) = all_50_0
% 17.71/3.45 |
% 17.71/3.45 | DELTA: instantiating (28) with fresh symbols all_52_0, all_52_1, all_52_2
% 17.71/3.45 | gives:
% 17.71/3.46 | (64) ~ (all_52_0 = all_52_1) & remove(3, all_13_1) = all_52_2 &
% 17.71/3.46 | count(all_52_2) = all_52_1 & count(all_13_1) = all_52_0 &
% 17.71/3.46 | collection(all_52_2)
% 17.71/3.46 |
% 17.71/3.46 | ALPHA: (64) implies:
% 17.71/3.46 | (65) count(all_13_1) = all_52_0
% 17.71/3.46 | (66) count(all_52_2) = all_52_1
% 17.71/3.46 | (67) remove(3, all_13_1) = all_52_2
% 17.71/3.46 |
% 17.71/3.46 | GROUND_INST: instantiating (13) with $sum(all_32_0, 1), all_36_0, all_13_1,
% 17.71/3.46 | simplifying with (42), (49) gives:
% 17.71/3.46 | (68) $difference(all_36_0, all_32_0) = 1
% 17.71/3.46 |
% 17.71/3.46 | GROUND_INST: instantiating (13) with all_36_0, $sum(all_40_0, 1), all_13_1,
% 17.71/3.46 | simplifying with (49), (53) gives:
% 17.71/3.46 | (69) $difference(all_40_0, all_36_0) = -1
% 17.71/3.46 |
% 17.71/3.46 | GROUND_INST: instantiating (13) with all_42_0, all_44_0, all_13_1, simplifying
% 17.71/3.46 | with (55), (57) gives:
% 17.71/3.46 | (70) all_44_0 = all_42_0
% 17.71/3.46 |
% 17.71/3.46 | GROUND_INST: instantiating (13) with all_38_0, all_44_0, all_13_1, simplifying
% 17.71/3.46 | with (51), (57) gives:
% 17.71/3.46 | (71) all_44_0 = all_38_0
% 17.71/3.46 |
% 17.71/3.46 | GROUND_INST: instantiating (13) with all_36_0, all_44_0, all_13_1, simplifying
% 17.71/3.46 | with (49), (57) gives:
% 17.71/3.46 | (72) all_44_0 = all_36_0
% 17.71/3.46 |
% 17.71/3.46 | GROUND_INST: instantiating (13) with all_46_0, all_48_0, all_13_1, simplifying
% 17.71/3.46 | with (59), (61) gives:
% 17.71/3.46 | (73) all_48_0 = all_46_0
% 17.71/3.46 |
% 17.71/3.46 | GROUND_INST: instantiating (13) with $sum(all_40_0, 1), all_48_0, all_13_1,
% 17.71/3.46 | simplifying with (53), (61) gives:
% 17.71/3.46 | (74) $difference(all_48_0, all_40_0) = 1
% 17.71/3.46 |
% 17.71/3.46 | GROUND_INST: instantiating (13) with $sum(all_34_0, 1), all_48_0, all_13_1,
% 17.71/3.46 | simplifying with (45), (61) gives:
% 17.71/3.46 | (75) $difference(all_48_0, all_34_0) = 1
% 17.71/3.46 |
% 17.71/3.46 | GROUND_INST: instantiating (13) with 2, all_50_0, all_13_1, simplifying with
% 17.71/3.46 | (22), (63) gives:
% 17.71/3.46 | (76) all_50_0 = 2
% 17.71/3.46 |
% 17.71/3.46 | GROUND_INST: instantiating (13) with $sum(all_32_0, 1), all_50_0, all_13_1,
% 17.71/3.46 | simplifying with (42), (63) gives:
% 17.71/3.46 | (77) $difference(all_50_0, all_32_0) = 1
% 17.71/3.46 |
% 17.71/3.46 | GROUND_INST: instantiating (13) with all_42_0, all_52_0, all_13_1, simplifying
% 17.71/3.46 | with (55), (65) gives:
% 17.71/3.46 | (78) all_52_0 = all_42_0
% 17.71/3.46 |
% 17.71/3.46 | GROUND_INST: instantiating (13) with all_30_0, all_52_0, all_13_1, simplifying
% 17.71/3.46 | with (40), (65) gives:
% 17.71/3.46 | (79) all_52_0 = all_30_0
% 17.71/3.46 |
% 17.71/3.46 | GROUND_INST: instantiating (15) with all_34_1, all_52_2, all_13_1, 3,
% 17.71/3.46 | simplifying with (47), (67) gives:
% 17.71/3.46 | (80) all_52_2 = all_34_1
% 17.71/3.46 |
% 17.71/3.46 | GROUND_INST: instantiating (15) with all_28_0, all_52_2, all_13_1, 3,
% 17.71/3.46 | simplifying with (38), (67) gives:
% 17.71/3.46 | (81) all_52_2 = all_28_0
% 17.71/3.46 |
% 17.71/3.46 | COMBINE_EQS: (78), (79) imply:
% 17.71/3.46 | (82) all_42_0 = all_30_0
% 17.71/3.46 |
% 17.71/3.46 | SIMP: (82) implies:
% 17.71/3.46 | (83) all_42_0 = all_30_0
% 17.71/3.46 |
% 17.71/3.46 | COMBINE_EQS: (80), (81) imply:
% 17.71/3.47 | (84) all_34_1 = all_28_0
% 17.71/3.47 |
% 17.71/3.47 | SIMP: (84) implies:
% 17.71/3.47 | (85) all_34_1 = all_28_0
% 17.71/3.47 |
% 17.71/3.47 | COMBINE_EQS: (76), (77) imply:
% 17.71/3.47 | (86) all_32_0 = 1
% 17.71/3.47 |
% 17.71/3.47 | SIMP: (86) implies:
% 17.71/3.47 | (87) all_32_0 = 1
% 17.71/3.47 |
% 17.71/3.47 | COMBINE_EQS: (73), (74) imply:
% 17.71/3.47 | (88) $difference(all_46_0, all_40_0) = 1
% 17.71/3.47 |
% 17.71/3.47 | COMBINE_EQS: (73), (75) imply:
% 17.71/3.47 | (89) $difference(all_46_0, all_34_0) = 1
% 17.71/3.47 |
% 17.71/3.47 | COMBINE_EQS: (88), (89) imply:
% 17.71/3.47 | (90) all_40_0 = all_34_0
% 17.71/3.47 |
% 17.71/3.47 | SIMP: (90) implies:
% 17.71/3.47 | (91) all_40_0 = all_34_0
% 17.71/3.47 |
% 17.71/3.47 | COMBINE_EQS: (70), (71) imply:
% 17.71/3.47 | (92) all_42_0 = all_38_0
% 17.71/3.47 |
% 17.71/3.47 | SIMP: (92) implies:
% 17.71/3.47 | (93) all_42_0 = all_38_0
% 17.71/3.47 |
% 17.71/3.47 | COMBINE_EQS: (71), (72) imply:
% 17.71/3.47 | (94) all_38_0 = all_36_0
% 17.71/3.47 |
% 17.71/3.47 | COMBINE_EQS: (83), (93) imply:
% 17.71/3.47 | (95) all_38_0 = all_30_0
% 17.71/3.47 |
% 17.71/3.47 | SIMP: (95) implies:
% 17.71/3.47 | (96) all_38_0 = all_30_0
% 17.71/3.47 |
% 17.71/3.47 | COMBINE_EQS: (69), (91) imply:
% 17.71/3.47 | (97) $difference(all_36_0, all_34_0) = 1
% 17.71/3.47 |
% 17.71/3.47 | SIMP: (97) implies:
% 17.71/3.47 | (98) $difference(all_36_0, all_34_0) = 1
% 17.71/3.47 |
% 17.71/3.47 | COMBINE_EQS: (94), (96) imply:
% 17.71/3.47 | (99) all_36_0 = all_30_0
% 17.71/3.47 |
% 17.71/3.47 | SIMP: (99) implies:
% 17.71/3.47 | (100) all_36_0 = all_30_0
% 17.71/3.47 |
% 17.71/3.47 | COMBINE_EQS: (68), (98) imply:
% 17.71/3.47 | (101) all_34_0 = all_32_0
% 17.71/3.47 |
% 17.71/3.47 | COMBINE_EQS: (98), (100) imply:
% 17.71/3.47 | (102) $difference(all_34_0, all_30_0) = -1
% 17.71/3.47 |
% 17.71/3.47 | COMBINE_EQS: (101), (102) imply:
% 17.71/3.47 | (103) $difference(all_32_0, all_30_0) = -1
% 17.71/3.47 |
% 17.71/3.47 | SIMP: (103) implies:
% 17.71/3.47 | (104) $difference(all_32_0, all_30_0) = -1
% 17.71/3.47 |
% 17.71/3.47 | COMBINE_EQS: (87), (104) imply:
% 17.71/3.47 | (105) all_30_0 = 2
% 17.71/3.47 |
% 17.71/3.47 | COMBINE_EQS: (102), (105) imply:
% 17.71/3.47 | (106) all_34_0 = 1
% 17.71/3.47 |
% 17.71/3.47 | REDUCE: (66), (81) imply:
% 17.71/3.47 | (107) count(all_28_0) = all_52_1
% 17.71/3.47 |
% 17.71/3.47 | REDUCE: (46), (85), (106) imply:
% 17.71/3.47 | (108) count(all_28_0) = 1
% 17.71/3.47 |
% 17.71/3.47 | REDUCE: (44), (85) imply:
% 17.71/3.47 | (109) collection(all_28_0)
% 17.71/3.47 |
% 17.71/3.47 | GROUND_INST: instantiating (13) with 1, all_52_1, all_28_0, simplifying with
% 17.71/3.47 | (107), (108) gives:
% 17.71/3.47 | (110) all_52_1 = 1
% 17.71/3.47 |
% 17.71/3.47 | GROUND_INST: instantiating (7) with all_13_0, all_28_0, 3, all_13_1,
% 17.71/3.47 | simplifying with (21), (37), (109) gives:
% 17.71/3.47 | (111) all_13_0 = 3 | in(all_13_0, all_28_0) = 0
% 17.71/3.47 |
% 17.71/3.47 | GROUND_INST: instantiating (7) with 2, all_28_0, 3, all_13_1, simplifying with
% 17.71/3.47 | (19), (37), (109) gives:
% 17.71/3.47 | (112) in(2, all_28_0) = 0
% 17.71/3.47 |
% 17.71/3.47 | GROUND_INST: instantiating (4) with 3, all_28_0, all_13_1, simplifying with
% 17.71/3.47 | (37), (109) gives:
% 17.71/3.48 | (113) ? [v0: int] : ? [v1: int] : ? [v2: int] : (( ~ (v2 = 0) & in(3,
% 17.71/3.48 | all_28_0) = v2) | ( ~ ($difference(v1, v0) = -1) &
% 17.71/3.48 | count(all_28_0) = v1 & count(all_13_1) = v0))
% 17.71/3.48 |
% 17.71/3.48 | GROUND_INST: instantiating (5) with 3, all_13_1, all_28_0, simplifying with
% 17.71/3.48 | (18), (38) gives:
% 17.71/3.48 | (114) ? [v0: int] : ( ~ (v0 = 0) & in(3, all_28_0) = v0)
% 17.71/3.48 |
% 17.71/3.48 | DELTA: instantiating (114) with fresh symbol all_70_0 gives:
% 17.71/3.48 | (115) ~ (all_70_0 = 0) & in(3, all_28_0) = all_70_0
% 17.71/3.48 |
% 17.71/3.48 | ALPHA: (115) implies:
% 17.71/3.48 | (116) in(3, all_28_0) = all_70_0
% 17.71/3.48 |
% 17.71/3.48 | DELTA: instantiating (113) with fresh symbols all_80_0, all_80_1, all_80_2
% 17.71/3.48 | gives:
% 17.71/3.48 | (117) ( ~ (all_80_0 = 0) & in(3, all_28_0) = all_80_0) | ( ~
% 17.71/3.48 | ($difference(all_80_1, all_80_2) = -1) & count(all_28_0) = all_80_1
% 17.71/3.48 | & count(all_13_1) = all_80_2)
% 17.71/3.48 |
% 17.71/3.48 | BETA: splitting (111) gives:
% 17.71/3.48 |
% 17.71/3.48 | Case 1:
% 17.71/3.48 | |
% 17.71/3.48 | | (118) in(all_13_0, all_28_0) = 0
% 17.71/3.48 | |
% 17.71/3.48 | | BETA: splitting (117) gives:
% 17.71/3.48 | |
% 17.71/3.48 | | Case 1:
% 17.71/3.48 | | |
% 17.71/3.48 | | | (119) ~ (all_80_0 = 0) & in(3, all_28_0) = all_80_0
% 17.71/3.48 | | |
% 17.71/3.48 | | | ALPHA: (119) implies:
% 17.71/3.48 | | | (120) ~ (all_80_0 = 0)
% 17.71/3.48 | | | (121) in(3, all_28_0) = all_80_0
% 17.71/3.48 | | |
% 17.71/3.48 | | | GROUND_INST: instantiating (14) with all_70_0, all_80_0, all_28_0, 3,
% 17.71/3.48 | | | simplifying with (116), (121) gives:
% 17.71/3.48 | | | (122) all_80_0 = all_70_0
% 17.71/3.48 | | |
% 17.71/3.48 | | | REDUCE: (120), (122) imply:
% 17.71/3.48 | | | (123) ~ (all_70_0 = 0)
% 17.71/3.48 | | |
% 17.71/3.48 | | | GROUND_INST: instantiating (3) with 2, all_28_0, simplifying with (109),
% 17.71/3.48 | | | (112) gives:
% 17.71/3.48 | | | (124) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~
% 17.71/3.48 | | | ($difference(v2, v1) = -1) & add(2, all_28_0) = v0 & count(v0)
% 17.71/3.48 | | | = v1 & count(all_28_0) = v2 & collection(v0))
% 17.71/3.48 | | |
% 17.71/3.48 | | | GROUND_INST: instantiating (10) with 2, all_28_0, simplifying with (109),
% 17.71/3.48 | | | (112) gives:
% 17.71/3.48 | | | (125) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1)
% 17.71/3.48 | | | & remove(2, all_28_0) = v0 & count(v0) = v1 & count(all_28_0) =
% 17.71/3.48 | | | v2 & collection(v0))
% 17.71/3.48 | | |
% 17.71/3.48 | | | GROUND_INST: instantiating (8) with 2, all_28_0, simplifying with (109),
% 17.71/3.48 | | | (112) gives:
% 17.71/3.48 | | | (126) ? [v0: collection] : ? [v1: int] : (remove(2, all_28_0) = v0 &
% 17.71/3.48 | | | count(v0) = v1 & count(all_28_0) = $sum(v1, 1) &
% 17.71/3.48 | | | collection(v0))
% 17.71/3.48 | | |
% 17.71/3.48 | | | GROUND_INST: instantiating (6) with 2, all_28_0, simplifying with (109),
% 17.71/3.48 | | | (112) gives:
% 17.71/3.48 | | | (127) ? [v0: collection] : ? [v1: int] : (add(2, all_28_0) = v0 &
% 17.71/3.48 | | | count(v0) = v1 & count(all_28_0) = v1 & collection(v0))
% 17.71/3.48 | | |
% 17.71/3.48 | | | GROUND_INST: instantiating (12) with 2, all_28_0, simplifying with (109),
% 17.71/3.48 | | | (112) gives:
% 17.71/3.48 | | | (128) ? [v0: collection] : (remove(2, all_28_0) = v0 & add(2, v0) =
% 17.71/3.48 | | | all_28_0 & collection(v0))
% 17.71/3.48 | | |
% 17.71/3.48 | | | GROUND_INST: instantiating (9) with 3, all_28_0, all_70_0, simplifying
% 17.71/3.48 | | | with (109), (116) gives:
% 17.71/3.49 | | | (129) all_70_0 = 0 | ? [v0: collection] : ? [v1: int] : ? [v2: int]
% 17.71/3.49 | | | : ( ~ ($difference(v2, v1) = 1) & remove(3, all_28_0) = v0 &
% 17.71/3.49 | | | count(v0) = v1 & count(all_28_0) = v2 & collection(v0))
% 17.71/3.49 | | |
% 17.71/3.49 | | | GROUND_INST: instantiating (11) with 3, all_28_0, all_70_0, simplifying
% 17.71/3.49 | | | with (109), (116) gives:
% 17.71/3.49 | | | (130) all_70_0 = 0 | ? [v0: collection] : ? [v1: int] : (remove(3,
% 17.71/3.49 | | | all_28_0) = v0 & count(v0) = v1 & count(all_28_0) = v1 &
% 17.71/3.49 | | | collection(v0))
% 17.71/3.49 | | |
% 17.71/3.49 | | | GROUND_INST: instantiating (3) with all_13_0, all_28_0, simplifying with
% 17.71/3.49 | | | (109), (118) gives:
% 17.71/3.49 | | | (131) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~
% 17.71/3.49 | | | ($difference(v2, v1) = -1) & add(all_13_0, all_28_0) = v0 &
% 17.71/3.49 | | | count(v0) = v1 & count(all_28_0) = v2 & collection(v0))
% 17.71/3.49 | | |
% 17.71/3.49 | | | GROUND_INST: instantiating (10) with all_13_0, all_28_0, simplifying with
% 17.71/3.49 | | | (109), (118) gives:
% 17.71/3.49 | | | (132) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~ (v2 = v1)
% 17.71/3.49 | | | & remove(all_13_0, all_28_0) = v0 & count(v0) = v1 &
% 17.71/3.49 | | | count(all_28_0) = v2 & collection(v0))
% 17.71/3.49 | | |
% 17.71/3.49 | | | GROUND_INST: instantiating (8) with all_13_0, all_28_0, simplifying with
% 17.71/3.49 | | | (109), (118) gives:
% 17.71/3.49 | | | (133) ? [v0: collection] : ? [v1: int] : (remove(all_13_0, all_28_0)
% 17.71/3.49 | | | = v0 & count(v0) = v1 & count(all_28_0) = $sum(v1, 1) &
% 17.71/3.49 | | | collection(v0))
% 17.71/3.49 | | |
% 17.71/3.49 | | | GROUND_INST: instantiating (6) with all_13_0, all_28_0, simplifying with
% 17.71/3.49 | | | (109), (118) gives:
% 17.71/3.49 | | | (134) ? [v0: collection] : ? [v1: int] : (add(all_13_0, all_28_0) =
% 17.71/3.49 | | | v0 & count(v0) = v1 & count(all_28_0) = v1 & collection(v0))
% 17.71/3.49 | | |
% 17.71/3.49 | | | DELTA: instantiating (128) with fresh symbol all_167_0 gives:
% 17.71/3.49 | | | (135) remove(2, all_28_0) = all_167_0 & add(2, all_167_0) = all_28_0 &
% 17.71/3.49 | | | collection(all_167_0)
% 17.71/3.49 | | |
% 17.71/3.49 | | | ALPHA: (135) implies:
% 17.71/3.49 | | | (136) add(2, all_167_0) = all_28_0
% 17.71/3.49 | | | (137) remove(2, all_28_0) = all_167_0
% 17.71/3.49 | | |
% 17.71/3.49 | | | DELTA: instantiating (126) with fresh symbols all_193_0, all_193_1 gives:
% 17.71/3.49 | | | (138) remove(2, all_28_0) = all_193_1 & count(all_193_1) = all_193_0 &
% 17.71/3.49 | | | count(all_28_0) = $sum(all_193_0, 1) & collection(all_193_1)
% 17.71/3.49 | | |
% 17.71/3.49 | | | ALPHA: (138) implies:
% 17.71/3.49 | | | (139) collection(all_193_1)
% 17.71/3.49 | | | (140) count(all_28_0) = $sum(all_193_0, 1)
% 17.71/3.49 | | | (141) count(all_193_1) = all_193_0
% 17.71/3.49 | | | (142) remove(2, all_28_0) = all_193_1
% 17.71/3.49 | | |
% 17.71/3.49 | | | DELTA: instantiating (133) with fresh symbols all_197_0, all_197_1 gives:
% 17.71/3.49 | | | (143) remove(all_13_0, all_28_0) = all_197_1 & count(all_197_1) =
% 17.71/3.49 | | | all_197_0 & count(all_28_0) = $sum(all_197_0, 1) &
% 17.71/3.49 | | | collection(all_197_1)
% 17.71/3.49 | | |
% 17.71/3.49 | | | ALPHA: (143) implies:
% 17.71/3.49 | | | (144) count(all_28_0) = $sum(all_197_0, 1)
% 17.71/3.49 | | |
% 17.71/3.49 | | | DELTA: instantiating (127) with fresh symbols all_203_0, all_203_1 gives:
% 17.71/3.49 | | | (145) add(2, all_28_0) = all_203_1 & count(all_203_1) = all_203_0 &
% 17.71/3.49 | | | count(all_28_0) = all_203_0 & collection(all_203_1)
% 17.71/3.49 | | |
% 17.71/3.49 | | | ALPHA: (145) implies:
% 17.71/3.49 | | | (146) count(all_28_0) = all_203_0
% 17.71/3.49 | | |
% 17.71/3.49 | | | DELTA: instantiating (134) with fresh symbols all_205_0, all_205_1 gives:
% 17.71/3.49 | | | (147) add(all_13_0, all_28_0) = all_205_1 & count(all_205_1) =
% 17.71/3.49 | | | all_205_0 & count(all_28_0) = all_205_0 & collection(all_205_1)
% 17.71/3.49 | | |
% 17.71/3.49 | | | ALPHA: (147) implies:
% 17.71/3.49 | | | (148) count(all_28_0) = all_205_0
% 17.71/3.49 | | |
% 17.71/3.49 | | | DELTA: instantiating (131) with fresh symbols all_223_0, all_223_1,
% 17.71/3.49 | | | all_223_2 gives:
% 17.71/3.49 | | | (149) ~ ($difference(all_223_0, all_223_1) = -1) & add(all_13_0,
% 17.71/3.49 | | | all_28_0) = all_223_2 & count(all_223_2) = all_223_1 &
% 17.71/3.49 | | | count(all_28_0) = all_223_0 & collection(all_223_2)
% 17.71/3.49 | | |
% 17.71/3.49 | | | ALPHA: (149) implies:
% 17.71/3.50 | | | (150) count(all_28_0) = all_223_0
% 17.71/3.50 | | |
% 17.71/3.50 | | | DELTA: instantiating (132) with fresh symbols all_233_0, all_233_1,
% 17.71/3.50 | | | all_233_2 gives:
% 17.71/3.50 | | | (151) ~ (all_233_0 = all_233_1) & remove(all_13_0, all_28_0) =
% 17.71/3.50 | | | all_233_2 & count(all_233_2) = all_233_1 & count(all_28_0) =
% 17.71/3.50 | | | all_233_0 & collection(all_233_2)
% 17.71/3.50 | | |
% 17.71/3.50 | | | ALPHA: (151) implies:
% 17.71/3.50 | | | (152) count(all_28_0) = all_233_0
% 17.71/3.50 | | |
% 17.71/3.50 | | | DELTA: instantiating (124) with fresh symbols all_245_0, all_245_1,
% 17.71/3.50 | | | all_245_2 gives:
% 17.71/3.50 | | | (153) ~ ($difference(all_245_0, all_245_1) = -1) & add(2, all_28_0) =
% 17.71/3.50 | | | all_245_2 & count(all_245_2) = all_245_1 & count(all_28_0) =
% 17.71/3.50 | | | all_245_0 & collection(all_245_2)
% 17.71/3.50 | | |
% 17.71/3.50 | | | ALPHA: (153) implies:
% 17.71/3.50 | | | (154) count(all_28_0) = all_245_0
% 17.71/3.50 | | |
% 17.71/3.50 | | | DELTA: instantiating (125) with fresh symbols all_251_0, all_251_1,
% 17.71/3.50 | | | all_251_2 gives:
% 17.71/3.50 | | | (155) ~ (all_251_0 = all_251_1) & remove(2, all_28_0) = all_251_2 &
% 17.71/3.50 | | | count(all_251_2) = all_251_1 & count(all_28_0) = all_251_0 &
% 17.71/3.50 | | | collection(all_251_2)
% 17.71/3.50 | | |
% 17.71/3.50 | | | ALPHA: (155) implies:
% 17.71/3.50 | | | (156) count(all_28_0) = all_251_0
% 17.71/3.50 | | | (157) count(all_251_2) = all_251_1
% 17.71/3.50 | | | (158) remove(2, all_28_0) = all_251_2
% 17.71/3.50 | | |
% 17.71/3.50 | | | BETA: splitting (129) gives:
% 17.71/3.50 | | |
% 17.71/3.50 | | | Case 1:
% 17.71/3.50 | | | |
% 17.71/3.50 | | | | (159) all_70_0 = 0
% 17.71/3.50 | | | |
% 17.71/3.50 | | | | REDUCE: (123), (159) imply:
% 17.71/3.50 | | | | (160) $false
% 17.71/3.50 | | | |
% 17.71/3.50 | | | | CLOSE: (160) is inconsistent.
% 17.71/3.50 | | | |
% 17.71/3.50 | | | Case 2:
% 17.71/3.50 | | | |
% 17.71/3.50 | | | | (161) ? [v0: collection] : ? [v1: int] : ? [v2: int] : ( ~
% 17.71/3.50 | | | | ($difference(v2, v1) = 1) & remove(3, all_28_0) = v0 &
% 17.71/3.50 | | | | count(v0) = v1 & count(all_28_0) = v2 & collection(v0))
% 17.71/3.50 | | | |
% 17.71/3.50 | | | | DELTA: instantiating (161) with fresh symbols all_257_0, all_257_1,
% 17.71/3.50 | | | | all_257_2 gives:
% 17.71/3.50 | | | | (162) ~ ($difference(all_257_0, all_257_1) = 1) & remove(3,
% 17.71/3.50 | | | | all_28_0) = all_257_2 & count(all_257_2) = all_257_1 &
% 17.71/3.50 | | | | count(all_28_0) = all_257_0 & collection(all_257_2)
% 17.71/3.50 | | | |
% 17.71/3.50 | | | | ALPHA: (162) implies:
% 17.71/3.50 | | | | (163) count(all_28_0) = all_257_0
% 17.71/3.50 | | | |
% 17.71/3.50 | | | | BETA: splitting (130) gives:
% 17.71/3.50 | | | |
% 17.71/3.50 | | | | Case 1:
% 17.71/3.50 | | | | |
% 17.71/3.50 | | | | | (164) all_70_0 = 0
% 17.71/3.50 | | | | |
% 17.71/3.50 | | | | | REDUCE: (123), (164) imply:
% 17.71/3.50 | | | | | (165) $false
% 17.71/3.50 | | | | |
% 17.71/3.50 | | | | | CLOSE: (165) is inconsistent.
% 17.71/3.50 | | | | |
% 17.71/3.50 | | | | Case 2:
% 17.71/3.50 | | | | |
% 17.71/3.50 | | | | | (166) ? [v0: collection] : ? [v1: int] : (remove(3, all_28_0) =
% 17.71/3.50 | | | | | v0 & count(v0) = v1 & count(all_28_0) = v1 &
% 17.71/3.50 | | | | | collection(v0))
% 17.71/3.50 | | | | |
% 17.71/3.50 | | | | | DELTA: instantiating (166) with fresh symbols all_277_0, all_277_1
% 17.71/3.50 | | | | | gives:
% 17.71/3.50 | | | | | (167) remove(3, all_28_0) = all_277_1 & count(all_277_1) =
% 17.71/3.50 | | | | | all_277_0 & count(all_28_0) = all_277_0 &
% 17.71/3.50 | | | | | collection(all_277_1)
% 17.71/3.50 | | | | |
% 17.71/3.50 | | | | | ALPHA: (167) implies:
% 17.71/3.50 | | | | | (168) count(all_28_0) = all_277_0
% 17.71/3.50 | | | | |
% 17.71/3.50 | | | | | GROUND_INST: instantiating (13) with all_203_0, all_233_0, all_28_0,
% 17.71/3.50 | | | | | simplifying with (146), (152) gives:
% 17.71/3.50 | | | | | (169) all_233_0 = all_203_0
% 17.71/3.50 | | | | |
% 17.71/3.50 | | | | | GROUND_INST: instantiating (13) with all_205_0, all_251_0, all_28_0,
% 17.71/3.50 | | | | | simplifying with (148), (156) gives:
% 17.71/3.50 | | | | | (170) all_251_0 = all_205_0
% 17.71/3.50 | | | | |
% 17.71/3.50 | | | | | GROUND_INST: instantiating (13) with all_233_0, all_257_0, all_28_0,
% 17.71/3.50 | | | | | simplifying with (152), (163) gives:
% 17.71/3.50 | | | | | (171) all_257_0 = all_233_0
% 17.71/3.50 | | | | |
% 17.71/3.50 | | | | | GROUND_INST: instantiating (13) with $sum(all_193_0, 1), all_257_0,
% 17.71/3.50 | | | | | all_28_0, simplifying with (140), (163) gives:
% 17.71/3.50 | | | | | (172) $difference(all_257_0, all_193_0) = 1
% 17.71/3.50 | | | | |
% 17.71/3.50 | | | | | GROUND_INST: instantiating (13) with 1, all_277_0, all_28_0,
% 17.71/3.51 | | | | | simplifying with (108), (168) gives:
% 17.71/3.51 | | | | | (173) all_277_0 = 1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | GROUND_INST: instantiating (13) with all_251_0, all_277_0, all_28_0,
% 17.71/3.51 | | | | | simplifying with (156), (168) gives:
% 17.71/3.51 | | | | | (174) all_277_0 = all_251_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | GROUND_INST: instantiating (13) with all_245_0, all_277_0, all_28_0,
% 17.71/3.51 | | | | | simplifying with (154), (168) gives:
% 17.71/3.51 | | | | | (175) all_277_0 = all_245_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | GROUND_INST: instantiating (13) with all_223_0, all_277_0, all_28_0,
% 17.71/3.51 | | | | | simplifying with (150), (168) gives:
% 17.71/3.51 | | | | | (176) all_277_0 = all_223_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | GROUND_INST: instantiating (13) with all_203_0, all_277_0, all_28_0,
% 17.71/3.51 | | | | | simplifying with (146), (168) gives:
% 17.71/3.51 | | | | | (177) all_277_0 = all_203_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | GROUND_INST: instantiating (13) with $sum(all_197_0, 1), all_277_0,
% 17.71/3.51 | | | | | all_28_0, simplifying with (144), (168) gives:
% 17.71/3.51 | | | | | (178) $difference(all_277_0, all_197_0) = 1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | GROUND_INST: instantiating (15) with all_193_1, all_251_2, all_28_0,
% 17.71/3.51 | | | | | 2, simplifying with (142), (158) gives:
% 17.71/3.51 | | | | | (179) all_251_2 = all_193_1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | GROUND_INST: instantiating (15) with all_167_0, all_251_2, all_28_0,
% 17.71/3.51 | | | | | 2, simplifying with (137), (158) gives:
% 17.71/3.51 | | | | | (180) all_251_2 = all_167_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (174), (175) imply:
% 17.71/3.51 | | | | | (181) all_251_0 = all_245_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | SIMP: (181) implies:
% 17.71/3.51 | | | | | (182) all_251_0 = all_245_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (173), (175) imply:
% 17.71/3.51 | | | | | (183) all_245_0 = 1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (175), (178) imply:
% 17.71/3.51 | | | | | (184) $difference(all_245_0, all_197_0) = 1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (175), (177) imply:
% 17.71/3.51 | | | | | (185) all_245_0 = all_203_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (175), (176) imply:
% 17.71/3.51 | | | | | (186) all_245_0 = all_223_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (171), (172) imply:
% 17.71/3.51 | | | | | (187) $difference(all_233_0, all_193_0) = 1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | SIMP: (187) implies:
% 17.71/3.51 | | | | | (188) $difference(all_233_0, all_193_0) = 1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (170), (182) imply:
% 17.71/3.51 | | | | | (189) all_245_0 = all_205_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | SIMP: (189) implies:
% 17.71/3.51 | | | | | (190) all_245_0 = all_205_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (179), (180) imply:
% 17.71/3.51 | | | | | (191) all_193_1 = all_167_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | SIMP: (191) implies:
% 17.71/3.51 | | | | | (192) all_193_1 = all_167_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (184), (186) imply:
% 17.71/3.51 | | | | | (193) $difference(all_223_0, all_197_0) = 1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (186), (190) imply:
% 17.71/3.51 | | | | | (194) all_223_0 = all_205_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (183), (186) imply:
% 17.71/3.51 | | | | | (195) all_223_0 = 1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (185), (186) imply:
% 17.71/3.51 | | | | | (196) all_223_0 = all_203_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (169), (188) imply:
% 17.71/3.51 | | | | | (197) $difference(all_203_0, all_193_0) = 1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | SIMP: (197) implies:
% 17.71/3.51 | | | | | (198) $difference(all_203_0, all_193_0) = 1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (194), (196) imply:
% 17.71/3.51 | | | | | (199) all_205_0 = all_203_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (194), (195) imply:
% 17.71/3.51 | | | | | (200) all_205_0 = 1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (193), (194) imply:
% 17.71/3.51 | | | | | (201) $difference(all_205_0, all_197_0) = 1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (199), (201) imply:
% 17.71/3.51 | | | | | (202) $difference(all_203_0, all_197_0) = 1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | SIMP: (202) implies:
% 17.71/3.51 | | | | | (203) $difference(all_203_0, all_197_0) = 1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (200), (201) imply:
% 17.71/3.51 | | | | | (204) all_197_0 = 0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (198), (203) imply:
% 17.71/3.51 | | | | | (205) all_197_0 = all_193_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | SIMP: (205) implies:
% 17.71/3.51 | | | | | (206) all_197_0 = all_193_0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | COMBINE_EQS: (204), (206) imply:
% 17.71/3.51 | | | | | (207) all_193_0 = 0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | REDUCE: (157), (180) imply:
% 17.71/3.51 | | | | | (208) count(all_167_0) = all_251_1
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | REDUCE: (141), (192), (207) imply:
% 17.71/3.51 | | | | | (209) count(all_167_0) = 0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | REDUCE: (139), (192) imply:
% 17.71/3.51 | | | | | (210) collection(all_167_0)
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | GROUND_INST: instantiating (13) with 0, all_251_1, all_167_0,
% 17.71/3.51 | | | | | simplifying with (208), (209) gives:
% 17.71/3.51 | | | | | (211) all_251_1 = 0
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | GROUND_INST: instantiating (2) with all_167_0, simplifying with (209),
% 17.71/3.51 | | | | | (210) gives:
% 17.71/3.51 | | | | | (212) all_167_0 = empty
% 17.71/3.51 | | | | |
% 17.71/3.51 | | | | | GROUND_INST: instantiating (7) with all_13_0, all_167_0, 2, all_28_0,
% 17.71/3.51 | | | | | simplifying with (118), (136), (210) gives:
% 17.71/3.52 | | | | | (213) all_13_0 = 2 | in(all_13_0, all_167_0) = 0
% 17.71/3.52 | | | | |
% 17.71/3.52 | | | | | BETA: splitting (213) gives:
% 17.71/3.52 | | | | |
% 17.71/3.52 | | | | | Case 1:
% 17.71/3.52 | | | | | |
% 17.71/3.52 | | | | | | (214) in(all_13_0, all_167_0) = 0
% 17.71/3.52 | | | | | |
% 17.71/3.52 | | | | | | REDUCE: (212), (214) imply:
% 17.71/3.52 | | | | | | (215) in(all_13_0, empty) = 0
% 17.71/3.52 | | | | | |
% 17.71/3.52 | | | | | | GROUND_INST: instantiating (1) with all_13_0, simplifying with (215)
% 17.71/3.52 | | | | | | gives:
% 17.71/3.52 | | | | | | (216) $false
% 17.71/3.52 | | | | | |
% 17.71/3.52 | | | | | | CLOSE: (216) is inconsistent.
% 17.71/3.52 | | | | | |
% 17.71/3.52 | | | | | Case 2:
% 17.71/3.52 | | | | | |
% 17.71/3.52 | | | | | | (217) all_13_0 = 2
% 17.71/3.52 | | | | | |
% 17.71/3.52 | | | | | | REDUCE: (17), (217) imply:
% 17.71/3.52 | | | | | | (218) $false
% 17.71/3.52 | | | | | |
% 17.71/3.52 | | | | | | CLOSE: (218) is inconsistent.
% 17.71/3.52 | | | | | |
% 17.71/3.52 | | | | | End of split
% 17.71/3.52 | | | | |
% 17.71/3.52 | | | | End of split
% 17.71/3.52 | | | |
% 17.71/3.52 | | | End of split
% 17.71/3.52 | | |
% 17.71/3.52 | | Case 2:
% 17.71/3.52 | | |
% 17.71/3.52 | | | (219) ~ ($difference(all_80_1, all_80_2) = -1) & count(all_28_0) =
% 17.71/3.52 | | | all_80_1 & count(all_13_1) = all_80_2
% 17.71/3.52 | | |
% 17.71/3.52 | | | ALPHA: (219) implies:
% 17.71/3.52 | | | (220) ~ ($difference(all_80_1, all_80_2) = -1)
% 17.71/3.52 | | | (221) count(all_13_1) = all_80_2
% 17.71/3.52 | | | (222) count(all_28_0) = all_80_1
% 17.71/3.52 | | |
% 17.71/3.52 | | | GROUND_INST: instantiating (13) with 2, all_80_2, all_13_1, simplifying
% 17.71/3.52 | | | with (22), (221) gives:
% 17.71/3.52 | | | (223) all_80_2 = 2
% 17.71/3.52 | | |
% 17.71/3.52 | | | GROUND_INST: instantiating (13) with 1, all_80_1, all_28_0, simplifying
% 17.71/3.52 | | | with (108), (222) gives:
% 17.71/3.52 | | | (224) all_80_1 = 1
% 17.71/3.52 | | |
% 17.71/3.52 | | | REDUCE: (220), (223), (224) imply:
% 17.71/3.52 | | | (225) $false
% 17.71/3.52 | | |
% 17.71/3.52 | | | CLOSE: (225) is inconsistent.
% 17.71/3.52 | | |
% 17.71/3.52 | | End of split
% 17.71/3.52 | |
% 17.71/3.52 | Case 2:
% 17.71/3.52 | |
% 17.71/3.52 | | (226) all_13_0 = 3
% 17.71/3.52 | |
% 17.71/3.52 | | REDUCE: (17), (226) imply:
% 17.71/3.52 | | (227) $false
% 17.71/3.52 | |
% 17.71/3.52 | | CLOSE: (227) is inconsistent.
% 17.71/3.52 | |
% 17.71/3.52 | End of split
% 17.71/3.52 |
% 17.71/3.52 End of proof
% 17.71/3.52 % SZS output end Proof for theBenchmark
% 17.71/3.52
% 17.71/3.52 2903ms
%------------------------------------------------------------------------------