TSTP Solution File: KRS251+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KRS251+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:51:45 EDT 2023
% Result : Theorem 18.80s 3.21s
% Output : Proof 23.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS251+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n013.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
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 02:01:17 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.03/1.17 Prover 1: Preprocessing ...
% 3.03/1.17 Prover 4: Preprocessing ...
% 3.75/1.20 Prover 2: Preprocessing ...
% 3.75/1.20 Prover 6: Preprocessing ...
% 3.75/1.20 Prover 5: Preprocessing ...
% 3.75/1.20 Prover 0: Preprocessing ...
% 3.75/1.20 Prover 3: Preprocessing ...
% 7.71/1.77 Prover 2: Proving ...
% 7.71/1.78 Prover 5: Proving ...
% 8.27/1.86 Prover 6: Proving ...
% 8.80/1.92 Prover 1: Constructing countermodel ...
% 8.80/1.95 Prover 3: Constructing countermodel ...
% 9.48/2.01 Prover 0: Proving ...
% 9.48/2.06 Prover 4: Constructing countermodel ...
% 10.86/2.18 Prover 3: gave up
% 10.86/2.19 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 11.46/2.28 Prover 7: Preprocessing ...
% 11.46/2.30 Prover 1: gave up
% 11.46/2.30 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 12.17/2.36 Prover 8: Preprocessing ...
% 12.61/2.39 Prover 7: Warning: ignoring some quantifiers
% 12.61/2.43 Prover 7: Constructing countermodel ...
% 13.76/2.64 Prover 8: Warning: ignoring some quantifiers
% 13.76/2.68 Prover 8: Constructing countermodel ...
% 15.91/2.86 Prover 8: gave up
% 15.91/2.88 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 16.43/2.93 Prover 9: Preprocessing ...
% 18.29/3.20 Prover 9: Constructing countermodel ...
% 18.80/3.20 Prover 6: proved (2588ms)
% 18.80/3.21
% 18.80/3.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.80/3.21
% 18.80/3.21 Prover 9: stopped
% 18.80/3.21 Prover 2: stopped
% 18.80/3.21 Prover 5: stopped
% 18.80/3.21 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 18.80/3.21 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 18.80/3.21 Prover 0: stopped
% 18.80/3.25 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 18.80/3.25 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 19.19/3.26 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 19.19/3.29 Prover 10: Preprocessing ...
% 19.19/3.29 Prover 13: Preprocessing ...
% 19.19/3.31 Prover 19: Preprocessing ...
% 19.19/3.31 Prover 16: Preprocessing ...
% 19.19/3.31 Prover 11: Preprocessing ...
% 19.89/3.38 Prover 10: Warning: ignoring some quantifiers
% 19.89/3.40 Prover 10: Constructing countermodel ...
% 19.89/3.40 Prover 16: Warning: ignoring some quantifiers
% 19.89/3.41 Prover 16: Constructing countermodel ...
% 19.89/3.43 Prover 13: Warning: ignoring some quantifiers
% 19.89/3.45 Prover 13: Constructing countermodel ...
% 21.74/3.61 Prover 11: Constructing countermodel ...
% 21.80/3.65 Prover 4: Found proof (size 239)
% 21.80/3.65 Prover 4: proved (3034ms)
% 21.80/3.65 Prover 11: stopped
% 21.80/3.65 Prover 10: stopped
% 21.80/3.65 Prover 16: stopped
% 21.80/3.65 Prover 7: stopped
% 21.80/3.65 Prover 13: stopped
% 21.80/3.68 Prover 19: Warning: ignoring some quantifiers
% 21.80/3.69 Prover 19: Constructing countermodel ...
% 21.80/3.70 Prover 19: stopped
% 21.80/3.70
% 21.80/3.70 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.80/3.70
% 22.29/3.71 % SZS output start Proof for theBenchmark
% 22.29/3.72 Assumptions after simplification:
% 22.29/3.72 ---------------------------------
% 22.29/3.72
% 22.29/3.72 (completeness)
% 22.29/3.75 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (not(v1)
% 22.29/3.75 = v2) | ~ (model(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | model(v0, v1) =
% 22.29/3.75 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (model(v0, v1)
% 22.29/3.75 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (not(v1) = v3 & model(v0,
% 22.29/3.75 v3) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 22.29/3.75 (not(v1) = v2) | ~ (model(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 22.29/3.75 int] : ( ~ (v3 = 0) & model(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : (
% 22.29/3.75 ~ (model(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] :
% 22.29/3.75 ( ~ (v3 = 0) & not(v1) = v2 & model(v0, v2) = v3 & $i(v2)))
% 22.29/3.75
% 22.29/3.75 (csa)
% 22.29/3.75 $i(csa) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (status(v0,
% 22.29/3.75 v1, csa) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (not(v1) = v3 &
% 22.29/3.75 $i(v3) & ! [v4: $i] : ( ~ (model(v4, v3) = 0) | ~ $i(v4) | ? [v5: int]
% 22.29/3.75 : ( ~ (v5 = 0) & model(v4, v0) = v5)) & ! [v4: $i] : ( ~ (model(v4, v0)
% 22.29/3.75 = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & model(v4, v3) =
% 22.29/3.75 v5)))) & ! [v0: $i] : ! [v1: $i] : ( ~ (status(v0, v1, csa) = 0) |
% 22.29/3.75 ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : (not(v1) = v2 & model(v3,
% 22.29/3.75 v2) = 0 & model(v3, v0) = 0 & $i(v3) & $i(v2)))
% 22.29/3.75
% 22.29/3.75 (mixed_pair)
% 22.29/3.75 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: $i] : ? [v5:
% 22.29/3.75 int] : ? [v6: $i] : ( ~ (v5 = 0) & ~ (v3 = 0) & model(v6, v0) = 0 &
% 22.29/3.75 model(v4, v1) = 0 & model(v4, v0) = v5 & model(v2, v1) = v3 & $i(v6) &
% 22.29/3.75 $i(v4) & $i(v2) & $i(v1) & $i(v0) & ! [v7: $i] : ! [v8: int] : (v8 = 0 |
% 22.29/3.75 ~ (model(v7, v1) = v8) | ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0) &
% 22.29/3.75 model(v7, v0) = v9)) & ! [v7: $i] : ( ~ (model(v7, v0) = 0) | ~ $i(v7)
% 22.29/3.75 | model(v7, v1) = 0))
% 22.29/3.75
% 22.29/3.75 (non_thm_spt)
% 22.29/3.76 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4: $i] : ( ~ (v3
% 22.29/3.76 = 0) & model(v4, v2) = 0 & model(v0, v2) = v3 & model(v0, v1) = 0 & $i(v4)
% 22.29/3.76 & $i(v2) & $i(v1) & $i(v0))
% 22.29/3.76
% 22.29/3.76 (not)
% 22.29/3.76 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (not(v1)
% 22.29/3.76 = v2) | ~ (model(v0, v2) = v3) | ~ $i(v1) | ~ $i(v0) | model(v0, v1) =
% 22.29/3.76 0) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (model(v0, v1)
% 22.29/3.76 = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (not(v1) = v3 & model(v0,
% 22.29/3.76 v3) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 22.29/3.76 (not(v1) = v2) | ~ (model(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3:
% 22.29/3.76 int] : ( ~ (v3 = 0) & model(v0, v1) = v3)) & ! [v0: $i] : ! [v1: $i] : (
% 22.29/3.76 ~ (model(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v2: $i] : ? [v3: int] :
% 22.29/3.76 ( ~ (v3 = 0) & not(v1) = v2 & model(v0, v2) = v3 & $i(v2)))
% 22.29/3.76
% 22.29/3.76 (sat_non_taut_pair)
% 22.29/3.76 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] : ?
% 22.29/3.76 [v5: $i] : (model(v5, v1) = 0 & model(v5, v0) = 0 & model(v2, v1) = v4 &
% 22.29/3.76 model(v2, v0) = v3 & $i(v5) & $i(v2) & $i(v1) & $i(v0) & ( ~ (v4 = 0) | ~
% 22.29/3.76 (v3 = 0)))
% 22.29/3.76
% 22.29/3.76 (thm)
% 22.29/3.76 $i(thm) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 |
% 22.29/3.76 ~ (status(v0, v1, thm) = 0) | ~ (model(v2, v1) = v3) | ~ $i(v2) | ~
% 22.29/3.76 $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & model(v2, v0) = v4)) & !
% 22.29/3.76 [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (status(v0, v1, thm) =
% 22.29/3.76 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) &
% 22.29/3.76 model(v3, v1) = v4 & model(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1:
% 22.29/3.76 $i] : ! [v2: $i] : ( ~ (status(v0, v1, thm) = 0) | ~ (model(v2, v0) = 0) |
% 22.29/3.76 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | model(v2, v1) = 0)
% 22.29/3.76
% 22.29/3.76 (xora)
% 22.29/3.77 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 22.29/3.77 | ~ (xora(v0, v1) = 0) | ~ (status(v2, v3, v1) = v4) | ~ $i(v3) | ~
% 22.29/3.77 $i(v2) | ~ $i(v1) | ~ $i(v0) | status(v2, v3, v0) = 0) & ! [v0: $i] : !
% 22.29/3.77 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (xora(v0,
% 22.29/3.77 v1) = 0) | ~ (status(v2, v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~
% 22.29/3.77 $i(v1) | ~ $i(v0) | status(v2, v3, v1) = 0) & ! [v0: $i] : ! [v1: $i] :
% 22.29/3.77 ! [v2: $i] : ! [v3: $i] : ( ~ (xora(v0, v1) = 0) | ~ (status(v2, v3, v1) =
% 22.29/3.77 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~
% 22.29/3.77 (v4 = 0) & status(v2, v3, v0) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 22.29/3.77 $i] : ! [v3: $i] : ( ~ (xora(v0, v1) = 0) | ~ (status(v2, v3, v0) = 0) |
% 22.29/3.77 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) &
% 22.29/3.77 status(v2, v3, v1) = v4)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2
% 22.29/3.77 = 0 | ~ (xora(v0, v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4:
% 22.29/3.77 $i] : ? [v5: any] : ? [v6: any] : (status(v3, v4, v1) = v6 & status(v3,
% 22.29/3.77 v4, v0) = v5 & $i(v4) & $i(v3) & ( ~ (v6 = 0) | v5 = 0) & ( ~ (v5 = 0) |
% 22.29/3.77 v6 = 0)))
% 22.29/3.77
% 22.29/3.77 (xora_csa_thm)
% 22.29/3.77 $i(csa) & $i(thm) & ? [v0: int] : ( ~ (v0 = 0) & xora(csa, thm) = v0)
% 22.29/3.77
% 22.29/3.77 (function-axioms)
% 22.29/3.77 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 22.29/3.77 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (status(v4, v3, v2) = v1) | ~
% 22.29/3.77 (status(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 22.29/3.77 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (xora(v3, v2)
% 22.29/3.77 = v1) | ~ (xora(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 22.29/3.77 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (nevera(v3,
% 22.29/3.77 v2) = v1) | ~ (nevera(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 22.29/3.77 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (nota(v3,
% 22.29/3.77 v2) = v1) | ~ (nota(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 22.29/3.77 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (isa(v3,
% 22.29/3.77 v2) = v1) | ~ (isa(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 22.29/3.77 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.29/3.77 (mighta(v3, v2) = v1) | ~ (mighta(v3, v2) = v0)) & ! [v0:
% 22.29/3.77 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 22.29/3.77 : (v1 = v0 | ~ (model(v3, v2) = v1) | ~ (model(v3, v2) = v0)) & ! [v0: $i]
% 22.29/3.77 : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (not(v2) = v1) | ~ (not(v2) =
% 22.29/3.77 v0))
% 22.29/3.77
% 22.29/3.77 Further assumptions not needed in the proof:
% 22.29/3.77 --------------------------------------------
% 22.29/3.77 cax, contradiction, eqv, esa, eth, isa, mighta, nevera, noc, nota, sap, sat,
% 22.29/3.77 satisfiable, sca, tac, tau, tautology, tca, unp, uns, wca, wec, wtc, wth
% 22.29/3.77
% 22.29/3.77 Those formulas are unsatisfiable:
% 22.29/3.77 ---------------------------------
% 22.29/3.77
% 22.29/3.77 Begin of proof
% 22.29/3.77 |
% 22.29/3.77 | ALPHA: (thm) implies:
% 22.29/3.78 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (status(v0, v1, thm) = 0)
% 22.29/3.78 | | ~ (model(v2, v0) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 22.29/3.78 | model(v2, v1) = 0)
% 22.29/3.78 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (status(v0, v1,
% 22.29/3.78 | thm) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] :
% 22.29/3.78 | ( ~ (v4 = 0) & model(v3, v1) = v4 & model(v3, v0) = 0 & $i(v3)))
% 22.29/3.78 |
% 22.29/3.78 | ALPHA: (csa) implies:
% 22.29/3.78 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (status(v0, v1, csa) = 0) | ~ $i(v1) |
% 22.29/3.78 | ~ $i(v0) | ? [v2: $i] : ? [v3: $i] : (not(v1) = v2 & model(v3, v2)
% 22.29/3.78 | = 0 & model(v3, v0) = 0 & $i(v3) & $i(v2)))
% 22.29/3.78 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (status(v0, v1,
% 22.29/3.78 | csa) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (not(v1) = v3
% 22.29/3.78 | & $i(v3) & ! [v4: $i] : ( ~ (model(v4, v3) = 0) | ~ $i(v4) | ?
% 22.29/3.78 | [v5: int] : ( ~ (v5 = 0) & model(v4, v0) = v5)) & ! [v4: $i] : (
% 22.29/3.78 | ~ (model(v4, v0) = 0) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) &
% 22.29/3.78 | model(v4, v3) = v5))))
% 22.29/3.78 |
% 22.29/3.78 | ALPHA: (xora) implies:
% 22.29/3.78 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (xora(v0, v1) =
% 22.29/3.78 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: $i] : ? [v5:
% 22.29/3.78 | any] : ? [v6: any] : (status(v3, v4, v1) = v6 & status(v3, v4, v0)
% 22.29/3.78 | = v5 & $i(v4) & $i(v3) & ( ~ (v6 = 0) | v5 = 0) & ( ~ (v5 = 0) | v6
% 22.29/3.78 | = 0)))
% 22.29/3.78 |
% 22.29/3.78 | ALPHA: (not) implies:
% 22.66/3.78 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (model(v0, v1) = 0) | ~ $i(v1) | ~
% 22.66/3.78 | $i(v0) | ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) & not(v1) = v2 &
% 22.66/3.78 | model(v0, v2) = v3 & $i(v2)))
% 22.66/3.78 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (not(v1) = v2) | ~
% 22.66/3.78 | (model(v0, v2) = 0) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3
% 22.66/3.78 | = 0) & model(v0, v1) = v3))
% 22.66/3.78 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (model(v0, v1)
% 22.66/3.78 | = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (not(v1) = v3 &
% 22.66/3.78 | model(v0, v3) = 0 & $i(v3)))
% 22.66/3.78 |
% 22.66/3.78 | ALPHA: (xora_csa_thm) implies:
% 22.66/3.78 | (9) $i(thm)
% 22.66/3.78 | (10) $i(csa)
% 22.66/3.78 | (11) ? [v0: int] : ( ~ (v0 = 0) & xora(csa, thm) = v0)
% 22.66/3.78 |
% 22.66/3.78 | ALPHA: (function-axioms) implies:
% 22.66/3.79 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (not(v2) = v1)
% 22.66/3.79 | | ~ (not(v2) = v0))
% 22.66/3.79 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 22.66/3.79 | : ! [v3: $i] : (v1 = v0 | ~ (model(v3, v2) = v1) | ~ (model(v3, v2)
% 22.66/3.79 | = v0))
% 22.66/3.79 |
% 22.66/3.79 | DELTA: instantiating (11) with fresh symbol all_30_0 gives:
% 22.66/3.79 | (14) ~ (all_30_0 = 0) & xora(csa, thm) = all_30_0
% 22.66/3.79 |
% 22.66/3.79 | ALPHA: (14) implies:
% 22.66/3.79 | (15) ~ (all_30_0 = 0)
% 22.66/3.79 | (16) xora(csa, thm) = all_30_0
% 22.66/3.79 |
% 22.66/3.79 | DELTA: instantiating (non_thm_spt) with fresh symbols all_40_0, all_40_1,
% 22.66/3.79 | all_40_2, all_40_3, all_40_4 gives:
% 22.66/3.79 | (17) ~ (all_40_1 = 0) & model(all_40_0, all_40_2) = 0 & model(all_40_4,
% 22.66/3.79 | all_40_2) = all_40_1 & model(all_40_4, all_40_3) = 0 & $i(all_40_0)
% 22.66/3.79 | & $i(all_40_2) & $i(all_40_3) & $i(all_40_4)
% 22.66/3.79 |
% 22.66/3.79 | ALPHA: (17) implies:
% 22.66/3.79 | (18) $i(all_40_4)
% 22.66/3.79 | (19) $i(all_40_3)
% 22.66/3.79 | (20) model(all_40_4, all_40_3) = 0
% 22.66/3.79 |
% 22.66/3.79 | DELTA: instantiating (sat_non_taut_pair) with fresh symbols all_42_0,
% 22.66/3.79 | all_42_1, all_42_2, all_42_3, all_42_4, all_42_5 gives:
% 22.66/3.79 | (21) model(all_42_0, all_42_4) = 0 & model(all_42_0, all_42_5) = 0 &
% 22.66/3.79 | model(all_42_3, all_42_4) = all_42_1 & model(all_42_3, all_42_5) =
% 22.66/3.79 | all_42_2 & $i(all_42_0) & $i(all_42_3) & $i(all_42_4) & $i(all_42_5) &
% 22.66/3.79 | ( ~ (all_42_1 = 0) | ~ (all_42_2 = 0))
% 22.66/3.79 |
% 22.66/3.79 | ALPHA: (21) implies:
% 22.66/3.79 | (22) $i(all_42_5)
% 22.66/3.79 | (23) $i(all_42_3)
% 22.66/3.79 | (24) model(all_42_3, all_42_5) = all_42_2
% 22.66/3.79 |
% 22.66/3.79 | DELTA: instantiating (mixed_pair) with fresh symbols all_44_0, all_44_1,
% 22.66/3.79 | all_44_2, all_44_3, all_44_4, all_44_5, all_44_6 gives:
% 22.66/3.79 | (25) ~ (all_44_1 = 0) & ~ (all_44_3 = 0) & model(all_44_0, all_44_6) = 0
% 22.66/3.79 | & model(all_44_2, all_44_5) = 0 & model(all_44_2, all_44_6) = all_44_1
% 22.66/3.79 | & model(all_44_4, all_44_5) = all_44_3 & $i(all_44_0) & $i(all_44_2) &
% 22.66/3.79 | $i(all_44_4) & $i(all_44_5) & $i(all_44_6) & ! [v0: $i] : ! [v1:
% 22.66/3.79 | int] : (v1 = 0 | ~ (model(v0, all_44_5) = v1) | ~ $i(v0) | ? [v2:
% 22.66/3.79 | int] : ( ~ (v2 = 0) & model(v0, all_44_6) = v2)) & ! [v0: $i] : (
% 22.66/3.79 | ~ (model(v0, all_44_6) = 0) | ~ $i(v0) | model(v0, all_44_5) = 0)
% 22.66/3.79 |
% 22.66/3.79 | ALPHA: (25) implies:
% 22.66/3.79 | (26) ~ (all_44_3 = 0)
% 22.66/3.79 | (27) ~ (all_44_1 = 0)
% 22.66/3.79 | (28) $i(all_44_6)
% 22.66/3.79 | (29) $i(all_44_5)
% 22.66/3.79 | (30) $i(all_44_4)
% 22.66/3.79 | (31) $i(all_44_2)
% 22.66/3.79 | (32) $i(all_44_0)
% 22.66/3.79 | (33) model(all_44_4, all_44_5) = all_44_3
% 22.66/3.79 | (34) model(all_44_2, all_44_6) = all_44_1
% 22.66/3.79 | (35) model(all_44_2, all_44_5) = 0
% 22.66/3.79 | (36) model(all_44_0, all_44_6) = 0
% 22.66/3.79 | (37) ! [v0: $i] : ! [v1: int] : (v1 = 0 | ~ (model(v0, all_44_5) = v1) |
% 22.66/3.79 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & model(v0, all_44_6) = v2))
% 22.66/3.79 |
% 22.66/3.79 | GROUND_INST: instantiating (6) with all_40_4, all_40_3, simplifying with (18),
% 22.66/3.79 | (19), (20) gives:
% 22.66/3.80 | (38) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & not(all_40_3) = v0 &
% 22.66/3.80 | model(all_40_4, v0) = v1 & $i(v0))
% 22.66/3.80 |
% 22.66/3.80 | GROUND_INST: instantiating (8) with all_42_3, all_42_5, all_42_2, simplifying
% 22.66/3.80 | with (22), (23), (24) gives:
% 22.66/3.80 | (39) all_42_2 = 0 | ? [v0: $i] : (not(all_42_5) = v0 & model(all_42_3, v0)
% 22.66/3.80 | = 0 & $i(v0))
% 22.66/3.80 |
% 22.66/3.80 | GROUND_INST: instantiating (37) with all_44_4, all_44_3, simplifying with
% 22.66/3.80 | (30), (33) gives:
% 22.66/3.80 | (40) all_44_3 = 0 | ? [v0: int] : ( ~ (v0 = 0) & model(all_44_4, all_44_6)
% 22.66/3.80 | = v0)
% 22.66/3.80 |
% 22.66/3.80 | GROUND_INST: instantiating (8) with all_44_4, all_44_5, all_44_3, simplifying
% 22.66/3.80 | with (29), (30), (33) gives:
% 22.66/3.80 | (41) all_44_3 = 0 | ? [v0: $i] : (not(all_44_5) = v0 & model(all_44_4, v0)
% 22.66/3.80 | = 0 & $i(v0))
% 22.66/3.80 |
% 22.66/3.80 | GROUND_INST: instantiating (8) with all_44_2, all_44_6, all_44_1, simplifying
% 22.66/3.80 | with (28), (31), (34) gives:
% 22.66/3.80 | (42) all_44_1 = 0 | ? [v0: $i] : (not(all_44_6) = v0 & model(all_44_2, v0)
% 22.66/3.80 | = 0 & $i(v0))
% 22.66/3.80 |
% 22.66/3.80 | GROUND_INST: instantiating (6) with all_44_2, all_44_5, simplifying with (29),
% 22.66/3.80 | (31), (35) gives:
% 22.66/3.80 | (43) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & not(all_44_5) = v0 &
% 22.66/3.80 | model(all_44_2, v0) = v1 & $i(v0))
% 22.66/3.80 |
% 22.66/3.80 | GROUND_INST: instantiating (6) with all_44_0, all_44_6, simplifying with (28),
% 22.66/3.80 | (32), (36) gives:
% 22.66/3.80 | (44) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & not(all_44_6) = v0 &
% 22.66/3.80 | model(all_44_0, v0) = v1 & $i(v0))
% 22.66/3.80 |
% 22.66/3.80 | GROUND_INST: instantiating (5) with csa, thm, all_30_0, simplifying with (9),
% 22.66/3.80 | (10), (16) gives:
% 22.66/3.80 | (45) all_30_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any]
% 22.66/3.80 | : (status(v0, v1, csa) = v2 & status(v0, v1, thm) = v3 & $i(v1) &
% 22.66/3.80 | $i(v0) & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))
% 22.66/3.80 |
% 22.66/3.80 | DELTA: instantiating (44) with fresh symbols all_53_0, all_53_1 gives:
% 22.66/3.80 | (46) ~ (all_53_0 = 0) & not(all_44_6) = all_53_1 & model(all_44_0,
% 22.66/3.80 | all_53_1) = all_53_0 & $i(all_53_1)
% 22.66/3.80 |
% 22.66/3.80 | ALPHA: (46) implies:
% 22.66/3.80 | (47) ~ (all_53_0 = 0)
% 22.66/3.80 | (48) model(all_44_0, all_53_1) = all_53_0
% 22.66/3.80 | (49) not(all_44_6) = all_53_1
% 22.66/3.80 |
% 22.66/3.80 | DELTA: instantiating (43) with fresh symbols all_57_0, all_57_1 gives:
% 22.66/3.80 | (50) ~ (all_57_0 = 0) & not(all_44_5) = all_57_1 & model(all_44_2,
% 22.66/3.80 | all_57_1) = all_57_0 & $i(all_57_1)
% 22.66/3.80 |
% 22.66/3.80 | ALPHA: (50) implies:
% 22.66/3.80 | (51) ~ (all_57_0 = 0)
% 22.66/3.80 | (52) model(all_44_2, all_57_1) = all_57_0
% 22.66/3.80 | (53) not(all_44_5) = all_57_1
% 22.66/3.80 |
% 22.66/3.80 | DELTA: instantiating (38) with fresh symbols all_61_0, all_61_1 gives:
% 22.66/3.80 | (54) ~ (all_61_0 = 0) & not(all_40_3) = all_61_1 & model(all_40_4,
% 22.66/3.80 | all_61_1) = all_61_0 & $i(all_61_1)
% 22.66/3.80 |
% 22.66/3.80 | ALPHA: (54) implies:
% 22.66/3.81 | (55) ~ (all_61_0 = 0)
% 22.66/3.81 | (56) $i(all_61_1)
% 22.66/3.81 | (57) model(all_40_4, all_61_1) = all_61_0
% 22.66/3.81 |
% 22.66/3.81 | BETA: splitting (41) gives:
% 22.66/3.81 |
% 22.66/3.81 | Case 1:
% 22.66/3.81 | |
% 22.66/3.81 | | (58) all_44_3 = 0
% 22.66/3.81 | |
% 22.66/3.81 | | REDUCE: (26), (58) imply:
% 22.66/3.81 | | (59) $false
% 22.66/3.81 | |
% 22.66/3.81 | | CLOSE: (59) is inconsistent.
% 22.66/3.81 | |
% 22.66/3.81 | Case 2:
% 22.66/3.81 | |
% 22.66/3.81 | | (60) ? [v0: $i] : (not(all_44_5) = v0 & model(all_44_4, v0) = 0 &
% 22.66/3.81 | | $i(v0))
% 22.66/3.81 | |
% 22.66/3.81 | | DELTA: instantiating (60) with fresh symbol all_71_0 gives:
% 22.66/3.81 | | (61) not(all_44_5) = all_71_0 & model(all_44_4, all_71_0) = 0 &
% 22.66/3.81 | | $i(all_71_0)
% 22.66/3.81 | |
% 22.66/3.81 | | ALPHA: (61) implies:
% 22.66/3.81 | | (62) $i(all_71_0)
% 22.66/3.81 | | (63) model(all_44_4, all_71_0) = 0
% 22.66/3.81 | | (64) not(all_44_5) = all_71_0
% 22.66/3.81 | |
% 22.66/3.81 | | BETA: splitting (42) gives:
% 22.66/3.81 | |
% 22.66/3.81 | | Case 1:
% 22.66/3.81 | | |
% 22.66/3.81 | | | (65) all_44_1 = 0
% 22.66/3.81 | | |
% 22.66/3.81 | | | REDUCE: (27), (65) imply:
% 22.66/3.81 | | | (66) $false
% 22.66/3.81 | | |
% 22.66/3.81 | | | CLOSE: (66) is inconsistent.
% 22.66/3.81 | | |
% 22.66/3.81 | | Case 2:
% 22.66/3.81 | | |
% 22.66/3.81 | | | (67) ? [v0: $i] : (not(all_44_6) = v0 & model(all_44_2, v0) = 0 &
% 22.66/3.81 | | | $i(v0))
% 22.66/3.81 | | |
% 22.66/3.81 | | | DELTA: instantiating (67) with fresh symbol all_77_0 gives:
% 22.66/3.81 | | | (68) not(all_44_6) = all_77_0 & model(all_44_2, all_77_0) = 0 &
% 22.66/3.81 | | | $i(all_77_0)
% 22.66/3.81 | | |
% 22.66/3.81 | | | ALPHA: (68) implies:
% 22.66/3.81 | | | (69) $i(all_77_0)
% 22.66/3.81 | | | (70) model(all_44_2, all_77_0) = 0
% 22.66/3.81 | | | (71) not(all_44_6) = all_77_0
% 22.66/3.81 | | |
% 22.66/3.81 | | | BETA: splitting (45) gives:
% 22.66/3.81 | | |
% 22.66/3.81 | | | Case 1:
% 22.66/3.81 | | | |
% 22.66/3.81 | | | | (72) all_30_0 = 0
% 22.66/3.81 | | | |
% 22.66/3.81 | | | | REDUCE: (15), (72) imply:
% 22.66/3.81 | | | | (73) $false
% 22.66/3.81 | | | |
% 22.66/3.81 | | | | CLOSE: (73) is inconsistent.
% 22.66/3.81 | | | |
% 22.66/3.81 | | | Case 2:
% 22.66/3.81 | | | |
% 22.66/3.81 | | | | (74) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 22.66/3.81 | | | | (status(v0, v1, csa) = v2 & status(v0, v1, thm) = v3 & $i(v1) &
% 22.66/3.81 | | | | $i(v0) & ( ~ (v3 = 0) | v2 = 0) & ( ~ (v2 = 0) | v3 = 0))
% 22.66/3.81 | | | |
% 22.66/3.81 | | | | DELTA: instantiating (74) with fresh symbols all_82_0, all_82_1,
% 22.66/3.81 | | | | all_82_2, all_82_3 gives:
% 22.66/3.81 | | | | (75) status(all_82_3, all_82_2, csa) = all_82_1 & status(all_82_3,
% 22.66/3.81 | | | | all_82_2, thm) = all_82_0 & $i(all_82_2) & $i(all_82_3) & ( ~
% 22.66/3.81 | | | | (all_82_0 = 0) | all_82_1 = 0) & ( ~ (all_82_1 = 0) | all_82_0
% 22.66/3.81 | | | | = 0)
% 22.66/3.81 | | | |
% 22.66/3.81 | | | | ALPHA: (75) implies:
% 22.66/3.81 | | | | (76) $i(all_82_3)
% 22.66/3.81 | | | | (77) $i(all_82_2)
% 22.66/3.81 | | | | (78) status(all_82_3, all_82_2, thm) = all_82_0
% 22.66/3.81 | | | | (79) status(all_82_3, all_82_2, csa) = all_82_1
% 22.66/3.81 | | | | (80) ~ (all_82_1 = 0) | all_82_0 = 0
% 22.66/3.81 | | | | (81) ~ (all_82_0 = 0) | all_82_1 = 0
% 22.66/3.81 | | | |
% 22.66/3.81 | | | | BETA: splitting (40) gives:
% 22.66/3.81 | | | |
% 22.66/3.81 | | | | Case 1:
% 22.66/3.81 | | | | |
% 22.66/3.81 | | | | | (82) all_44_3 = 0
% 22.66/3.81 | | | | |
% 22.66/3.81 | | | | | REDUCE: (26), (82) imply:
% 22.66/3.81 | | | | | (83) $false
% 22.66/3.81 | | | | |
% 22.66/3.81 | | | | | CLOSE: (83) is inconsistent.
% 22.66/3.81 | | | | |
% 22.66/3.81 | | | | Case 2:
% 22.66/3.81 | | | | |
% 22.66/3.81 | | | | |
% 22.66/3.81 | | | | | GROUND_INST: instantiating (12) with all_53_1, all_77_0, all_44_6,
% 22.66/3.81 | | | | | simplifying with (49), (71) gives:
% 22.66/3.82 | | | | | (84) all_77_0 = all_53_1
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | GROUND_INST: instantiating (12) with all_57_1, all_71_0, all_44_5,
% 22.66/3.82 | | | | | simplifying with (53), (64) gives:
% 22.66/3.82 | | | | | (85) all_71_0 = all_57_1
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | REDUCE: (70), (84) imply:
% 22.66/3.82 | | | | | (86) model(all_44_2, all_53_1) = 0
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | REDUCE: (63), (85) imply:
% 22.66/3.82 | | | | | (87) model(all_44_4, all_57_1) = 0
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | REDUCE: (69), (84) imply:
% 22.66/3.82 | | | | | (88) $i(all_53_1)
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | REDUCE: (62), (85) imply:
% 22.66/3.82 | | | | | (89) $i(all_57_1)
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | GROUND_INST: instantiating (8) with all_40_4, all_61_1, all_61_0,
% 22.66/3.82 | | | | | simplifying with (18), (56), (57) gives:
% 22.66/3.82 | | | | | (90) all_61_0 = 0 | ? [v0: $i] : (not(all_61_1) = v0 &
% 22.66/3.82 | | | | | model(all_40_4, v0) = 0 & $i(v0))
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | GROUND_INST: instantiating (6) with all_44_4, all_57_1, simplifying
% 22.66/3.82 | | | | | with (30), (87), (89) gives:
% 22.66/3.82 | | | | | (91) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & not(all_57_1) = v0
% 22.66/3.82 | | | | | & model(all_44_4, v0) = v1 & $i(v0))
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | GROUND_INST: instantiating (6) with all_44_2, all_53_1, simplifying
% 22.66/3.82 | | | | | with (31), (86), (88) gives:
% 22.66/3.82 | | | | | (92) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & not(all_53_1) = v0
% 22.66/3.82 | | | | | & model(all_44_2, v0) = v1 & $i(v0))
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | GROUND_INST: instantiating (8) with all_44_2, all_57_1, all_57_0,
% 22.66/3.82 | | | | | simplifying with (31), (52), (89) gives:
% 22.66/3.82 | | | | | (93) all_57_0 = 0 | ? [v0: $i] : (not(all_57_1) = v0 &
% 22.66/3.82 | | | | | model(all_44_2, v0) = 0 & $i(v0))
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | GROUND_INST: instantiating (8) with all_44_0, all_53_1, all_53_0,
% 22.66/3.82 | | | | | simplifying with (32), (48), (88) gives:
% 22.66/3.82 | | | | | (94) all_53_0 = 0 | ? [v0: $i] : (not(all_53_1) = v0 &
% 22.66/3.82 | | | | | model(all_44_0, v0) = 0 & $i(v0))
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | GROUND_INST: instantiating (2) with all_82_3, all_82_2, all_82_0,
% 22.66/3.82 | | | | | simplifying with (76), (77), (78) gives:
% 22.66/3.82 | | | | | (95) all_82_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 22.66/3.82 | | | | | model(v0, all_82_2) = v1 & model(v0, all_82_3) = 0 & $i(v0))
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | GROUND_INST: instantiating (4) with all_82_3, all_82_2, all_82_1,
% 22.66/3.82 | | | | | simplifying with (76), (77), (79) gives:
% 22.66/3.82 | | | | | (96) all_82_1 = 0 | ? [v0: $i] : (not(all_82_2) = v0 & $i(v0) & !
% 22.66/3.82 | | | | | [v1: $i] : ( ~ (model(v1, v0) = 0) | ~ $i(v1) | ? [v2:
% 22.66/3.82 | | | | | int] : ( ~ (v2 = 0) & model(v1, all_82_3) = v2)) & !
% 22.66/3.82 | | | | | [v1: $i] : ( ~ (model(v1, all_82_3) = 0) | ~ $i(v1) | ?
% 22.66/3.82 | | | | | [v2: int] : ( ~ (v2 = 0) & model(v1, v0) = v2)))
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | DELTA: instantiating (92) with fresh symbols all_113_0, all_113_1
% 22.66/3.82 | | | | | gives:
% 22.66/3.82 | | | | | (97) ~ (all_113_0 = 0) & not(all_53_1) = all_113_1 &
% 22.66/3.82 | | | | | model(all_44_2, all_113_1) = all_113_0 & $i(all_113_1)
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | ALPHA: (97) implies:
% 22.66/3.82 | | | | | (98) ~ (all_113_0 = 0)
% 22.66/3.82 | | | | | (99) model(all_44_2, all_113_1) = all_113_0
% 22.66/3.82 | | | | | (100) not(all_53_1) = all_113_1
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | DELTA: instantiating (91) with fresh symbols all_117_0, all_117_1
% 22.66/3.82 | | | | | gives:
% 22.66/3.82 | | | | | (101) ~ (all_117_0 = 0) & not(all_57_1) = all_117_1 &
% 22.66/3.82 | | | | | model(all_44_4, all_117_1) = all_117_0 & $i(all_117_1)
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | ALPHA: (101) implies:
% 22.66/3.82 | | | | | (102) ~ (all_117_0 = 0)
% 22.66/3.82 | | | | | (103) model(all_44_4, all_117_1) = all_117_0
% 22.66/3.82 | | | | | (104) not(all_57_1) = all_117_1
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | BETA: splitting (93) gives:
% 22.66/3.82 | | | | |
% 22.66/3.82 | | | | | Case 1:
% 22.66/3.82 | | | | | |
% 22.66/3.82 | | | | | | (105) all_57_0 = 0
% 22.66/3.82 | | | | | |
% 22.66/3.82 | | | | | | REDUCE: (51), (105) imply:
% 22.66/3.82 | | | | | | (106) $false
% 22.66/3.82 | | | | | |
% 22.66/3.82 | | | | | | CLOSE: (106) is inconsistent.
% 22.66/3.82 | | | | | |
% 22.66/3.82 | | | | | Case 2:
% 22.66/3.82 | | | | | |
% 22.66/3.82 | | | | | | (107) ? [v0: $i] : (not(all_57_1) = v0 & model(all_44_2, v0) = 0
% 22.66/3.82 | | | | | | & $i(v0))
% 22.66/3.82 | | | | | |
% 22.66/3.82 | | | | | | DELTA: instantiating (107) with fresh symbol all_137_0 gives:
% 22.66/3.82 | | | | | | (108) not(all_57_1) = all_137_0 & model(all_44_2, all_137_0) = 0
% 22.66/3.82 | | | | | | & $i(all_137_0)
% 22.66/3.82 | | | | | |
% 22.66/3.83 | | | | | | ALPHA: (108) implies:
% 22.66/3.83 | | | | | | (109) $i(all_137_0)
% 22.66/3.83 | | | | | | (110) model(all_44_2, all_137_0) = 0
% 22.66/3.83 | | | | | | (111) not(all_57_1) = all_137_0
% 22.66/3.83 | | | | | |
% 22.66/3.83 | | | | | | BETA: splitting (94) gives:
% 22.66/3.83 | | | | | |
% 22.66/3.83 | | | | | | Case 1:
% 22.66/3.83 | | | | | | |
% 22.66/3.83 | | | | | | | (112) all_53_0 = 0
% 22.66/3.83 | | | | | | |
% 22.66/3.83 | | | | | | | REDUCE: (47), (112) imply:
% 22.66/3.83 | | | | | | | (113) $false
% 22.66/3.83 | | | | | | |
% 22.66/3.83 | | | | | | | CLOSE: (113) is inconsistent.
% 22.66/3.83 | | | | | | |
% 22.66/3.83 | | | | | | Case 2:
% 22.66/3.83 | | | | | | |
% 22.66/3.83 | | | | | | | (114) ? [v0: $i] : (not(all_53_1) = v0 & model(all_44_0, v0) =
% 22.66/3.83 | | | | | | | 0 & $i(v0))
% 22.66/3.83 | | | | | | |
% 22.66/3.83 | | | | | | | DELTA: instantiating (114) with fresh symbol all_154_0 gives:
% 22.66/3.83 | | | | | | | (115) not(all_53_1) = all_154_0 & model(all_44_0, all_154_0) =
% 22.66/3.83 | | | | | | | 0 & $i(all_154_0)
% 22.66/3.83 | | | | | | |
% 22.66/3.83 | | | | | | | ALPHA: (115) implies:
% 22.66/3.83 | | | | | | | (116) $i(all_154_0)
% 22.66/3.83 | | | | | | | (117) model(all_44_0, all_154_0) = 0
% 22.66/3.83 | | | | | | | (118) not(all_53_1) = all_154_0
% 22.66/3.83 | | | | | | |
% 22.66/3.83 | | | | | | | BETA: splitting (90) gives:
% 22.66/3.83 | | | | | | |
% 22.66/3.83 | | | | | | | Case 1:
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | | (119) all_61_0 = 0
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | | REDUCE: (55), (119) imply:
% 22.66/3.83 | | | | | | | | (120) $false
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | | CLOSE: (120) is inconsistent.
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | Case 2:
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | | GROUND_INST: instantiating (12) with all_113_1, all_154_0,
% 22.66/3.83 | | | | | | | | all_53_1, simplifying with (100), (118) gives:
% 22.66/3.83 | | | | | | | | (121) all_154_0 = all_113_1
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | | GROUND_INST: instantiating (12) with all_117_1, all_137_0,
% 22.66/3.83 | | | | | | | | all_57_1, simplifying with (104), (111) gives:
% 22.66/3.83 | | | | | | | | (122) all_137_0 = all_117_1
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | | REDUCE: (117), (121) imply:
% 22.66/3.83 | | | | | | | | (123) model(all_44_0, all_113_1) = 0
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | | REDUCE: (110), (122) imply:
% 22.66/3.83 | | | | | | | | (124) model(all_44_2, all_117_1) = 0
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | | REDUCE: (116), (121) imply:
% 22.66/3.83 | | | | | | | | (125) $i(all_113_1)
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | | REDUCE: (109), (122) imply:
% 22.66/3.83 | | | | | | | | (126) $i(all_117_1)
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | | GROUND_INST: instantiating (8) with all_44_4, all_117_1,
% 22.66/3.83 | | | | | | | | all_117_0, simplifying with (30), (103), (126)
% 22.66/3.83 | | | | | | | | gives:
% 22.66/3.83 | | | | | | | | (127) all_117_0 = 0 | ? [v0: $i] : (not(all_117_1) = v0 &
% 22.66/3.83 | | | | | | | | model(all_44_4, v0) = 0 & $i(v0))
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | | GROUND_INST: instantiating (8) with all_44_2, all_113_1,
% 22.66/3.83 | | | | | | | | all_113_0, simplifying with (31), (99), (125)
% 22.66/3.83 | | | | | | | | gives:
% 22.66/3.83 | | | | | | | | (128) all_113_0 = 0 | ? [v0: $i] : (not(all_113_1) = v0 &
% 22.66/3.83 | | | | | | | | model(all_44_2, v0) = 0 & $i(v0))
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | | GROUND_INST: instantiating (6) with all_44_2, all_117_1,
% 22.66/3.83 | | | | | | | | simplifying with (31), (124), (126) gives:
% 22.66/3.83 | | | | | | | | (129) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 22.66/3.83 | | | | | | | | not(all_117_1) = v0 & model(all_44_2, v0) = v1 &
% 22.66/3.83 | | | | | | | | $i(v0))
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | | GROUND_INST: instantiating (6) with all_44_0, all_113_1,
% 22.66/3.83 | | | | | | | | simplifying with (32), (123), (125) gives:
% 22.66/3.83 | | | | | | | | (130) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 22.66/3.83 | | | | | | | | not(all_113_1) = v0 & model(all_44_0, v0) = v1 &
% 22.66/3.83 | | | | | | | | $i(v0))
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | | DELTA: instantiating (130) with fresh symbols all_175_0,
% 22.66/3.83 | | | | | | | | all_175_1 gives:
% 22.66/3.83 | | | | | | | | (131) ~ (all_175_0 = 0) & not(all_113_1) = all_175_1 &
% 22.66/3.83 | | | | | | | | model(all_44_0, all_175_1) = all_175_0 & $i(all_175_1)
% 22.66/3.83 | | | | | | | |
% 22.66/3.83 | | | | | | | | ALPHA: (131) implies:
% 22.66/3.84 | | | | | | | | (132) ~ (all_175_0 = 0)
% 22.66/3.84 | | | | | | | | (133) model(all_44_0, all_175_1) = all_175_0
% 22.66/3.84 | | | | | | | | (134) not(all_113_1) = all_175_1
% 22.66/3.84 | | | | | | | |
% 22.66/3.84 | | | | | | | | DELTA: instantiating (129) with fresh symbols all_187_0,
% 22.66/3.84 | | | | | | | | all_187_1 gives:
% 22.66/3.84 | | | | | | | | (135) ~ (all_187_0 = 0) & not(all_117_1) = all_187_1 &
% 22.66/3.84 | | | | | | | | model(all_44_2, all_187_1) = all_187_0 & $i(all_187_1)
% 22.66/3.84 | | | | | | | |
% 22.66/3.84 | | | | | | | | ALPHA: (135) implies:
% 22.66/3.84 | | | | | | | | (136) ~ (all_187_0 = 0)
% 22.66/3.84 | | | | | | | | (137) model(all_44_2, all_187_1) = all_187_0
% 22.66/3.84 | | | | | | | | (138) not(all_117_1) = all_187_1
% 22.66/3.84 | | | | | | | |
% 22.66/3.84 | | | | | | | | BETA: splitting (128) gives:
% 22.66/3.84 | | | | | | | |
% 22.66/3.84 | | | | | | | | Case 1:
% 22.66/3.84 | | | | | | | | |
% 22.66/3.84 | | | | | | | | | (139) all_113_0 = 0
% 22.66/3.84 | | | | | | | | |
% 22.66/3.84 | | | | | | | | | REDUCE: (98), (139) imply:
% 22.66/3.84 | | | | | | | | | (140) $false
% 22.66/3.84 | | | | | | | | |
% 22.66/3.84 | | | | | | | | | CLOSE: (140) is inconsistent.
% 22.66/3.84 | | | | | | | | |
% 22.66/3.84 | | | | | | | | Case 2:
% 22.66/3.84 | | | | | | | | |
% 22.66/3.84 | | | | | | | | | (141) ? [v0: $i] : (not(all_113_1) = v0 & model(all_44_2,
% 22.66/3.84 | | | | | | | | | v0) = 0 & $i(v0))
% 22.66/3.84 | | | | | | | | |
% 22.66/3.84 | | | | | | | | | DELTA: instantiating (141) with fresh symbol all_207_0 gives:
% 22.66/3.84 | | | | | | | | | (142) not(all_113_1) = all_207_0 & model(all_44_2,
% 22.66/3.84 | | | | | | | | | all_207_0) = 0 & $i(all_207_0)
% 22.66/3.84 | | | | | | | | |
% 22.66/3.84 | | | | | | | | | ALPHA: (142) implies:
% 22.66/3.84 | | | | | | | | | (143) $i(all_207_0)
% 22.66/3.84 | | | | | | | | | (144) model(all_44_2, all_207_0) = 0
% 22.66/3.84 | | | | | | | | | (145) not(all_113_1) = all_207_0
% 22.66/3.84 | | | | | | | | |
% 22.66/3.84 | | | | | | | | | BETA: splitting (127) gives:
% 22.66/3.84 | | | | | | | | |
% 22.66/3.84 | | | | | | | | | Case 1:
% 22.66/3.84 | | | | | | | | | |
% 22.66/3.84 | | | | | | | | | | (146) all_117_0 = 0
% 22.66/3.84 | | | | | | | | | |
% 22.66/3.84 | | | | | | | | | | REDUCE: (102), (146) imply:
% 22.66/3.84 | | | | | | | | | | (147) $false
% 22.66/3.84 | | | | | | | | | |
% 22.66/3.84 | | | | | | | | | | CLOSE: (147) is inconsistent.
% 22.66/3.84 | | | | | | | | | |
% 22.66/3.84 | | | | | | | | | Case 2:
% 22.66/3.84 | | | | | | | | | |
% 22.66/3.84 | | | | | | | | | | (148) ? [v0: $i] : (not(all_117_1) = v0 &
% 22.66/3.84 | | | | | | | | | | model(all_44_4, v0) = 0 & $i(v0))
% 22.66/3.84 | | | | | | | | | |
% 22.66/3.84 | | | | | | | | | | DELTA: instantiating (148) with fresh symbol all_219_0
% 22.66/3.84 | | | | | | | | | | gives:
% 22.66/3.84 | | | | | | | | | | (149) not(all_117_1) = all_219_0 & model(all_44_4,
% 22.66/3.84 | | | | | | | | | | all_219_0) = 0 & $i(all_219_0)
% 22.66/3.84 | | | | | | | | | |
% 22.66/3.84 | | | | | | | | | | ALPHA: (149) implies:
% 22.66/3.84 | | | | | | | | | | (150) $i(all_219_0)
% 22.66/3.84 | | | | | | | | | | (151) model(all_44_4, all_219_0) = 0
% 22.66/3.84 | | | | | | | | | | (152) not(all_117_1) = all_219_0
% 22.66/3.84 | | | | | | | | | |
% 22.66/3.84 | | | | | | | | | | GROUND_INST: instantiating (12) with all_175_1, all_207_0,
% 22.66/3.84 | | | | | | | | | | all_113_1, simplifying with (134), (145) gives:
% 22.66/3.84 | | | | | | | | | | (153) all_207_0 = all_175_1
% 22.66/3.84 | | | | | | | | | |
% 22.66/3.84 | | | | | | | | | | GROUND_INST: instantiating (12) with all_187_1, all_219_0,
% 22.66/3.84 | | | | | | | | | | all_117_1, simplifying with (138), (152) gives:
% 22.66/3.84 | | | | | | | | | | (154) all_219_0 = all_187_1
% 22.66/3.84 | | | | | | | | | |
% 22.66/3.84 | | | | | | | | | | REDUCE: (144), (153) imply:
% 22.66/3.84 | | | | | | | | | | (155) model(all_44_2, all_175_1) = 0
% 22.66/3.84 | | | | | | | | | |
% 22.66/3.84 | | | | | | | | | | REDUCE: (151), (154) imply:
% 22.66/3.84 | | | | | | | | | | (156) model(all_44_4, all_187_1) = 0
% 22.66/3.84 | | | | | | | | | |
% 22.66/3.84 | | | | | | | | | | REDUCE: (150), (154) imply:
% 22.66/3.84 | | | | | | | | | | (157) $i(all_187_1)
% 22.66/3.85 | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | REDUCE: (143), (153) imply:
% 22.66/3.85 | | | | | | | | | | (158) $i(all_175_1)
% 22.66/3.85 | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | BETA: splitting (39) gives:
% 22.66/3.85 | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | Case 1:
% 22.66/3.85 | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | GROUND_INST: instantiating (6) with all_44_4, all_187_1,
% 22.66/3.85 | | | | | | | | | | | simplifying with (30), (156), (157) gives:
% 22.66/3.85 | | | | | | | | | | | (159) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 22.66/3.85 | | | | | | | | | | | not(all_187_1) = v0 & model(all_44_4, v0) = v1 &
% 22.66/3.85 | | | | | | | | | | | $i(v0))
% 22.66/3.85 | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | GROUND_INST: instantiating (8) with all_44_2, all_187_1,
% 22.66/3.85 | | | | | | | | | | | all_187_0, simplifying with (31), (137), (157)
% 22.66/3.85 | | | | | | | | | | | gives:
% 22.66/3.85 | | | | | | | | | | | (160) all_187_0 = 0 | ? [v0: $i] : (not(all_187_1) = v0
% 22.66/3.85 | | | | | | | | | | | & model(all_44_2, v0) = 0 & $i(v0))
% 22.66/3.85 | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | DELTA: instantiating (159) with fresh symbols all_258_0,
% 22.66/3.85 | | | | | | | | | | | all_258_1 gives:
% 22.66/3.85 | | | | | | | | | | | (161) ~ (all_258_0 = 0) & not(all_187_1) = all_258_1 &
% 22.66/3.85 | | | | | | | | | | | model(all_44_4, all_258_1) = all_258_0 &
% 22.66/3.85 | | | | | | | | | | | $i(all_258_1)
% 22.66/3.85 | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | ALPHA: (161) implies:
% 22.66/3.85 | | | | | | | | | | | (162) ~ (all_258_0 = 0)
% 22.66/3.85 | | | | | | | | | | | (163) model(all_44_4, all_258_1) = all_258_0
% 22.66/3.85 | | | | | | | | | | | (164) not(all_187_1) = all_258_1
% 22.66/3.85 | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | BETA: splitting (160) gives:
% 22.66/3.85 | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | Case 1:
% 22.66/3.85 | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | (165) all_187_0 = 0
% 22.66/3.85 | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | REDUCE: (136), (165) imply:
% 22.66/3.85 | | | | | | | | | | | | (166) $false
% 22.66/3.85 | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | CLOSE: (166) is inconsistent.
% 22.66/3.85 | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | Case 2:
% 22.66/3.85 | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | (167) ? [v0: $i] : (not(all_187_1) = v0 &
% 22.66/3.85 | | | | | | | | | | | | model(all_44_2, v0) = 0 & $i(v0))
% 22.66/3.85 | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | DELTA: instantiating (167) with fresh symbol all_292_0
% 22.66/3.85 | | | | | | | | | | | | gives:
% 22.66/3.85 | | | | | | | | | | | | (168) not(all_187_1) = all_292_0 & model(all_44_2,
% 22.66/3.85 | | | | | | | | | | | | all_292_0) = 0 & $i(all_292_0)
% 22.66/3.85 | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | ALPHA: (168) implies:
% 22.66/3.85 | | | | | | | | | | | | (169) $i(all_292_0)
% 22.66/3.85 | | | | | | | | | | | | (170) not(all_187_1) = all_292_0
% 22.66/3.85 | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_258_1, all_292_0,
% 22.66/3.85 | | | | | | | | | | | | all_187_1, simplifying with (164), (170) gives:
% 22.66/3.85 | | | | | | | | | | | | (171) all_292_0 = all_258_1
% 22.66/3.85 | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | REDUCE: (169), (171) imply:
% 22.66/3.85 | | | | | | | | | | | | (172) $i(all_258_1)
% 22.66/3.85 | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | BETA: splitting (81) gives:
% 22.66/3.85 | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | Case 1:
% 22.66/3.85 | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | (173) ~ (all_82_0 = 0)
% 22.66/3.85 | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | REF_CLOSE: (8), (12), (13), (77), (80), (95), (96), (173) are
% 22.66/3.85 | | | | | | | | | | | | | inconsistent by sub-proof #1.
% 22.66/3.85 | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | Case 2:
% 22.66/3.85 | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | (174) all_82_1 = 0
% 22.66/3.85 | | | | | | | | | | | | | (175) all_82_0 = 0
% 22.66/3.85 | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | REDUCE: (79), (174) imply:
% 22.66/3.85 | | | | | | | | | | | | | (176) status(all_82_3, all_82_2, csa) = 0
% 22.66/3.85 | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | REDUCE: (78), (175) imply:
% 22.66/3.85 | | | | | | | | | | | | | (177) status(all_82_3, all_82_2, thm) = 0
% 22.66/3.85 | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_44_4, all_258_1,
% 22.66/3.85 | | | | | | | | | | | | | all_258_0, simplifying with (30), (163), (172)
% 22.66/3.85 | | | | | | | | | | | | | gives:
% 22.66/3.85 | | | | | | | | | | | | | (178) all_258_0 = 0 | ? [v0: $i] : (not(all_258_1) = v0
% 22.66/3.85 | | | | | | | | | | | | | & model(all_44_4, v0) = 0 & $i(v0))
% 22.66/3.85 | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_82_3, all_82_2,
% 22.66/3.85 | | | | | | | | | | | | | simplifying with (76), (77), (176) gives:
% 22.66/3.85 | | | | | | | | | | | | | (179) ? [v0: $i] : ? [v1: $i] : (not(all_82_2) = v0 &
% 22.66/3.85 | | | | | | | | | | | | | model(v1, v0) = 0 & model(v1, all_82_3) = 0 &
% 22.66/3.85 | | | | | | | | | | | | | $i(v1) & $i(v0))
% 22.66/3.85 | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | DELTA: instantiating (179) with fresh symbols all_343_0,
% 22.66/3.85 | | | | | | | | | | | | | all_343_1 gives:
% 22.66/3.85 | | | | | | | | | | | | | (180) not(all_82_2) = all_343_1 & model(all_343_0,
% 22.66/3.85 | | | | | | | | | | | | | all_343_1) = 0 & model(all_343_0, all_82_3) = 0
% 22.66/3.85 | | | | | | | | | | | | | & $i(all_343_0) & $i(all_343_1)
% 22.66/3.85 | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | ALPHA: (180) implies:
% 22.66/3.85 | | | | | | | | | | | | | (181) $i(all_343_0)
% 22.66/3.85 | | | | | | | | | | | | | (182) model(all_343_0, all_82_3) = 0
% 22.66/3.85 | | | | | | | | | | | | | (183) model(all_343_0, all_343_1) = 0
% 22.66/3.85 | | | | | | | | | | | | | (184) not(all_82_2) = all_343_1
% 22.66/3.85 | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | BETA: splitting (178) gives:
% 22.66/3.85 | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | Case 1:
% 22.66/3.85 | | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | | (185) all_258_0 = 0
% 22.66/3.85 | | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | | REDUCE: (162), (185) imply:
% 22.66/3.85 | | | | | | | | | | | | | | (186) $false
% 22.66/3.85 | | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | | CLOSE: (186) is inconsistent.
% 22.66/3.85 | | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | Case 2:
% 22.66/3.85 | | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_82_3, all_82_2,
% 22.66/3.85 | | | | | | | | | | | | | | all_343_0, simplifying with (76), (77), (177),
% 22.66/3.85 | | | | | | | | | | | | | | (181), (182) gives:
% 22.66/3.85 | | | | | | | | | | | | | | (187) model(all_343_0, all_82_2) = 0
% 22.66/3.85 | | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_343_0, all_82_2,
% 22.66/3.85 | | | | | | | | | | | | | | all_343_1, simplifying with (77), (181), (183),
% 22.66/3.85 | | | | | | | | | | | | | | (184) gives:
% 22.66/3.85 | | | | | | | | | | | | | | (188) ? [v0: int] : ( ~ (v0 = 0) & model(all_343_0,
% 22.66/3.85 | | | | | | | | | | | | | | all_82_2) = v0)
% 22.66/3.85 | | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | | DELTA: instantiating (188) with fresh symbol all_397_0
% 22.66/3.85 | | | | | | | | | | | | | | gives:
% 22.66/3.85 | | | | | | | | | | | | | | (189) ~ (all_397_0 = 0) & model(all_343_0, all_82_2) =
% 22.66/3.85 | | | | | | | | | | | | | | all_397_0
% 22.66/3.85 | | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | | ALPHA: (189) implies:
% 22.66/3.85 | | | | | | | | | | | | | | (190) ~ (all_397_0 = 0)
% 22.66/3.85 | | | | | | | | | | | | | | (191) model(all_343_0, all_82_2) = all_397_0
% 22.66/3.85 | | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_397_0, all_82_2,
% 22.66/3.85 | | | | | | | | | | | | | | all_343_0, simplifying with (187), (191) gives:
% 22.66/3.85 | | | | | | | | | | | | | | (192) all_397_0 = 0
% 22.66/3.85 | | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | | REDUCE: (190), (192) imply:
% 22.66/3.85 | | | | | | | | | | | | | | (193) $false
% 22.66/3.85 | | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | | CLOSE: (193) is inconsistent.
% 22.66/3.85 | | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | | End of split
% 22.66/3.85 | | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | End of split
% 22.66/3.85 | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | End of split
% 22.66/3.85 | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | Case 2:
% 22.66/3.85 | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | (194) ~ (all_42_2 = 0)
% 22.66/3.85 | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | BETA: splitting (39) gives:
% 22.66/3.85 | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | Case 1:
% 22.66/3.85 | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | (195) all_42_2 = 0
% 22.66/3.85 | | | | | | | | | | | |
% 22.66/3.85 | | | | | | | | | | | | REDUCE: (194), (195) imply:
% 22.66/3.85 | | | | | | | | | | | | (196) $false
% 22.66/3.85 | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | CLOSE: (196) is inconsistent.
% 22.66/3.86 | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | Case 2:
% 22.66/3.86 | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | GROUND_INST: instantiating (6) with all_44_2, all_175_1,
% 22.66/3.86 | | | | | | | | | | | | simplifying with (31), (155), (158) gives:
% 22.66/3.86 | | | | | | | | | | | | (197) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) &
% 22.66/3.86 | | | | | | | | | | | | not(all_175_1) = v0 & model(all_44_2, v0) = v1 &
% 22.66/3.86 | | | | | | | | | | | | $i(v0))
% 22.66/3.86 | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_44_0, all_175_1,
% 22.66/3.86 | | | | | | | | | | | | all_175_0, simplifying with (32), (133), (158)
% 22.66/3.86 | | | | | | | | | | | | gives:
% 22.66/3.86 | | | | | | | | | | | | (198) all_175_0 = 0 | ? [v0: $i] : (not(all_175_1) = v0
% 22.66/3.86 | | | | | | | | | | | | & model(all_44_0, v0) = 0 & $i(v0))
% 22.66/3.86 | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | DELTA: instantiating (197) with fresh symbols all_248_0,
% 22.66/3.86 | | | | | | | | | | | | all_248_1 gives:
% 22.66/3.86 | | | | | | | | | | | | (199) ~ (all_248_0 = 0) & not(all_175_1) = all_248_1 &
% 22.66/3.86 | | | | | | | | | | | | model(all_44_2, all_248_1) = all_248_0 &
% 22.66/3.86 | | | | | | | | | | | | $i(all_248_1)
% 22.66/3.86 | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | ALPHA: (199) implies:
% 22.66/3.86 | | | | | | | | | | | | (200) ~ (all_248_0 = 0)
% 22.66/3.86 | | | | | | | | | | | | (201) model(all_44_2, all_248_1) = all_248_0
% 22.66/3.86 | | | | | | | | | | | | (202) not(all_175_1) = all_248_1
% 22.66/3.86 | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | BETA: splitting (198) gives:
% 22.66/3.86 | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | Case 1:
% 22.66/3.86 | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | (203) all_175_0 = 0
% 22.66/3.86 | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | REDUCE: (132), (203) imply:
% 22.66/3.86 | | | | | | | | | | | | | (204) $false
% 22.66/3.86 | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | CLOSE: (204) is inconsistent.
% 22.66/3.86 | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | Case 2:
% 22.66/3.86 | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | (205) ? [v0: $i] : (not(all_175_1) = v0 &
% 22.66/3.86 | | | | | | | | | | | | | model(all_44_0, v0) = 0 & $i(v0))
% 22.66/3.86 | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | DELTA: instantiating (205) with fresh symbol all_298_0
% 22.66/3.86 | | | | | | | | | | | | | gives:
% 22.66/3.86 | | | | | | | | | | | | | (206) not(all_175_1) = all_298_0 & model(all_44_0,
% 22.66/3.86 | | | | | | | | | | | | | all_298_0) = 0 & $i(all_298_0)
% 22.66/3.86 | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | ALPHA: (206) implies:
% 22.66/3.86 | | | | | | | | | | | | | (207) $i(all_298_0)
% 22.66/3.86 | | | | | | | | | | | | | (208) not(all_175_1) = all_298_0
% 22.66/3.86 | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | GROUND_INST: instantiating (12) with all_248_1, all_298_0,
% 22.66/3.86 | | | | | | | | | | | | | all_175_1, simplifying with (202), (208) gives:
% 22.66/3.86 | | | | | | | | | | | | | (209) all_298_0 = all_248_1
% 22.66/3.86 | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | REDUCE: (207), (209) imply:
% 22.66/3.86 | | | | | | | | | | | | | (210) $i(all_248_1)
% 22.66/3.86 | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | BETA: splitting (81) gives:
% 22.66/3.86 | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | Case 1:
% 22.66/3.86 | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | (211) ~ (all_82_0 = 0)
% 22.66/3.86 | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | REF_CLOSE: (8), (12), (13), (77), (80), (95), (96), (211) are
% 22.66/3.86 | | | | | | | | | | | | | | inconsistent by sub-proof #1.
% 22.66/3.86 | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | Case 2:
% 22.66/3.86 | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | (212) all_82_1 = 0
% 22.66/3.86 | | | | | | | | | | | | | | (213) all_82_0 = 0
% 22.66/3.86 | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | REDUCE: (79), (212) imply:
% 22.66/3.86 | | | | | | | | | | | | | | (214) status(all_82_3, all_82_2, csa) = 0
% 22.66/3.86 | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | REDUCE: (78), (213) imply:
% 22.66/3.86 | | | | | | | | | | | | | | (215) status(all_82_3, all_82_2, thm) = 0
% 22.66/3.86 | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_44_2, all_248_1,
% 22.66/3.86 | | | | | | | | | | | | | | all_248_0, simplifying with (31), (201), (210)
% 22.66/3.86 | | | | | | | | | | | | | | gives:
% 22.66/3.86 | | | | | | | | | | | | | | (216) all_248_0 = 0 | ? [v0: $i] : (not(all_248_1) = v0
% 22.66/3.86 | | | | | | | | | | | | | | & model(all_44_2, v0) = 0 & $i(v0))
% 22.66/3.86 | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | GROUND_INST: instantiating (3) with all_82_3, all_82_2,
% 22.66/3.86 | | | | | | | | | | | | | | simplifying with (76), (77), (214) gives:
% 22.66/3.86 | | | | | | | | | | | | | | (217) ? [v0: $i] : ? [v1: $i] : (not(all_82_2) = v0 &
% 22.66/3.86 | | | | | | | | | | | | | | model(v1, v0) = 0 & model(v1, all_82_3) = 0 &
% 22.66/3.86 | | | | | | | | | | | | | | $i(v1) & $i(v0))
% 22.66/3.86 | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | DELTA: instantiating (217) with fresh symbols all_337_0,
% 22.66/3.86 | | | | | | | | | | | | | | all_337_1 gives:
% 22.66/3.86 | | | | | | | | | | | | | | (218) not(all_82_2) = all_337_1 & model(all_337_0,
% 22.66/3.86 | | | | | | | | | | | | | | all_337_1) = 0 & model(all_337_0, all_82_3) = 0
% 22.66/3.86 | | | | | | | | | | | | | | & $i(all_337_0) & $i(all_337_1)
% 22.66/3.86 | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | ALPHA: (218) implies:
% 22.66/3.86 | | | | | | | | | | | | | | (219) $i(all_337_0)
% 22.66/3.86 | | | | | | | | | | | | | | (220) model(all_337_0, all_82_3) = 0
% 22.66/3.86 | | | | | | | | | | | | | | (221) model(all_337_0, all_337_1) = 0
% 22.66/3.86 | | | | | | | | | | | | | | (222) not(all_82_2) = all_337_1
% 22.66/3.86 | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 22.66/3.86 | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | Case 1:
% 22.66/3.86 | | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | | (223) all_248_0 = 0
% 22.66/3.86 | | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | | REDUCE: (200), (223) imply:
% 22.66/3.86 | | | | | | | | | | | | | | | (224) $false
% 22.66/3.86 | | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | | CLOSE: (224) is inconsistent.
% 22.66/3.86 | | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | Case 2:
% 22.66/3.86 | | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (1) with all_82_3, all_82_2,
% 22.66/3.86 | | | | | | | | | | | | | | | all_337_0, simplifying with (76), (77), (215),
% 22.66/3.86 | | | | | | | | | | | | | | | (219), (220) gives:
% 22.66/3.86 | | | | | | | | | | | | | | | (225) model(all_337_0, all_82_2) = 0
% 22.66/3.86 | | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | | GROUND_INST: instantiating (7) with all_337_0, all_82_2,
% 22.66/3.86 | | | | | | | | | | | | | | | all_337_1, simplifying with (77), (219), (221),
% 22.66/3.86 | | | | | | | | | | | | | | | (222) gives:
% 22.66/3.86 | | | | | | | | | | | | | | | (226) ? [v0: int] : ( ~ (v0 = 0) & model(all_337_0,
% 22.66/3.86 | | | | | | | | | | | | | | | all_82_2) = v0)
% 22.66/3.86 | | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | | DELTA: instantiating (226) with fresh symbol all_391_0
% 22.66/3.86 | | | | | | | | | | | | | | | gives:
% 22.66/3.86 | | | | | | | | | | | | | | | (227) ~ (all_391_0 = 0) & model(all_337_0, all_82_2) =
% 22.66/3.86 | | | | | | | | | | | | | | | all_391_0
% 22.66/3.86 | | | | | | | | | | | | | | |
% 22.66/3.86 | | | | | | | | | | | | | | | ALPHA: (227) implies:
% 22.66/3.87 | | | | | | | | | | | | | | | (228) ~ (all_391_0 = 0)
% 22.66/3.87 | | | | | | | | | | | | | | | (229) model(all_337_0, all_82_2) = all_391_0
% 22.66/3.87 | | | | | | | | | | | | | | |
% 22.66/3.87 | | | | | | | | | | | | | | | GROUND_INST: instantiating (13) with 0, all_391_0, all_82_2,
% 22.66/3.87 | | | | | | | | | | | | | | | all_337_0, simplifying with (225), (229) gives:
% 22.66/3.87 | | | | | | | | | | | | | | | (230) all_391_0 = 0
% 22.66/3.87 | | | | | | | | | | | | | | |
% 22.66/3.87 | | | | | | | | | | | | | | | REDUCE: (228), (230) imply:
% 22.66/3.87 | | | | | | | | | | | | | | | (231) $false
% 22.66/3.87 | | | | | | | | | | | | | | |
% 22.66/3.87 | | | | | | | | | | | | | | | CLOSE: (231) is inconsistent.
% 22.66/3.87 | | | | | | | | | | | | | | |
% 22.66/3.87 | | | | | | | | | | | | | | End of split
% 22.66/3.87 | | | | | | | | | | | | | |
% 22.66/3.87 | | | | | | | | | | | | | End of split
% 22.66/3.87 | | | | | | | | | | | | |
% 22.66/3.87 | | | | | | | | | | | | End of split
% 22.66/3.87 | | | | | | | | | | | |
% 22.66/3.87 | | | | | | | | | | | End of split
% 22.66/3.87 | | | | | | | | | | |
% 22.66/3.87 | | | | | | | | | | End of split
% 22.66/3.87 | | | | | | | | | |
% 22.66/3.87 | | | | | | | | | End of split
% 22.66/3.87 | | | | | | | | |
% 22.66/3.87 | | | | | | | | End of split
% 22.66/3.87 | | | | | | | |
% 22.66/3.87 | | | | | | | End of split
% 22.66/3.87 | | | | | | |
% 22.66/3.87 | | | | | | End of split
% 22.66/3.87 | | | | | |
% 22.66/3.87 | | | | | End of split
% 22.66/3.87 | | | | |
% 22.66/3.87 | | | | End of split
% 22.66/3.87 | | | |
% 22.66/3.87 | | | End of split
% 22.66/3.87 | | |
% 22.66/3.87 | | End of split
% 22.66/3.87 | |
% 22.66/3.87 | End of split
% 22.66/3.87 |
% 22.66/3.87 End of proof
% 22.66/3.87
% 22.66/3.87 Sub-proof #1 shows that the following formulas are inconsistent:
% 22.66/3.87 ----------------------------------------------------------------
% 22.66/3.87 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 22.66/3.87 ! [v3: $i] : (v1 = v0 | ~ (model(v3, v2) = v1) | ~ (model(v3, v2) =
% 22.66/3.87 v0))
% 22.66/3.87 (2) $i(all_82_2)
% 22.66/3.87 (3) all_82_0 = 0 | ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & model(v0,
% 22.66/3.87 all_82_2) = v1 & model(v0, all_82_3) = 0 & $i(v0))
% 22.66/3.87 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (not(v2) = v1) |
% 22.66/3.87 ~ (not(v2) = v0))
% 22.66/3.87 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (model(v0, v1) =
% 22.66/3.87 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (not(v1) = v3 & model(v0,
% 22.66/3.87 v3) = 0 & $i(v3)))
% 22.66/3.87 (6) ~ (all_82_0 = 0)
% 22.66/3.87 (7) ~ (all_82_1 = 0) | all_82_0 = 0
% 22.66/3.87 (8) all_82_1 = 0 | ? [v0: $i] : (not(all_82_2) = v0 & $i(v0) & ! [v1: $i] :
% 22.66/3.87 ( ~ (model(v1, v0) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) &
% 22.66/3.87 model(v1, all_82_3) = v2)) & ! [v1: $i] : ( ~ (model(v1, all_82_3)
% 22.66/3.87 = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & model(v1, v0) =
% 22.66/3.87 v2)))
% 22.66/3.87
% 22.66/3.87 Begin of proof
% 22.66/3.87 |
% 22.66/3.87 | BETA: splitting (7) gives:
% 22.66/3.87 |
% 22.66/3.87 | Case 1:
% 22.66/3.87 | |
% 22.66/3.87 | | (9) ~ (all_82_1 = 0)
% 22.66/3.87 | |
% 22.66/3.87 | | BETA: splitting (3) gives:
% 22.66/3.87 | |
% 22.66/3.87 | | Case 1:
% 22.66/3.87 | | |
% 22.66/3.87 | | | (10) all_82_0 = 0
% 22.66/3.87 | | |
% 22.66/3.87 | | | REDUCE: (6), (10) imply:
% 22.66/3.87 | | | (11) $false
% 22.66/3.87 | | |
% 22.66/3.87 | | | CLOSE: (11) is inconsistent.
% 22.66/3.87 | | |
% 22.66/3.87 | | Case 2:
% 22.66/3.87 | | |
% 22.66/3.87 | | | (12) ? [v0: $i] : ? [v1: int] : ( ~ (v1 = 0) & model(v0, all_82_2) =
% 22.66/3.87 | | | v1 & model(v0, all_82_3) = 0 & $i(v0))
% 22.66/3.87 | | |
% 22.66/3.87 | | | DELTA: instantiating (12) with fresh symbols all_324_0, all_324_1 gives:
% 22.66/3.87 | | | (13) ~ (all_324_0 = 0) & model(all_324_1, all_82_2) = all_324_0 &
% 22.66/3.87 | | | model(all_324_1, all_82_3) = 0 & $i(all_324_1)
% 22.66/3.87 | | |
% 22.66/3.87 | | | ALPHA: (13) implies:
% 22.66/3.87 | | | (14) ~ (all_324_0 = 0)
% 22.66/3.87 | | | (15) $i(all_324_1)
% 22.66/3.87 | | | (16) model(all_324_1, all_82_3) = 0
% 22.66/3.87 | | | (17) model(all_324_1, all_82_2) = all_324_0
% 22.66/3.87 | | |
% 22.66/3.87 | | | BETA: splitting (8) gives:
% 22.66/3.87 | | |
% 22.66/3.87 | | | Case 1:
% 22.66/3.87 | | | |
% 22.66/3.87 | | | | (18) all_82_1 = 0
% 22.66/3.87 | | | |
% 22.66/3.87 | | | | REDUCE: (9), (18) imply:
% 22.66/3.87 | | | | (19) $false
% 22.66/3.87 | | | |
% 22.66/3.87 | | | | CLOSE: (19) is inconsistent.
% 22.66/3.87 | | | |
% 22.66/3.87 | | | Case 2:
% 22.66/3.87 | | | |
% 22.66/3.87 | | | | (20) ? [v0: $i] : (not(all_82_2) = v0 & $i(v0) & ! [v1: $i] : ( ~
% 22.66/3.87 | | | | (model(v1, v0) = 0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 =
% 22.66/3.87 | | | | 0) & model(v1, all_82_3) = v2)) & ! [v1: $i] : ( ~
% 22.66/3.87 | | | | (model(v1, all_82_3) = 0) | ~ $i(v1) | ? [v2: int] : ( ~
% 22.66/3.87 | | | | (v2 = 0) & model(v1, v0) = v2)))
% 22.66/3.87 | | | |
% 22.66/3.87 | | | | DELTA: instantiating (20) with fresh symbol all_329_0 gives:
% 23.12/3.88 | | | | (21) not(all_82_2) = all_329_0 & $i(all_329_0) & ! [v0: $i] : ( ~
% 23.12/3.88 | | | | (model(v0, all_329_0) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 23.12/3.88 | | | | (v1 = 0) & model(v0, all_82_3) = v1)) & ! [v0: $i] : ( ~
% 23.12/3.88 | | | | (model(v0, all_82_3) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 23.12/3.88 | | | | = 0) & model(v0, all_329_0) = v1))
% 23.12/3.88 | | | |
% 23.12/3.88 | | | | ALPHA: (21) implies:
% 23.12/3.88 | | | | (22) not(all_82_2) = all_329_0
% 23.12/3.88 | | | | (23) ! [v0: $i] : ( ~ (model(v0, all_82_3) = 0) | ~ $i(v0) | ?
% 23.12/3.88 | | | | [v1: int] : ( ~ (v1 = 0) & model(v0, all_329_0) = v1))
% 23.12/3.88 | | | |
% 23.12/3.88 | | | | GROUND_INST: instantiating (23) with all_324_1, simplifying with (15),
% 23.12/3.88 | | | | (16) gives:
% 23.12/3.88 | | | | (24) ? [v0: int] : ( ~ (v0 = 0) & model(all_324_1, all_329_0) = v0)
% 23.12/3.88 | | | |
% 23.12/3.88 | | | | GROUND_INST: instantiating (5) with all_324_1, all_82_2, all_324_0,
% 23.12/3.88 | | | | simplifying with (2), (15), (17) gives:
% 23.12/3.88 | | | | (25) all_324_0 = 0 | ? [v0: $i] : (not(all_82_2) = v0 &
% 23.12/3.88 | | | | model(all_324_1, v0) = 0 & $i(v0))
% 23.12/3.88 | | | |
% 23.12/3.88 | | | | DELTA: instantiating (24) with fresh symbol all_337_0 gives:
% 23.12/3.88 | | | | (26) ~ (all_337_0 = 0) & model(all_324_1, all_329_0) = all_337_0
% 23.12/3.88 | | | |
% 23.12/3.88 | | | | ALPHA: (26) implies:
% 23.12/3.88 | | | | (27) ~ (all_337_0 = 0)
% 23.12/3.88 | | | | (28) model(all_324_1, all_329_0) = all_337_0
% 23.12/3.88 | | | |
% 23.12/3.88 | | | | BETA: splitting (25) gives:
% 23.12/3.88 | | | |
% 23.12/3.88 | | | | Case 1:
% 23.12/3.88 | | | | |
% 23.12/3.88 | | | | | (29) all_324_0 = 0
% 23.12/3.88 | | | | |
% 23.12/3.88 | | | | | REDUCE: (14), (29) imply:
% 23.12/3.88 | | | | | (30) $false
% 23.12/3.88 | | | | |
% 23.12/3.88 | | | | | CLOSE: (30) is inconsistent.
% 23.12/3.88 | | | | |
% 23.12/3.88 | | | | Case 2:
% 23.12/3.88 | | | | |
% 23.12/3.88 | | | | | (31) ? [v0: $i] : (not(all_82_2) = v0 & model(all_324_1, v0) = 0 &
% 23.12/3.88 | | | | | $i(v0))
% 23.12/3.88 | | | | |
% 23.12/3.88 | | | | | DELTA: instantiating (31) with fresh symbol all_361_0 gives:
% 23.12/3.88 | | | | | (32) not(all_82_2) = all_361_0 & model(all_324_1, all_361_0) = 0 &
% 23.12/3.88 | | | | | $i(all_361_0)
% 23.12/3.88 | | | | |
% 23.12/3.88 | | | | | ALPHA: (32) implies:
% 23.12/3.88 | | | | | (33) model(all_324_1, all_361_0) = 0
% 23.12/3.88 | | | | | (34) not(all_82_2) = all_361_0
% 23.12/3.88 | | | | |
% 23.12/3.88 | | | | | GROUND_INST: instantiating (4) with all_329_0, all_361_0, all_82_2,
% 23.12/3.88 | | | | | simplifying with (22), (34) gives:
% 23.12/3.88 | | | | | (35) all_361_0 = all_329_0
% 23.12/3.88 | | | | |
% 23.12/3.88 | | | | | REDUCE: (33), (35) imply:
% 23.12/3.88 | | | | | (36) model(all_324_1, all_329_0) = 0
% 23.12/3.88 | | | | |
% 23.12/3.88 | | | | | GROUND_INST: instantiating (1) with all_337_0, 0, all_329_0,
% 23.12/3.88 | | | | | all_324_1, simplifying with (28), (36) gives:
% 23.12/3.88 | | | | | (37) all_337_0 = 0
% 23.12/3.88 | | | | |
% 23.12/3.88 | | | | | REDUCE: (27), (37) imply:
% 23.12/3.88 | | | | | (38) $false
% 23.12/3.88 | | | | |
% 23.12/3.88 | | | | | CLOSE: (38) is inconsistent.
% 23.12/3.88 | | | | |
% 23.12/3.88 | | | | End of split
% 23.12/3.88 | | | |
% 23.12/3.88 | | | End of split
% 23.12/3.88 | | |
% 23.12/3.88 | | End of split
% 23.12/3.88 | |
% 23.12/3.88 | Case 2:
% 23.12/3.88 | |
% 23.12/3.88 | | (39) all_82_0 = 0
% 23.12/3.88 | |
% 23.12/3.88 | | REDUCE: (6), (39) imply:
% 23.12/3.88 | | (40) $false
% 23.12/3.88 | |
% 23.12/3.88 | | CLOSE: (40) is inconsistent.
% 23.12/3.88 | |
% 23.12/3.88 | End of split
% 23.12/3.88 |
% 23.12/3.88 End of proof
% 23.12/3.88 % SZS output end Proof for theBenchmark
% 23.12/3.88
% 23.12/3.88 3286ms
%------------------------------------------------------------------------------