TSTP Solution File: SET718+4 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET718+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 15:26:07 EDT 2023
% Result : Theorem 25.58s 4.28s
% Output : Proof 59.90s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.15 % Problem : SET718+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.07/0.16 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.36 % Computer : n007.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8042.1875MB
% 0.12/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sat Aug 26 14:35:11 EDT 2023
% 0.12/0.36 % CPUTime :
% 0.17/0.63 ________ _____
% 0.17/0.63 ___ __ \_________(_)________________________________
% 0.17/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.17/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.17/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.17/0.63
% 0.17/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.17/0.63 (2023-06-19)
% 0.17/0.63
% 0.17/0.63 (c) Philipp Rümmer, 2009-2023
% 0.17/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.17/0.63 Amanda Stjerna.
% 0.17/0.63 Free software under BSD-3-Clause.
% 0.17/0.63
% 0.17/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.17/0.63
% 0.17/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.17/0.65 Running up to 7 provers in parallel.
% 0.17/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.17/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.17/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.17/0.68 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.17/0.68 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.17/0.68 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.57/0.68 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.09/1.36 Prover 4: Preprocessing ...
% 4.09/1.36 Prover 1: Preprocessing ...
% 4.09/1.39 Prover 3: Preprocessing ...
% 4.09/1.39 Prover 6: Preprocessing ...
% 4.09/1.39 Prover 2: Preprocessing ...
% 4.09/1.39 Prover 5: Preprocessing ...
% 4.09/1.39 Prover 0: Preprocessing ...
% 11.39/2.36 Prover 5: Proving ...
% 11.39/2.36 Prover 2: Proving ...
% 12.69/2.53 Prover 6: Proving ...
% 12.69/2.54 Prover 1: Constructing countermodel ...
% 12.69/2.56 Prover 3: Constructing countermodel ...
% 12.69/2.68 Prover 3: gave up
% 13.60/2.69 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 14.30/2.72 Prover 1: gave up
% 14.30/2.74 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.30/2.76 Prover 7: Preprocessing ...
% 15.02/2.85 Prover 8: Preprocessing ...
% 15.68/2.91 Prover 7: Warning: ignoring some quantifiers
% 16.41/2.99 Prover 7: Constructing countermodel ...
% 17.95/3.19 Prover 4: Constructing countermodel ...
% 17.95/3.26 Prover 8: Warning: ignoring some quantifiers
% 17.95/3.27 Prover 0: Proving ...
% 17.95/3.28 Prover 8: Constructing countermodel ...
% 20.33/3.51 Prover 8: gave up
% 20.33/3.53 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 20.99/3.62 Prover 9: Preprocessing ...
% 25.58/4.27 Prover 0: proved (3612ms)
% 25.58/4.28
% 25.58/4.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.58/4.28
% 25.58/4.28 Prover 5: stopped
% 25.58/4.28 Prover 6: stopped
% 26.32/4.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 26.32/4.30 Prover 2: stopped
% 26.32/4.30 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 26.32/4.30 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 26.32/4.31 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 26.32/4.32 Prover 9: Constructing countermodel ...
% 26.32/4.34 Prover 9: stopped
% 26.32/4.34 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 26.32/4.38 Prover 10: Preprocessing ...
% 27.07/4.39 Prover 16: Preprocessing ...
% 27.09/4.40 Prover 11: Preprocessing ...
% 27.15/4.41 Prover 13: Preprocessing ...
% 27.15/4.43 Prover 19: Preprocessing ...
% 27.15/4.51 Prover 10: Warning: ignoring some quantifiers
% 27.15/4.53 Prover 10: Constructing countermodel ...
% 27.15/4.54 Prover 16: Warning: ignoring some quantifiers
% 27.15/4.56 Prover 16: Constructing countermodel ...
% 27.15/4.62 Prover 13: Warning: ignoring some quantifiers
% 27.15/4.64 Prover 13: Constructing countermodel ...
% 28.10/4.74 Prover 10: gave up
% 30.88/4.90 Prover 19: Warning: ignoring some quantifiers
% 30.88/4.93 Prover 19: Constructing countermodel ...
% 32.02/5.07 Prover 11: Constructing countermodel ...
% 37.93/5.85 Prover 19: gave up
% 58.10/8.49 Prover 4: Found proof (size 689)
% 58.10/8.49 Prover 4: proved (7822ms)
% 58.10/8.49 Prover 13: stopped
% 58.10/8.50 Prover 7: stopped
% 58.10/8.50 Prover 16: stopped
% 58.10/8.50 Prover 11: stopped
% 58.10/8.50
% 58.10/8.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 58.10/8.50
% 58.10/8.54 % SZS output start Proof for theBenchmark
% 58.10/8.55 Assumptions after simplification:
% 58.10/8.55 ---------------------------------
% 58.10/8.55
% 58.10/8.55 (compose_function)
% 58.43/8.61 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 58.43/8.61 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~
% 58.43/8.61 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) |
% 58.43/8.61 ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) |
% 58.43/8.61 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any]
% 58.43/8.61 : ((apply(v0, v9, v6) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10
% 58.43/8.61 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 =
% 58.43/8.61 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 58.43/8.61 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 58.43/8.61 int] : ! [v9: $i] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) =
% 58.43/8.61 v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9)
% 58.43/8.61 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 58.43/8.61 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v11 &
% 58.43/8.61 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4)
% 58.43/8.61 = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & !
% 58.43/8.61 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 58.43/8.61 : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~
% 58.43/8.61 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) |
% 58.43/8.61 ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~
% 58.43/8.61 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] :
% 58.43/8.61 ((apply(v1, v5, v9) = v10 & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~
% 58.43/8.61 (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11
% 58.43/8.61 = 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 58.43/8.61 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 58.43/8.61 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) |
% 58.43/8.61 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 58.43/8.61 $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ?
% 58.43/8.61 [v12: int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 &
% 58.43/8.61 apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, v3) = 0)
% 58.43/8.61 | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 =
% 58.43/8.61 0))))))
% 58.43/8.61
% 58.43/8.61 (injective)
% 58.43/8.62 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 58.43/8.62 $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0)
% 58.43/8.62 | ~ (apply(v0, v3, v5) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2)
% 58.43/8.62 | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 58.43/8.62 (member(v5, v2) = v8 & member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 =
% 58.43/8.62 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 58.43/8.62 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~
% 58.43/8.62 (injective(v0, v1, v2) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ (member(v3,
% 58.43/8.62 v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 58.43/8.62 ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v5) =
% 58.43/8.62 v8 & member(v5, v2) = v7 & member(v4, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 =
% 58.43/8.62 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 58.43/8.62 [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) =
% 58.43/8.62 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v1) = 0) | ~ $i(v5) | ~
% 58.43/8.62 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ?
% 58.43/8.62 [v7: any] : ? [v8: any] : (apply(v0, v4, v5) = v8 & member(v5, v2) = v7 &
% 58.43/8.62 member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & !
% 58.43/8.62 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 58.43/8.62 : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~
% 58.43/8.62 (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 58.43/8.62 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 58.43/8.62 (apply(v0, v4, v5) = v7 & apply(v0, v3, v5) = v6 & ( ~ (v7 = 0) | ~ (v6 =
% 58.43/8.62 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 =
% 58.43/8.62 0 | ~ (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 58.43/8.62 [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5, v6) = 0
% 58.43/8.62 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5, v1) = 0 &
% 58.43/8.62 member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4)))
% 58.43/8.62
% 58.43/8.62 (maps)
% 58.43/8.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 58.43/8.64 $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~
% 58.43/8.64 (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 58.43/8.64 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 58.43/8.64 (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 =
% 58.43/8.64 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 58.43/8.64 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0,
% 58.43/8.64 v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ~
% 58.43/8.64 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 58.43/8.64 any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5,
% 58.43/8.64 v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 =
% 58.43/8.64 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 58.43/8.64 [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0,
% 58.43/8.64 v3, v4) = 0) | ~ (member(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 58.43/8.64 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 58.43/8.64 ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v4, v2) = v7 & member(v3, v1)
% 58.43/8.64 = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1:
% 58.43/8.64 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 58.43/8.64 (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) |
% 58.43/8.64 ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 58.43/8.64 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 &
% 58.43/8.64 apply(v0, v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : !
% 58.43/8.64 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) |
% 58.43/8.64 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 58.43/8.64 : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int]
% 58.43/8.64 : ? [v12: $i] : ? [v13: int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13
% 58.43/8.64 = 0 & member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) =
% 58.43/8.64 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & member(v14, v2)
% 58.43/8.64 = v15)) & ! [v14: $i] : ( ~ (member(v14, v2) = 0) | ~ $i(v14) |
% 58.43/8.64 ? [v15: int] : ( ~ (v15 = 0) & apply(v0, v12, v14) = v15))) | (v11 =
% 58.43/8.64 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4,
% 58.43/8.64 v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5,
% 58.43/8.64 v2) = 0 & member(v4, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 58.43/8.64 [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0)
% 58.43/8.64 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0,
% 58.43/8.64 v3, v4) = 0 & member(v4, v2) = 0 & $i(v4)))
% 58.43/8.64
% 58.43/8.64 (one_to_one)
% 58.43/8.64 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 58.43/8.64 (one_to_one(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 58.43/8.64 any] : ? [v5: any] : (surjective(v0, v1, v2) = v5 & injective(v0, v1, v2)
% 58.43/8.64 = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 58.43/8.64 $i] : ! [v3: any] : ( ~ (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~
% 58.43/8.64 $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (one_to_one(v0, v1, v2) =
% 58.43/8.64 v4 & injective(v0, v1, v2) = v5 & ( ~ (v4 = 0) | (v5 = 0 & v3 = 0)))) & !
% 58.43/8.64 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: any] : ( ~ (injective(v0, v1,
% 58.43/8.64 v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 58.43/8.64 any] : (one_to_one(v0, v1, v2) = v4 & surjective(v0, v1, v2) = v5 & ( ~
% 58.43/8.64 (v4 = 0) | (v5 = 0 & v3 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2:
% 58.43/8.64 $i] : ( ~ (one_to_one(v0, v1, v2) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 58.43/8.64 (surjective(v0, v1, v2) = 0 & injective(v0, v1, v2) = 0)) & ! [v0: $i] : !
% 58.43/8.64 [v1: $i] : ! [v2: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ $i(v2) | ~
% 58.43/8.65 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) =
% 58.43/8.65 v4 & injective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0: $i] :
% 58.43/8.65 ! [v1: $i] : ! [v2: $i] : ( ~ (injective(v0, v1, v2) = 0) | ~ $i(v2) | ~
% 58.43/8.65 $i(v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] : (one_to_one(v0, v1, v2) =
% 58.43/8.65 v4 & surjective(v0, v1, v2) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 58.43/8.65
% 58.43/8.65 (surjective)
% 58.43/8.65 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 58.43/8.65 (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 58.43/8.65 $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~ (apply(v0, v5, v4)
% 58.43/8.65 = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) & member(v5, v1) = v6))
% 58.43/8.65 & ! [v5: $i] : ( ~ (member(v5, v1) = 0) | ~ $i(v5) | ? [v6: int] : ( ~
% 58.43/8.65 (v6 = 0) & apply(v0, v5, v4) = v6)))) & ! [v0: $i] : ! [v1: $i] : !
% 58.43/8.65 [v2: $i] : ! [v3: $i] : ( ~ (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2)
% 58.43/8.65 = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] :
% 58.43/8.65 (apply(v0, v4, v3) = 0 & member(v4, v1) = 0 & $i(v4)))
% 58.43/8.65
% 58.43/8.65 (thII09)
% 58.43/8.65 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 58.43/8.65 $i] : ? [v6: int] : ( ~ (v6 = 0) & one_to_one(v5, v2, v4) = v6 &
% 58.43/8.65 one_to_one(v1, v3, v4) = 0 & one_to_one(v0, v2, v3) = 0 &
% 58.43/8.65 compose_function(v1, v0, v2, v3, v4) = v5 & maps(v1, v3, v4) = 0 & maps(v0,
% 58.43/8.65 v2, v3) = 0 & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 58.43/8.65
% 58.43/8.65 (function-axioms)
% 58.62/8.67 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 58.62/8.67 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 58.62/8.67 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~
% 58.62/8.67 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 58.62/8.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 58.62/8.67 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5,
% 58.62/8.67 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 58.62/8.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 58.62/8.67 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5,
% 58.62/8.67 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 58.62/8.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 58.62/8.67 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5,
% 58.62/8.67 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 58.62/8.67 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 58.62/8.67 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~
% 58.62/8.67 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 58.62/8.67 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 58.62/8.67 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~
% 58.62/8.67 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 58.62/8.67 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 58.62/8.67 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5,
% 58.62/8.67 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 58.62/8.67 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~
% 58.62/8.67 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 58.62/8.67 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~
% 58.62/8.67 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 58.62/8.67 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) |
% 58.62/8.67 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 58.62/8.67 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 58.62/8.67 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & !
% 58.62/8.67 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 58.62/8.67 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~
% 58.62/8.67 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 58.62/8.67 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 58.62/8.67 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0:
% 58.62/8.67 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 58.62/8.67 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) =
% 58.62/8.67 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 58.62/8.67 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 58.62/8.67 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 58.62/8.67 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~
% 58.62/8.67 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 58.62/8.67 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) &
% 58.62/8.67 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 58.62/8.67 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 58.62/8.67 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 58.62/8.67 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 58.62/8.67 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 58.62/8.67 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 58.62/8.67 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 58.62/8.67 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 58.62/8.67 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 58.62/8.67 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 58.62/8.67 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 58.62/8.67 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 58.62/8.67 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 58.62/8.67 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 58.62/8.67 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 58.62/8.67 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 58.62/8.67 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 58.62/8.67 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 58.62/8.67 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 58.62/8.67 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 58.62/8.67 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 58.62/8.67 (power_set(v2) = v0))
% 58.62/8.67
% 58.62/8.67 Further assumptions not needed in the proof:
% 58.62/8.67 --------------------------------------------
% 58.62/8.67 compose_predicate, decreasing_function, difference, empty_set, equal_maps,
% 58.62/8.67 equal_set, identity, image2, image3, increasing_function, intersection,
% 58.62/8.67 inverse_function, inverse_image2, inverse_image3, inverse_predicate,
% 58.62/8.67 isomorphism, power_set, product, singleton, subset, sum, union, unordered_pair
% 58.62/8.67
% 58.62/8.67 Those formulas are unsatisfiable:
% 58.62/8.67 ---------------------------------
% 58.62/8.67
% 58.62/8.67 Begin of proof
% 58.62/8.67 |
% 58.62/8.67 | ALPHA: (maps) implies:
% 58.62/8.68 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (maps(v0,
% 58.62/8.68 | v1, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) |
% 58.62/8.68 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v3, v4) = 0 &
% 58.62/8.68 | member(v4, v2) = 0 & $i(v4)))
% 58.62/8.68 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 58.62/8.68 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2)
% 58.62/8.68 | = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~
% 58.62/8.68 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 58.62/8.68 | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & apply(v0, v3,
% 58.62/8.68 | v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 58.62/8.68 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 58.62/8.68 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3,
% 58.62/8.68 | v5) = 0) | ~ (member(v4, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 58.62/8.68 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 58.62/8.68 | any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, v2) = v7
% 58.62/8.68 | & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 58.62/8.68 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 58.62/8.68 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3,
% 58.62/8.68 | v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) |
% 58.62/8.68 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 58.62/8.68 | any] : ? [v8: any] : (member(v5, v2) = v8 & member(v4, v2) = v7 &
% 58.62/8.68 | member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 58.62/8.68 |
% 58.62/8.68 | ALPHA: (compose_function) implies:
% 58.62/8.69 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 58.62/8.69 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (compose_function(v0, v1,
% 58.62/8.69 | v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | ~ $i(v6) | ~
% 58.62/8.69 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 58.62/8.69 | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ? [v12:
% 58.62/8.69 | int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 &
% 58.62/8.69 | apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10,
% 58.62/8.69 | v3) = 0) | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~
% 58.62/8.69 | (v9 = 0) | ~ (v8 = 0))))))
% 58.62/8.69 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 58.62/8.69 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] :
% 58.62/8.69 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~
% 58.62/8.69 | (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) |
% 58.62/8.69 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 58.62/8.69 | | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) =
% 58.62/8.69 | v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) |
% 58.62/8.69 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~
% 58.62/8.69 | (v10 = 0)))))
% 58.62/8.69 |
% 58.62/8.69 | ALPHA: (injective) implies:
% 58.62/8.69 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 58.62/8.69 | (injective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 58.62/8.69 | [v4: $i] : ? [v5: $i] : ? [v6: $i] : ( ~ (v5 = v4) & apply(v0, v5,
% 58.62/8.69 | v6) = 0 & apply(v0, v4, v6) = 0 & member(v6, v2) = 0 & member(v5,
% 58.62/8.69 | v1) = 0 & member(v4, v1) = 0 & $i(v6) & $i(v5) & $i(v4)))
% 58.62/8.69 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 58.62/8.69 | ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (member(v5,
% 58.62/8.69 | v2) = 0) | ~ (member(v4, v1) = 0) | ~ (member(v3, v1) = 0) | ~
% 58.62/8.69 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 58.62/8.69 | ? [v6: any] : ? [v7: any] : (apply(v0, v4, v5) = v7 & apply(v0, v3,
% 58.62/8.69 | v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 58.62/8.69 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 58.62/8.69 | ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0,
% 58.62/8.69 | v4, v5) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) |
% 58.62/8.69 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 58.62/8.69 | any] : ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v5, v2) = v7
% 58.62/8.69 | & member(v4, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 58.62/8.69 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 58.62/8.69 | ! [v5: $i] : (v4 = v3 | ~ (injective(v0, v1, v2) = 0) | ~ (apply(v0,
% 58.62/8.69 | v4, v5) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ $i(v5) | ~
% 58.62/8.69 | $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 58.62/8.69 | any] : ? [v7: any] : ? [v8: any] : (member(v5, v2) = v8 &
% 58.62/8.69 | member(v4, v1) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7
% 58.62/8.69 | = 0) | ~ (v6 = 0))))
% 58.62/8.69 |
% 58.62/8.69 | ALPHA: (surjective) implies:
% 58.62/8.69 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 58.62/8.69 | (surjective(v0, v1, v2) = 0) | ~ (member(v3, v2) = 0) | ~ $i(v3) |
% 58.62/8.69 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v4, v3)
% 58.62/8.69 | = 0 & member(v4, v1) = 0 & $i(v4)))
% 59.08/8.70 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 59.08/8.70 | (surjective(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 59.08/8.70 | ? [v4: $i] : (member(v4, v2) = 0 & $i(v4) & ! [v5: $i] : ( ~
% 59.08/8.70 | (apply(v0, v5, v4) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 =
% 59.08/8.70 | 0) & member(v5, v1) = v6)) & ! [v5: $i] : ( ~ (member(v5,
% 59.08/8.70 | v1) = 0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) &
% 59.08/8.70 | apply(v0, v5, v4) = v6))))
% 59.08/8.70 |
% 59.08/8.70 | ALPHA: (one_to_one) implies:
% 59.08/8.70 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (one_to_one(v0, v1, v2)
% 59.08/8.70 | = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (surjective(v0, v1, v2)
% 59.08/8.70 | = 0 & injective(v0, v1, v2) = 0))
% 59.08/8.70 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 59.08/8.70 | (one_to_one(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 59.08/8.70 | ? [v4: any] : ? [v5: any] : (surjective(v0, v1, v2) = v5 &
% 59.08/8.70 | injective(v0, v1, v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))
% 59.08/8.70 |
% 59.08/8.70 | ALPHA: (function-axioms) implies:
% 59.08/8.70 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 59.08/8.70 | : ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3,
% 59.08/8.70 | v2) = v0))
% 59.08/8.70 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 59.08/8.70 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 59.08/8.70 | ~ (apply(v4, v3, v2) = v0))
% 59.08/8.70 |
% 59.08/8.70 | DELTA: instantiating (thII09) with fresh symbols all_32_0, all_32_1, all_32_2,
% 59.08/8.70 | all_32_3, all_32_4, all_32_5, all_32_6 gives:
% 59.08/8.70 | (17) ~ (all_32_0 = 0) & one_to_one(all_32_1, all_32_4, all_32_2) =
% 59.08/8.70 | all_32_0 & one_to_one(all_32_5, all_32_3, all_32_2) = 0 &
% 59.08/8.70 | one_to_one(all_32_6, all_32_4, all_32_3) = 0 &
% 59.08/8.70 | compose_function(all_32_5, all_32_6, all_32_4, all_32_3, all_32_2) =
% 59.08/8.70 | all_32_1 & maps(all_32_5, all_32_3, all_32_2) = 0 & maps(all_32_6,
% 59.08/8.70 | all_32_4, all_32_3) = 0 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3)
% 59.08/8.70 | & $i(all_32_4) & $i(all_32_5) & $i(all_32_6)
% 59.08/8.70 |
% 59.08/8.70 | ALPHA: (17) implies:
% 59.08/8.70 | (18) ~ (all_32_0 = 0)
% 59.08/8.70 | (19) $i(all_32_6)
% 59.08/8.70 | (20) $i(all_32_5)
% 59.08/8.70 | (21) $i(all_32_4)
% 59.08/8.70 | (22) $i(all_32_3)
% 59.08/8.70 | (23) $i(all_32_2)
% 59.08/8.70 | (24) $i(all_32_1)
% 59.08/8.70 | (25) maps(all_32_6, all_32_4, all_32_3) = 0
% 59.08/8.70 | (26) maps(all_32_5, all_32_3, all_32_2) = 0
% 59.08/8.70 | (27) compose_function(all_32_5, all_32_6, all_32_4, all_32_3, all_32_2) =
% 59.08/8.70 | all_32_1
% 59.08/8.70 | (28) one_to_one(all_32_6, all_32_4, all_32_3) = 0
% 59.08/8.70 | (29) one_to_one(all_32_5, all_32_3, all_32_2) = 0
% 59.08/8.70 | (30) one_to_one(all_32_1, all_32_4, all_32_2) = all_32_0
% 59.08/8.70 |
% 59.08/8.70 | GROUND_INST: instantiating (13) with all_32_6, all_32_4, all_32_3, simplifying
% 59.08/8.70 | with (19), (21), (22), (28) gives:
% 59.08/8.70 | (31) surjective(all_32_6, all_32_4, all_32_3) = 0 & injective(all_32_6,
% 59.08/8.70 | all_32_4, all_32_3) = 0
% 59.08/8.70 |
% 59.08/8.70 | ALPHA: (31) implies:
% 59.08/8.70 | (32) injective(all_32_6, all_32_4, all_32_3) = 0
% 59.08/8.70 | (33) surjective(all_32_6, all_32_4, all_32_3) = 0
% 59.08/8.70 |
% 59.08/8.70 | GROUND_INST: instantiating (13) with all_32_5, all_32_3, all_32_2, simplifying
% 59.08/8.70 | with (20), (22), (23), (29) gives:
% 59.08/8.70 | (34) surjective(all_32_5, all_32_3, all_32_2) = 0 & injective(all_32_5,
% 59.08/8.70 | all_32_3, all_32_2) = 0
% 59.08/8.70 |
% 59.08/8.70 | ALPHA: (34) implies:
% 59.08/8.70 | (35) injective(all_32_5, all_32_3, all_32_2) = 0
% 59.08/8.70 | (36) surjective(all_32_5, all_32_3, all_32_2) = 0
% 59.08/8.70 |
% 59.08/8.70 | GROUND_INST: instantiating (14) with all_32_1, all_32_4, all_32_2, all_32_0,
% 59.08/8.70 | simplifying with (21), (23), (24), (30) gives:
% 59.08/8.71 | (37) all_32_0 = 0 | ? [v0: any] : ? [v1: any] : (surjective(all_32_1,
% 59.08/8.71 | all_32_4, all_32_2) = v1 & injective(all_32_1, all_32_4, all_32_2)
% 59.08/8.71 | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.08/8.71 |
% 59.08/8.71 | BETA: splitting (37) gives:
% 59.08/8.71 |
% 59.08/8.71 | Case 1:
% 59.08/8.71 | |
% 59.08/8.71 | | (38) all_32_0 = 0
% 59.08/8.71 | |
% 59.08/8.71 | | REDUCE: (18), (38) imply:
% 59.08/8.71 | | (39) $false
% 59.08/8.71 | |
% 59.08/8.71 | | CLOSE: (39) is inconsistent.
% 59.08/8.71 | |
% 59.08/8.71 | Case 2:
% 59.08/8.71 | |
% 59.08/8.71 | | (40) ? [v0: any] : ? [v1: any] : (surjective(all_32_1, all_32_4,
% 59.08/8.71 | | all_32_2) = v1 & injective(all_32_1, all_32_4, all_32_2) = v0 &
% 59.08/8.71 | | ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.08/8.71 | |
% 59.08/8.71 | | DELTA: instantiating (40) with fresh symbols all_44_0, all_44_1 gives:
% 59.08/8.71 | | (41) surjective(all_32_1, all_32_4, all_32_2) = all_44_0 &
% 59.08/8.71 | | injective(all_32_1, all_32_4, all_32_2) = all_44_1 & ( ~ (all_44_0 =
% 59.08/8.71 | | 0) | ~ (all_44_1 = 0))
% 59.08/8.71 | |
% 59.08/8.71 | | ALPHA: (41) implies:
% 59.08/8.71 | | (42) injective(all_32_1, all_32_4, all_32_2) = all_44_1
% 59.08/8.71 | | (43) surjective(all_32_1, all_32_4, all_32_2) = all_44_0
% 59.08/8.71 | | (44) ~ (all_44_0 = 0) | ~ (all_44_1 = 0)
% 59.08/8.71 | |
% 59.08/8.71 | | GROUND_INST: instantiating (7) with all_32_1, all_32_4, all_32_2, all_44_1,
% 59.08/8.71 | | simplifying with (21), (23), (24), (42) gives:
% 59.08/8.71 | | (45) all_44_1 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 =
% 59.08/8.71 | | v0) & apply(all_32_1, v1, v2) = 0 & apply(all_32_1, v0, v2) = 0
% 59.08/8.71 | | & member(v2, all_32_2) = 0 & member(v1, all_32_4) = 0 & member(v0,
% 59.08/8.71 | | all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0))
% 59.08/8.71 | |
% 59.08/8.71 | | GROUND_INST: instantiating (12) with all_32_1, all_32_4, all_32_2, all_44_0,
% 59.08/8.71 | | simplifying with (21), (23), (24), (43) gives:
% 59.08/8.71 | | (46) all_44_0 = 0 | ? [v0: $i] : (member(v0, all_32_2) = 0 & $i(v0) & !
% 59.08/8.71 | | [v1: $i] : ( ~ (apply(all_32_1, v1, v0) = 0) | ~ $i(v1) | ? [v2:
% 59.08/8.71 | | int] : ( ~ (v2 = 0) & member(v1, all_32_4) = v2)) & ! [v1:
% 59.08/8.71 | | $i] : ( ~ (member(v1, all_32_4) = 0) | ~ $i(v1) | ? [v2: int]
% 59.08/8.71 | | : ( ~ (v2 = 0) & apply(all_32_1, v1, v0) = v2)))
% 59.08/8.71 | |
% 59.08/8.71 | | BETA: splitting (44) gives:
% 59.08/8.71 | |
% 59.08/8.71 | | Case 1:
% 59.08/8.71 | | |
% 59.08/8.71 | | | (47) ~ (all_44_0 = 0)
% 59.08/8.71 | | |
% 59.08/8.71 | | | BETA: splitting (46) gives:
% 59.08/8.71 | | |
% 59.08/8.71 | | | Case 1:
% 59.08/8.71 | | | |
% 59.08/8.71 | | | | (48) all_44_0 = 0
% 59.08/8.71 | | | |
% 59.08/8.71 | | | | REDUCE: (47), (48) imply:
% 59.08/8.71 | | | | (49) $false
% 59.08/8.71 | | | |
% 59.08/8.71 | | | | CLOSE: (49) is inconsistent.
% 59.08/8.71 | | | |
% 59.08/8.71 | | | Case 2:
% 59.08/8.71 | | | |
% 59.08/8.71 | | | | (50) ? [v0: $i] : (member(v0, all_32_2) = 0 & $i(v0) & ! [v1: $i] :
% 59.08/8.71 | | | | ( ~ (apply(all_32_1, v1, v0) = 0) | ~ $i(v1) | ? [v2: int] :
% 59.08/8.71 | | | | ( ~ (v2 = 0) & member(v1, all_32_4) = v2)) & ! [v1: $i] : (
% 59.08/8.71 | | | | ~ (member(v1, all_32_4) = 0) | ~ $i(v1) | ? [v2: int] : (
% 59.08/8.71 | | | | ~ (v2 = 0) & apply(all_32_1, v1, v0) = v2)))
% 59.08/8.71 | | | |
% 59.08/8.71 | | | | DELTA: instantiating (50) with fresh symbol all_57_0 gives:
% 59.08/8.72 | | | | (51) member(all_57_0, all_32_2) = 0 & $i(all_57_0) & ! [v0: $i] : (
% 59.08/8.72 | | | | ~ (apply(all_32_1, v0, all_57_0) = 0) | ~ $i(v0) | ? [v1:
% 59.08/8.72 | | | | int] : ( ~ (v1 = 0) & member(v0, all_32_4) = v1)) & ! [v0:
% 59.08/8.72 | | | | $i] : ( ~ (member(v0, all_32_4) = 0) | ~ $i(v0) | ? [v1:
% 59.08/8.72 | | | | int] : ( ~ (v1 = 0) & apply(all_32_1, v0, all_57_0) = v1))
% 59.08/8.72 | | | |
% 59.08/8.72 | | | | ALPHA: (51) implies:
% 59.08/8.72 | | | | (52) $i(all_57_0)
% 59.08/8.72 | | | | (53) member(all_57_0, all_32_2) = 0
% 59.08/8.72 | | | | (54) ! [v0: $i] : ( ~ (member(v0, all_32_4) = 0) | ~ $i(v0) | ?
% 59.08/8.72 | | | | [v1: int] : ( ~ (v1 = 0) & apply(all_32_1, v0, all_57_0) =
% 59.08/8.72 | | | | v1))
% 59.08/8.72 | | | |
% 59.08/8.72 | | | | GROUND_INST: instantiating (11) with all_32_5, all_32_3, all_32_2,
% 59.08/8.72 | | | | all_57_0, simplifying with (20), (22), (23), (36), (52),
% 59.08/8.72 | | | | (53) gives:
% 59.08/8.72 | | | | (55) ? [v0: $i] : (apply(all_32_5, v0, all_57_0) = 0 & member(v0,
% 59.08/8.72 | | | | all_32_3) = 0 & $i(v0))
% 59.08/8.72 | | | |
% 59.08/8.72 | | | | DELTA: instantiating (55) with fresh symbol all_65_0 gives:
% 59.08/8.72 | | | | (56) apply(all_32_5, all_65_0, all_57_0) = 0 & member(all_65_0,
% 59.08/8.72 | | | | all_32_3) = 0 & $i(all_65_0)
% 59.08/8.72 | | | |
% 59.08/8.72 | | | | ALPHA: (56) implies:
% 59.08/8.72 | | | | (57) $i(all_65_0)
% 59.08/8.72 | | | | (58) member(all_65_0, all_32_3) = 0
% 59.08/8.72 | | | | (59) apply(all_32_5, all_65_0, all_57_0) = 0
% 59.08/8.72 | | | |
% 59.08/8.72 | | | | GROUND_INST: instantiating (1) with all_32_5, all_32_3, all_32_2,
% 59.08/8.72 | | | | all_65_0, simplifying with (20), (22), (23), (26), (57),
% 59.08/8.72 | | | | (58) gives:
% 59.08/8.72 | | | | (60) ? [v0: $i] : (apply(all_32_5, all_65_0, v0) = 0 & member(v0,
% 59.08/8.72 | | | | all_32_2) = 0 & $i(v0))
% 59.08/8.72 | | | |
% 59.20/8.72 | | | | GROUND_INST: instantiating (11) with all_32_6, all_32_4, all_32_3,
% 59.20/8.72 | | | | all_65_0, simplifying with (19), (21), (22), (33), (57),
% 59.20/8.72 | | | | (58) gives:
% 59.20/8.72 | | | | (61) ? [v0: $i] : (apply(all_32_6, v0, all_65_0) = 0 & member(v0,
% 59.20/8.72 | | | | all_32_4) = 0 & $i(v0))
% 59.20/8.72 | | | |
% 59.20/8.72 | | | | DELTA: instantiating (61) with fresh symbol all_72_0 gives:
% 59.20/8.72 | | | | (62) apply(all_32_6, all_72_0, all_65_0) = 0 & member(all_72_0,
% 59.20/8.72 | | | | all_32_4) = 0 & $i(all_72_0)
% 59.20/8.72 | | | |
% 59.20/8.72 | | | | ALPHA: (62) implies:
% 59.20/8.72 | | | | (63) $i(all_72_0)
% 59.20/8.72 | | | | (64) member(all_72_0, all_32_4) = 0
% 59.20/8.72 | | | | (65) apply(all_32_6, all_72_0, all_65_0) = 0
% 59.20/8.72 | | | |
% 59.20/8.72 | | | | DELTA: instantiating (60) with fresh symbol all_74_0 gives:
% 59.20/8.72 | | | | (66) apply(all_32_5, all_65_0, all_74_0) = 0 & member(all_74_0,
% 59.20/8.72 | | | | all_32_2) = 0 & $i(all_74_0)
% 59.20/8.72 | | | |
% 59.20/8.72 | | | | ALPHA: (66) implies:
% 59.20/8.72 | | | | (67) $i(all_74_0)
% 59.20/8.72 | | | | (68) member(all_74_0, all_32_2) = 0
% 59.20/8.72 | | | | (69) apply(all_32_5, all_65_0, all_74_0) = 0
% 59.20/8.72 | | | |
% 59.22/8.72 | | | | GROUND_INST: instantiating (1) with all_32_6, all_32_4, all_32_3,
% 59.22/8.72 | | | | all_72_0, simplifying with (19), (21), (22), (25), (63),
% 59.22/8.72 | | | | (64) gives:
% 59.22/8.72 | | | | (70) ? [v0: $i] : (apply(all_32_6, all_72_0, v0) = 0 & member(v0,
% 59.22/8.72 | | | | all_32_3) = 0 & $i(v0))
% 59.22/8.72 | | | |
% 59.22/8.73 | | | | GROUND_INST: instantiating (54) with all_72_0, simplifying with (63),
% 59.22/8.73 | | | | (64) gives:
% 59.22/8.73 | | | | (71) ? [v0: int] : ( ~ (v0 = 0) & apply(all_32_1, all_72_0,
% 59.22/8.73 | | | | all_57_0) = v0)
% 59.22/8.73 | | | |
% 59.22/8.73 | | | | GROUND_INST: instantiating (2) with all_32_5, all_32_3, all_32_2,
% 59.22/8.73 | | | | all_65_0, all_74_0, all_57_0, simplifying with (20), (22),
% 59.22/8.73 | | | | (23), (26), (52), (53), (57), (58), (67), (68) gives:
% 59.22/8.73 | | | | (72) all_74_0 = all_57_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.73 | | | | (apply(all_32_5, all_65_0, all_74_0) = v0 & apply(all_32_5,
% 59.22/8.73 | | | | all_65_0, all_57_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.73 | | | |
% 59.22/8.73 | | | | GROUND_INST: instantiating (11) with all_32_5, all_32_3, all_32_2,
% 59.22/8.73 | | | | all_74_0, simplifying with (20), (22), (23), (36), (67),
% 59.22/8.73 | | | | (68) gives:
% 59.22/8.73 | | | | (73) ? [v0: $i] : (apply(all_32_5, v0, all_74_0) = 0 & member(v0,
% 59.22/8.73 | | | | all_32_3) = 0 & $i(v0))
% 59.22/8.73 | | | |
% 59.22/8.73 | | | | GROUND_INST: instantiating (3) with all_32_5, all_32_3, all_32_2,
% 59.22/8.73 | | | | all_65_0, all_57_0, all_74_0, simplifying with (20), (22),
% 59.22/8.73 | | | | (23), (26), (52), (53), (57), (67), (69) gives:
% 59.22/8.73 | | | | (74) all_74_0 = all_57_0 | ? [v0: any] : ? [v1: any] : ? [v2: any]
% 59.22/8.73 | | | | : (apply(all_32_5, all_65_0, all_57_0) = v2 & member(all_74_0,
% 59.22/8.73 | | | | all_32_2) = v1 & member(all_65_0, all_32_3) = v0 & ( ~ (v2 =
% 59.22/8.73 | | | | 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.73 | | | |
% 59.22/8.73 | | | | DELTA: instantiating (71) with fresh symbol all_81_0 gives:
% 59.22/8.73 | | | | (75) ~ (all_81_0 = 0) & apply(all_32_1, all_72_0, all_57_0) =
% 59.22/8.73 | | | | all_81_0
% 59.22/8.73 | | | |
% 59.22/8.73 | | | | ALPHA: (75) implies:
% 59.22/8.73 | | | | (76) ~ (all_81_0 = 0)
% 59.22/8.73 | | | | (77) apply(all_32_1, all_72_0, all_57_0) = all_81_0
% 59.22/8.73 | | | |
% 59.22/8.73 | | | | DELTA: instantiating (70) with fresh symbol all_83_0 gives:
% 59.22/8.73 | | | | (78) apply(all_32_6, all_72_0, all_83_0) = 0 & member(all_83_0,
% 59.22/8.73 | | | | all_32_3) = 0 & $i(all_83_0)
% 59.22/8.73 | | | |
% 59.22/8.73 | | | | ALPHA: (78) implies:
% 59.22/8.73 | | | | (79) $i(all_83_0)
% 59.22/8.73 | | | | (80) member(all_83_0, all_32_3) = 0
% 59.22/8.73 | | | | (81) apply(all_32_6, all_72_0, all_83_0) = 0
% 59.22/8.73 | | | |
% 59.22/8.73 | | | | DELTA: instantiating (73) with fresh symbol all_85_0 gives:
% 59.22/8.73 | | | | (82) apply(all_32_5, all_85_0, all_74_0) = 0 & member(all_85_0,
% 59.22/8.73 | | | | all_32_3) = 0 & $i(all_85_0)
% 59.22/8.73 | | | |
% 59.22/8.73 | | | | ALPHA: (82) implies:
% 59.22/8.73 | | | | (83) $i(all_85_0)
% 59.22/8.73 | | | | (84) member(all_85_0, all_32_3) = 0
% 59.22/8.73 | | | | (85) apply(all_32_5, all_85_0, all_74_0) = 0
% 59.22/8.73 | | | |
% 59.22/8.73 | | | | BETA: splitting (74) gives:
% 59.22/8.73 | | | |
% 59.22/8.73 | | | | Case 1:
% 59.22/8.73 | | | | |
% 59.22/8.73 | | | | | (86) all_74_0 = all_57_0
% 59.22/8.73 | | | | |
% 59.22/8.73 | | | | | REDUCE: (85), (86) imply:
% 59.22/8.73 | | | | | (87) apply(all_32_5, all_85_0, all_57_0) = 0
% 59.22/8.73 | | | | |
% 59.22/8.73 | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_3,
% 59.22/8.73 | | | | | all_72_0, all_65_0, all_83_0, simplifying with (19),
% 59.22/8.73 | | | | | (21), (22), (25), (57), (58), (63), (64), (79), (80)
% 59.22/8.73 | | | | | gives:
% 59.22/8.73 | | | | | (88) all_83_0 = all_65_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.73 | | | | | (apply(all_32_6, all_72_0, all_83_0) = v1 & apply(all_32_6,
% 59.22/8.73 | | | | | all_72_0, all_65_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.73 | | | | |
% 59.22/8.74 | | | | | GROUND_INST: instantiating (8) with all_32_5, all_32_3, all_32_2,
% 59.22/8.74 | | | | | all_85_0, all_83_0, all_57_0, simplifying with (20),
% 59.22/8.74 | | | | | (22), (23), (35), (52), (53), (79), (80), (83), (84)
% 59.22/8.74 | | | | | gives:
% 59.22/8.74 | | | | | (89) all_85_0 = all_83_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.74 | | | | | (apply(all_32_5, all_85_0, all_57_0) = v0 & apply(all_32_5,
% 59.22/8.74 | | | | | all_83_0, all_57_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.74 | | | | |
% 59.22/8.74 | | | | | GROUND_INST: instantiating (10) with all_32_5, all_32_3, all_32_2,
% 59.22/8.74 | | | | | all_85_0, all_65_0, all_57_0, simplifying with (20),
% 59.22/8.74 | | | | | (22), (23), (35), (52), (57), (59), (83), (87) gives:
% 59.22/8.74 | | | | | (90) all_85_0 = all_65_0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 59.22/8.74 | | | | | any] : (member(all_85_0, all_32_3) = v0 & member(all_65_0,
% 59.22/8.74 | | | | | all_32_3) = v1 & member(all_57_0, all_32_2) = v2 & ( ~ (v2
% 59.22/8.74 | | | | | = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.74 | | | | |
% 59.22/8.74 | | | | | GROUND_INST: instantiating (6) with all_32_5, all_32_6, all_32_4,
% 59.22/8.74 | | | | | all_32_3, all_32_2, all_72_0, all_57_0, all_32_1,
% 59.22/8.74 | | | | | all_81_0, all_65_0, simplifying with (19), (20), (21),
% 59.22/8.74 | | | | | (22), (23), (27), (52), (57), (59), (63), (77) gives:
% 59.22/8.74 | | | | | (91) all_81_0 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_6,
% 59.22/8.74 | | | | | all_72_0, all_65_0) = v1 & member(all_65_0, all_32_3) =
% 59.22/8.74 | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_72_0,
% 59.22/8.74 | | | | | all_32_4) = v0 & member(all_57_0, all_32_2) = v1 & ( ~
% 59.22/8.74 | | | | | (v1 = 0) | ~ (v0 = 0))))
% 59.22/8.74 | | | | |
% 59.22/8.74 | | | | | GROUND_INST: instantiating (6) with all_32_5, all_32_6, all_32_4,
% 59.22/8.74 | | | | | all_32_3, all_32_2, all_72_0, all_57_0, all_32_1,
% 59.22/8.74 | | | | | all_81_0, all_85_0, simplifying with (19), (20), (21),
% 59.22/8.74 | | | | | (22), (23), (27), (52), (63), (77), (83), (87) gives:
% 59.22/8.74 | | | | | (92) all_81_0 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_6,
% 59.22/8.74 | | | | | all_72_0, all_85_0) = v1 & member(all_85_0, all_32_3) =
% 59.22/8.74 | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_72_0,
% 59.22/8.74 | | | | | all_32_4) = v0 & member(all_57_0, all_32_2) = v1 & ( ~
% 59.22/8.74 | | | | | (v1 = 0) | ~ (v0 = 0))))
% 59.22/8.74 | | | | |
% 59.22/8.74 | | | | | BETA: splitting (88) gives:
% 59.22/8.74 | | | | |
% 59.22/8.74 | | | | | Case 1:
% 59.22/8.74 | | | | | |
% 59.22/8.74 | | | | | | (93) all_83_0 = all_65_0
% 59.22/8.74 | | | | | |
% 59.22/8.74 | | | | | | BETA: splitting (92) gives:
% 59.22/8.74 | | | | | |
% 59.22/8.74 | | | | | | Case 1:
% 59.22/8.74 | | | | | | |
% 59.22/8.74 | | | | | | | (94) all_81_0 = 0
% 59.22/8.74 | | | | | | |
% 59.22/8.74 | | | | | | | REDUCE: (76), (94) imply:
% 59.22/8.74 | | | | | | | (95) $false
% 59.22/8.74 | | | | | | |
% 59.22/8.74 | | | | | | | CLOSE: (95) is inconsistent.
% 59.22/8.74 | | | | | | |
% 59.22/8.74 | | | | | | Case 2:
% 59.22/8.74 | | | | | | |
% 59.22/8.74 | | | | | | | (96) ? [v0: any] : ? [v1: any] : ((apply(all_32_6, all_72_0,
% 59.22/8.74 | | | | | | | all_85_0) = v1 & member(all_85_0, all_32_3) = v0 & (
% 59.22/8.74 | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_72_0,
% 59.22/8.74 | | | | | | | all_32_4) = v0 & member(all_57_0, all_32_2) = v1 & (
% 59.22/8.74 | | | | | | | ~ (v1 = 0) | ~ (v0 = 0))))
% 59.22/8.74 | | | | | | |
% 59.22/8.74 | | | | | | | DELTA: instantiating (96) with fresh symbols all_133_0, all_133_1
% 59.22/8.74 | | | | | | | gives:
% 59.22/8.74 | | | | | | | (97) (apply(all_32_6, all_72_0, all_85_0) = all_133_0 &
% 59.22/8.74 | | | | | | | member(all_85_0, all_32_3) = all_133_1 & ( ~ (all_133_0
% 59.22/8.74 | | | | | | | = 0) | ~ (all_133_1 = 0))) | (member(all_72_0,
% 59.22/8.74 | | | | | | | all_32_4) = all_133_1 & member(all_57_0, all_32_2) =
% 59.22/8.74 | | | | | | | all_133_0 & ( ~ (all_133_0 = 0) | ~ (all_133_1 = 0)))
% 59.22/8.74 | | | | | | |
% 59.22/8.74 | | | | | | | REF_CLOSE: (15), (16), (53), (59), (64), (65), (76), (84), (87),
% 59.22/8.74 | | | | | | | (89), (91), (93), (97) are inconsistent by sub-proof
% 59.22/8.74 | | | | | | | #5.
% 59.22/8.74 | | | | | | |
% 59.22/8.74 | | | | | | End of split
% 59.22/8.74 | | | | | |
% 59.22/8.74 | | | | | Case 2:
% 59.22/8.74 | | | | | |
% 59.22/8.75 | | | | | | (98) ? [v0: any] : ? [v1: any] : (apply(all_32_6, all_72_0,
% 59.22/8.75 | | | | | | all_83_0) = v1 & apply(all_32_6, all_72_0, all_65_0) =
% 59.22/8.75 | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.75 | | | | | |
% 59.22/8.75 | | | | | | DELTA: instantiating (98) with fresh symbols all_117_0, all_117_1
% 59.22/8.75 | | | | | | gives:
% 59.22/8.75 | | | | | | (99) apply(all_32_6, all_72_0, all_83_0) = all_117_0 &
% 59.22/8.75 | | | | | | apply(all_32_6, all_72_0, all_65_0) = all_117_1 & ( ~
% 59.22/8.75 | | | | | | (all_117_0 = 0) | ~ (all_117_1 = 0))
% 59.22/8.75 | | | | | |
% 59.22/8.75 | | | | | | ALPHA: (99) implies:
% 59.22/8.75 | | | | | | (100) apply(all_32_6, all_72_0, all_65_0) = all_117_1
% 59.22/8.75 | | | | | | (101) apply(all_32_6, all_72_0, all_83_0) = all_117_0
% 59.22/8.75 | | | | | | (102) ~ (all_117_0 = 0) | ~ (all_117_1 = 0)
% 59.22/8.75 | | | | | |
% 59.22/8.75 | | | | | | BETA: splitting (92) gives:
% 59.22/8.75 | | | | | |
% 59.22/8.75 | | | | | | Case 1:
% 59.22/8.75 | | | | | | |
% 59.22/8.75 | | | | | | | (103) all_81_0 = 0
% 59.22/8.75 | | | | | | |
% 59.22/8.75 | | | | | | | REDUCE: (76), (103) imply:
% 59.22/8.75 | | | | | | | (104) $false
% 59.22/8.75 | | | | | | |
% 59.22/8.75 | | | | | | | CLOSE: (104) is inconsistent.
% 59.22/8.75 | | | | | | |
% 59.22/8.75 | | | | | | Case 2:
% 59.22/8.75 | | | | | | |
% 59.22/8.75 | | | | | | | (105) ? [v0: any] : ? [v1: any] : ((apply(all_32_6, all_72_0,
% 59.22/8.75 | | | | | | | all_85_0) = v1 & member(all_85_0, all_32_3) = v0 &
% 59.22/8.75 | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_72_0,
% 59.22/8.75 | | | | | | | all_32_4) = v0 & member(all_57_0, all_32_2) = v1 &
% 59.22/8.75 | | | | | | | ( ~ (v1 = 0) | ~ (v0 = 0))))
% 59.22/8.75 | | | | | | |
% 59.22/8.75 | | | | | | | BETA: splitting (90) gives:
% 59.22/8.75 | | | | | | |
% 59.22/8.75 | | | | | | | Case 1:
% 59.22/8.75 | | | | | | | |
% 59.22/8.75 | | | | | | | | (106) all_85_0 = all_65_0
% 59.22/8.75 | | | | | | | |
% 59.22/8.75 | | | | | | | | BETA: splitting (89) gives:
% 59.22/8.75 | | | | | | | |
% 59.22/8.75 | | | | | | | | Case 1:
% 59.22/8.75 | | | | | | | | |
% 59.22/8.75 | | | | | | | | | (107) all_85_0 = all_83_0
% 59.22/8.75 | | | | | | | | |
% 59.22/8.75 | | | | | | | | | COMBINE_EQS: (106), (107) imply:
% 59.22/8.75 | | | | | | | | | (108) all_83_0 = all_65_0
% 59.22/8.75 | | | | | | | | |
% 59.22/8.75 | | | | | | | | | SIMP: (108) implies:
% 59.22/8.75 | | | | | | | | | (109) all_83_0 = all_65_0
% 59.22/8.75 | | | | | | | | |
% 59.22/8.75 | | | | | | | | | DELTA: instantiating (105) with fresh symbols all_133_0,
% 59.22/8.75 | | | | | | | | | all_133_1 gives:
% 59.22/8.75 | | | | | | | | | (110) (apply(all_32_6, all_72_0, all_85_0) = all_133_0 &
% 59.22/8.75 | | | | | | | | | member(all_85_0, all_32_3) = all_133_1 & ( ~
% 59.22/8.75 | | | | | | | | | (all_133_0 = 0) | ~ (all_133_1 = 0))) |
% 59.22/8.75 | | | | | | | | | (member(all_72_0, all_32_4) = all_133_1 &
% 59.22/8.75 | | | | | | | | | member(all_57_0, all_32_2) = all_133_0 & ( ~
% 59.22/8.75 | | | | | | | | | (all_133_0 = 0) | ~ (all_133_1 = 0)))
% 59.22/8.75 | | | | | | | | |
% 59.22/8.75 | | | | | | | | | REF_CLOSE: (15), (16), (53), (59), (64), (65), (76), (84),
% 59.22/8.75 | | | | | | | | | (87), (89), (91), (109), (110) are inconsistent by
% 59.22/8.75 | | | | | | | | | sub-proof #5.
% 59.22/8.75 | | | | | | | | |
% 59.22/8.75 | | | | | | | | Case 2:
% 59.22/8.75 | | | | | | | | |
% 59.22/8.75 | | | | | | | | |
% 59.22/8.75 | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_117_1, all_65_0,
% 59.22/8.75 | | | | | | | | | all_72_0, all_32_6, simplifying with (65), (100)
% 59.22/8.75 | | | | | | | | | gives:
% 59.22/8.75 | | | | | | | | | (111) all_117_1 = 0
% 59.22/8.75 | | | | | | | | |
% 59.22/8.75 | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_117_0, all_83_0,
% 59.22/8.75 | | | | | | | | | all_72_0, all_32_6, simplifying with (81), (101)
% 59.22/8.75 | | | | | | | | | gives:
% 59.22/8.75 | | | | | | | | | (112) all_117_0 = 0
% 59.22/8.75 | | | | | | | | |
% 59.22/8.75 | | | | | | | | | REF_CLOSE: (102), (111), (112) are inconsistent by sub-proof
% 59.22/8.75 | | | | | | | | | #4.
% 59.22/8.75 | | | | | | | | |
% 59.22/8.75 | | | | | | | | End of split
% 59.22/8.75 | | | | | | | |
% 59.22/8.75 | | | | | | | Case 2:
% 59.22/8.75 | | | | | | | |
% 59.22/8.75 | | | | | | | |
% 59.22/8.75 | | | | | | | | GROUND_INST: instantiating (16) with 0, all_117_1, all_65_0,
% 59.22/8.75 | | | | | | | | all_72_0, all_32_6, simplifying with (65), (100)
% 59.22/8.75 | | | | | | | | gives:
% 59.22/8.75 | | | | | | | | (113) all_117_1 = 0
% 59.22/8.75 | | | | | | | |
% 59.22/8.75 | | | | | | | | GROUND_INST: instantiating (16) with 0, all_117_0, all_83_0,
% 59.22/8.75 | | | | | | | | all_72_0, all_32_6, simplifying with (81), (101)
% 59.22/8.75 | | | | | | | | gives:
% 59.22/8.75 | | | | | | | | (114) all_117_0 = 0
% 59.22/8.75 | | | | | | | |
% 59.22/8.75 | | | | | | | | REF_CLOSE: (102), (113), (114) are inconsistent by sub-proof #4.
% 59.22/8.75 | | | | | | | |
% 59.22/8.75 | | | | | | | End of split
% 59.22/8.75 | | | | | | |
% 59.22/8.75 | | | | | | End of split
% 59.22/8.75 | | | | | |
% 59.22/8.75 | | | | | End of split
% 59.22/8.75 | | | | |
% 59.22/8.75 | | | | Case 2:
% 59.22/8.75 | | | | |
% 59.22/8.75 | | | | | (115) ~ (all_74_0 = all_57_0)
% 59.22/8.75 | | | | |
% 59.22/8.75 | | | | | BETA: splitting (72) gives:
% 59.22/8.75 | | | | |
% 59.22/8.75 | | | | | Case 1:
% 59.22/8.75 | | | | | |
% 59.22/8.75 | | | | | | (116) all_74_0 = all_57_0
% 59.22/8.75 | | | | | |
% 59.22/8.75 | | | | | | REDUCE: (115), (116) imply:
% 59.22/8.75 | | | | | | (117) $false
% 59.22/8.75 | | | | | |
% 59.22/8.75 | | | | | | CLOSE: (117) is inconsistent.
% 59.22/8.75 | | | | | |
% 59.22/8.75 | | | | | Case 2:
% 59.22/8.75 | | | | | |
% 59.22/8.75 | | | | | | (118) ? [v0: any] : ? [v1: any] : (apply(all_32_5, all_65_0,
% 59.22/8.75 | | | | | | all_74_0) = v0 & apply(all_32_5, all_65_0, all_57_0) =
% 59.22/8.75 | | | | | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.75 | | | | | |
% 59.22/8.75 | | | | | | DELTA: instantiating (118) with fresh symbols all_97_0, all_97_1
% 59.22/8.75 | | | | | | gives:
% 59.22/8.75 | | | | | | (119) apply(all_32_5, all_65_0, all_74_0) = all_97_1 &
% 59.22/8.75 | | | | | | apply(all_32_5, all_65_0, all_57_0) = all_97_0 & ( ~
% 59.22/8.75 | | | | | | (all_97_0 = 0) | ~ (all_97_1 = 0))
% 59.22/8.75 | | | | | |
% 59.22/8.75 | | | | | | ALPHA: (119) implies:
% 59.22/8.75 | | | | | | (120) apply(all_32_5, all_65_0, all_57_0) = all_97_0
% 59.22/8.75 | | | | | | (121) apply(all_32_5, all_65_0, all_74_0) = all_97_1
% 59.22/8.75 | | | | | | (122) ~ (all_97_0 = 0) | ~ (all_97_1 = 0)
% 59.22/8.75 | | | | | |
% 59.22/8.75 | | | | | | GROUND_INST: instantiating (16) with 0, all_97_0, all_57_0,
% 59.22/8.75 | | | | | | all_65_0, all_32_5, simplifying with (59), (120) gives:
% 59.22/8.75 | | | | | | (123) all_97_0 = 0
% 59.22/8.76 | | | | | |
% 59.22/8.76 | | | | | | GROUND_INST: instantiating (16) with 0, all_97_1, all_74_0,
% 59.22/8.76 | | | | | | all_65_0, all_32_5, simplifying with (69), (121) gives:
% 59.22/8.76 | | | | | | (124) all_97_1 = 0
% 59.22/8.76 | | | | | |
% 59.22/8.76 | | | | | | BETA: splitting (122) gives:
% 59.22/8.76 | | | | | |
% 59.22/8.76 | | | | | | Case 1:
% 59.22/8.76 | | | | | | |
% 59.22/8.76 | | | | | | | (125) ~ (all_97_0 = 0)
% 59.22/8.76 | | | | | | |
% 59.22/8.76 | | | | | | | REDUCE: (123), (125) imply:
% 59.22/8.76 | | | | | | | (126) $false
% 59.22/8.76 | | | | | | |
% 59.22/8.76 | | | | | | | CLOSE: (126) is inconsistent.
% 59.22/8.76 | | | | | | |
% 59.22/8.76 | | | | | | Case 2:
% 59.22/8.76 | | | | | | |
% 59.22/8.76 | | | | | | | (127) ~ (all_97_1 = 0)
% 59.22/8.76 | | | | | | |
% 59.22/8.76 | | | | | | | REDUCE: (124), (127) imply:
% 59.22/8.76 | | | | | | | (128) $false
% 59.22/8.76 | | | | | | |
% 59.22/8.76 | | | | | | | CLOSE: (128) is inconsistent.
% 59.22/8.76 | | | | | | |
% 59.22/8.76 | | | | | | End of split
% 59.22/8.76 | | | | | |
% 59.22/8.76 | | | | | End of split
% 59.22/8.76 | | | | |
% 59.22/8.76 | | | | End of split
% 59.22/8.76 | | | |
% 59.22/8.76 | | | End of split
% 59.22/8.76 | | |
% 59.22/8.76 | | Case 2:
% 59.22/8.76 | | |
% 59.22/8.76 | | | (129) all_44_0 = 0
% 59.22/8.76 | | | (130) ~ (all_44_1 = 0)
% 59.22/8.76 | | |
% 59.22/8.76 | | | REDUCE: (43), (129) imply:
% 59.22/8.76 | | | (131) surjective(all_32_1, all_32_4, all_32_2) = 0
% 59.22/8.76 | | |
% 59.22/8.76 | | | BETA: splitting (45) gives:
% 59.22/8.76 | | |
% 59.22/8.76 | | | Case 1:
% 59.22/8.76 | | | |
% 59.22/8.76 | | | | (132) all_44_1 = 0
% 59.22/8.76 | | | |
% 59.22/8.76 | | | | REDUCE: (130), (132) imply:
% 59.22/8.76 | | | | (133) $false
% 59.22/8.76 | | | |
% 59.22/8.76 | | | | CLOSE: (133) is inconsistent.
% 59.22/8.76 | | | |
% 59.22/8.76 | | | Case 2:
% 59.22/8.76 | | | |
% 59.22/8.76 | | | | (134) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v1 = v0) &
% 59.22/8.76 | | | | apply(all_32_1, v1, v2) = 0 & apply(all_32_1, v0, v2) = 0 &
% 59.22/8.76 | | | | member(v2, all_32_2) = 0 & member(v1, all_32_4) = 0 &
% 59.22/8.76 | | | | member(v0, all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0))
% 59.22/8.76 | | | |
% 59.22/8.76 | | | | DELTA: instantiating (134) with fresh symbols all_57_0, all_57_1,
% 59.22/8.76 | | | | all_57_2 gives:
% 59.22/8.76 | | | | (135) ~ (all_57_1 = all_57_2) & apply(all_32_1, all_57_1, all_57_0)
% 59.22/8.76 | | | | = 0 & apply(all_32_1, all_57_2, all_57_0) = 0 &
% 59.22/8.76 | | | | member(all_57_0, all_32_2) = 0 & member(all_57_1, all_32_4) = 0
% 59.22/8.76 | | | | & member(all_57_2, all_32_4) = 0 & $i(all_57_0) & $i(all_57_1)
% 59.22/8.76 | | | | & $i(all_57_2)
% 59.22/8.76 | | | |
% 59.22/8.76 | | | | ALPHA: (135) implies:
% 59.22/8.76 | | | | (136) ~ (all_57_1 = all_57_2)
% 59.22/8.76 | | | | (137) $i(all_57_2)
% 59.22/8.76 | | | | (138) $i(all_57_1)
% 59.22/8.76 | | | | (139) $i(all_57_0)
% 59.22/8.76 | | | | (140) member(all_57_2, all_32_4) = 0
% 59.22/8.76 | | | | (141) member(all_57_1, all_32_4) = 0
% 59.22/8.76 | | | | (142) member(all_57_0, all_32_2) = 0
% 59.22/8.76 | | | | (143) apply(all_32_1, all_57_2, all_57_0) = 0
% 59.22/8.76 | | | | (144) apply(all_32_1, all_57_1, all_57_0) = 0
% 59.22/8.76 | | | |
% 59.22/8.76 | | | | GROUND_INST: instantiating (1) with all_32_6, all_32_4, all_32_3,
% 59.22/8.76 | | | | all_57_2, simplifying with (19), (21), (22), (25), (137),
% 59.22/8.76 | | | | (140) gives:
% 59.22/8.76 | | | | (145) ? [v0: $i] : (apply(all_32_6, all_57_2, v0) = 0 & member(v0,
% 59.22/8.76 | | | | all_32_3) = 0 & $i(v0))
% 59.22/8.76 | | | |
% 59.22/8.76 | | | | GROUND_INST: instantiating (1) with all_32_6, all_32_4, all_32_3,
% 59.22/8.76 | | | | all_57_1, simplifying with (19), (21), (22), (25), (138),
% 59.22/8.76 | | | | (141) gives:
% 59.22/8.76 | | | | (146) ? [v0: $i] : (apply(all_32_6, all_57_1, v0) = 0 & member(v0,
% 59.22/8.76 | | | | all_32_3) = 0 & $i(v0))
% 59.22/8.76 | | | |
% 59.22/8.76 | | | | GROUND_INST: instantiating (11) with all_32_5, all_32_3, all_32_2,
% 59.22/8.76 | | | | all_57_0, simplifying with (20), (22), (23), (36), (139),
% 59.22/8.76 | | | | (142) gives:
% 59.22/8.76 | | | | (147) ? [v0: $i] : (apply(all_32_5, v0, all_57_0) = 0 & member(v0,
% 59.22/8.76 | | | | all_32_3) = 0 & $i(v0))
% 59.22/8.76 | | | |
% 59.22/8.76 | | | | GROUND_INST: instantiating (5) with all_32_5, all_32_6, all_32_4,
% 59.22/8.76 | | | | all_32_3, all_32_2, all_57_2, all_57_0, all_32_1,
% 59.22/8.76 | | | | simplifying with (19), (20), (21), (22), (23), (27), (137),
% 59.22/8.76 | | | | (139), (143) gives:
% 59.22/8.76 | | | | (148) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: int] : ?
% 59.22/8.76 | | | | [v4: int] : ? [v5: int] : ($i(v2) & ((v5 = 0 & v4 = 0 & v3 = 0
% 59.22/8.76 | | | | & apply(all_32_5, v2, all_57_0) = 0 & apply(all_32_6,
% 59.22/8.76 | | | | all_57_2, v2) = 0 & member(v2, all_32_3) = 0) |
% 59.22/8.76 | | | | (member(all_57_0, all_32_2) = v1 & member(all_57_2,
% 59.22/8.76 | | | | all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))))
% 59.22/8.76 | | | |
% 59.22/8.76 | | | | GROUND_INST: instantiating (5) with all_32_5, all_32_6, all_32_4,
% 59.22/8.76 | | | | all_32_3, all_32_2, all_57_1, all_57_0, all_32_1,
% 59.22/8.76 | | | | simplifying with (19), (20), (21), (22), (23), (27), (138),
% 59.22/8.76 | | | | (139), (144) gives:
% 59.22/8.77 | | | | (149) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: int] : ?
% 59.22/8.77 | | | | [v4: int] : ? [v5: int] : ($i(v2) & ((v5 = 0 & v4 = 0 & v3 = 0
% 59.22/8.77 | | | | & apply(all_32_5, v2, all_57_0) = 0 & apply(all_32_6,
% 59.22/8.77 | | | | all_57_1, v2) = 0 & member(v2, all_32_3) = 0) |
% 59.22/8.77 | | | | (member(all_57_0, all_32_2) = v1 & member(all_57_1,
% 59.22/8.77 | | | | all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))))
% 59.22/8.77 | | | |
% 59.22/8.77 | | | | GROUND_INST: instantiating (11) with all_32_1, all_32_4, all_32_2,
% 59.22/8.77 | | | | all_57_0, simplifying with (21), (23), (24), (131), (139),
% 59.22/8.77 | | | | (142) gives:
% 59.22/8.77 | | | | (150) ? [v0: $i] : (apply(all_32_1, v0, all_57_0) = 0 & member(v0,
% 59.22/8.77 | | | | all_32_4) = 0 & $i(v0))
% 59.22/8.77 | | | |
% 59.22/8.77 | | | | DELTA: instantiating (150) with fresh symbol all_64_0 gives:
% 59.22/8.77 | | | | (151) apply(all_32_1, all_64_0, all_57_0) = 0 & member(all_64_0,
% 59.22/8.77 | | | | all_32_4) = 0 & $i(all_64_0)
% 59.22/8.77 | | | |
% 59.22/8.77 | | | | ALPHA: (151) implies:
% 59.22/8.77 | | | | (152) $i(all_64_0)
% 59.22/8.77 | | | | (153) member(all_64_0, all_32_4) = 0
% 59.22/8.77 | | | |
% 59.22/8.77 | | | | DELTA: instantiating (147) with fresh symbol all_66_0 gives:
% 59.22/8.77 | | | | (154) apply(all_32_5, all_66_0, all_57_0) = 0 & member(all_66_0,
% 59.22/8.77 | | | | all_32_3) = 0 & $i(all_66_0)
% 59.22/8.77 | | | |
% 59.22/8.77 | | | | ALPHA: (154) implies:
% 59.22/8.77 | | | | (155) $i(all_66_0)
% 59.22/8.77 | | | | (156) member(all_66_0, all_32_3) = 0
% 59.22/8.77 | | | | (157) apply(all_32_5, all_66_0, all_57_0) = 0
% 59.22/8.77 | | | |
% 59.22/8.77 | | | | DELTA: instantiating (146) with fresh symbol all_68_0 gives:
% 59.22/8.77 | | | | (158) apply(all_32_6, all_57_1, all_68_0) = 0 & member(all_68_0,
% 59.22/8.77 | | | | all_32_3) = 0 & $i(all_68_0)
% 59.22/8.77 | | | |
% 59.22/8.77 | | | | ALPHA: (158) implies:
% 59.22/8.77 | | | | (159) $i(all_68_0)
% 59.22/8.77 | | | | (160) member(all_68_0, all_32_3) = 0
% 59.22/8.77 | | | | (161) apply(all_32_6, all_57_1, all_68_0) = 0
% 59.22/8.77 | | | |
% 59.22/8.77 | | | | DELTA: instantiating (145) with fresh symbol all_70_0 gives:
% 59.22/8.77 | | | | (162) apply(all_32_6, all_57_2, all_70_0) = 0 & member(all_70_0,
% 59.22/8.77 | | | | all_32_3) = 0 & $i(all_70_0)
% 59.22/8.77 | | | |
% 59.22/8.77 | | | | ALPHA: (162) implies:
% 59.22/8.77 | | | | (163) $i(all_70_0)
% 59.22/8.77 | | | | (164) member(all_70_0, all_32_3) = 0
% 59.22/8.77 | | | | (165) apply(all_32_6, all_57_2, all_70_0) = 0
% 59.22/8.77 | | | |
% 59.22/8.77 | | | | DELTA: instantiating (148) with fresh symbols all_72_0, all_72_1,
% 59.22/8.77 | | | | all_72_2, all_72_3, all_72_4, all_72_5 gives:
% 59.22/8.77 | | | | (166) $i(all_72_3) & ((all_72_0 = 0 & all_72_1 = 0 & all_72_2 = 0 &
% 59.22/8.77 | | | | apply(all_32_5, all_72_3, all_57_0) = 0 & apply(all_32_6,
% 59.22/8.77 | | | | all_57_2, all_72_3) = 0 & member(all_72_3, all_32_3) = 0)
% 59.22/8.77 | | | | | (member(all_57_0, all_32_2) = all_72_4 & member(all_57_2,
% 59.22/8.77 | | | | all_32_4) = all_72_5 & ( ~ (all_72_4 = 0) | ~ (all_72_5
% 59.22/8.77 | | | | = 0))))
% 59.22/8.77 | | | |
% 59.22/8.77 | | | | ALPHA: (166) implies:
% 59.22/8.77 | | | | (167) $i(all_72_3)
% 59.22/8.77 | | | | (168) (all_72_0 = 0 & all_72_1 = 0 & all_72_2 = 0 & apply(all_32_5,
% 59.22/8.77 | | | | all_72_3, all_57_0) = 0 & apply(all_32_6, all_57_2,
% 59.22/8.77 | | | | all_72_3) = 0 & member(all_72_3, all_32_3) = 0) |
% 59.22/8.77 | | | | (member(all_57_0, all_32_2) = all_72_4 & member(all_57_2,
% 59.22/8.77 | | | | all_32_4) = all_72_5 & ( ~ (all_72_4 = 0) | ~ (all_72_5 =
% 59.22/8.77 | | | | 0)))
% 59.22/8.77 | | | |
% 59.22/8.77 | | | | DELTA: instantiating (149) with fresh symbols all_74_0, all_74_1,
% 59.22/8.77 | | | | all_74_2, all_74_3, all_74_4, all_74_5 gives:
% 59.22/8.77 | | | | (169) $i(all_74_3) & ((all_74_0 = 0 & all_74_1 = 0 & all_74_2 = 0 &
% 59.22/8.77 | | | | apply(all_32_5, all_74_3, all_57_0) = 0 & apply(all_32_6,
% 59.22/8.77 | | | | all_57_1, all_74_3) = 0 & member(all_74_3, all_32_3) = 0)
% 59.22/8.77 | | | | | (member(all_57_0, all_32_2) = all_74_4 & member(all_57_1,
% 59.22/8.77 | | | | all_32_4) = all_74_5 & ( ~ (all_74_4 = 0) | ~ (all_74_5
% 59.22/8.77 | | | | = 0))))
% 59.22/8.77 | | | |
% 59.22/8.77 | | | | ALPHA: (169) implies:
% 59.22/8.77 | | | | (170) $i(all_74_3)
% 59.22/8.77 | | | | (171) (all_74_0 = 0 & all_74_1 = 0 & all_74_2 = 0 & apply(all_32_5,
% 59.22/8.77 | | | | all_74_3, all_57_0) = 0 & apply(all_32_6, all_57_1,
% 59.22/8.77 | | | | all_74_3) = 0 & member(all_74_3, all_32_3) = 0) |
% 59.22/8.77 | | | | (member(all_57_0, all_32_2) = all_74_4 & member(all_57_1,
% 59.22/8.77 | | | | all_32_4) = all_74_5 & ( ~ (all_74_4 = 0) | ~ (all_74_5 =
% 59.22/8.77 | | | | 0)))
% 59.22/8.77 | | | |
% 59.22/8.77 | | | | BETA: splitting (171) gives:
% 59.22/8.77 | | | |
% 59.22/8.77 | | | | Case 1:
% 59.22/8.77 | | | | |
% 59.22/8.77 | | | | | (172) all_74_0 = 0 & all_74_1 = 0 & all_74_2 = 0 & apply(all_32_5,
% 59.22/8.77 | | | | | all_74_3, all_57_0) = 0 & apply(all_32_6, all_57_1,
% 59.22/8.77 | | | | | all_74_3) = 0 & member(all_74_3, all_32_3) = 0
% 59.22/8.77 | | | | |
% 59.22/8.77 | | | | | ALPHA: (172) implies:
% 59.22/8.78 | | | | | (173) member(all_74_3, all_32_3) = 0
% 59.22/8.78 | | | | | (174) apply(all_32_6, all_57_1, all_74_3) = 0
% 59.22/8.78 | | | | | (175) apply(all_32_5, all_74_3, all_57_0) = 0
% 59.22/8.78 | | | | |
% 59.22/8.78 | | | | | BETA: splitting (168) gives:
% 59.22/8.78 | | | | |
% 59.22/8.78 | | | | | Case 1:
% 59.22/8.78 | | | | | |
% 59.22/8.78 | | | | | | (176) all_72_0 = 0 & all_72_1 = 0 & all_72_2 = 0 &
% 59.22/8.78 | | | | | | apply(all_32_5, all_72_3, all_57_0) = 0 & apply(all_32_6,
% 59.22/8.78 | | | | | | all_57_2, all_72_3) = 0 & member(all_72_3, all_32_3) = 0
% 59.22/8.78 | | | | | |
% 59.22/8.78 | | | | | | ALPHA: (176) implies:
% 59.22/8.78 | | | | | | (177) member(all_72_3, all_32_3) = 0
% 59.22/8.78 | | | | | | (178) apply(all_32_6, all_57_2, all_72_3) = 0
% 59.22/8.78 | | | | | | (179) apply(all_32_5, all_72_3, all_57_0) = 0
% 59.22/8.78 | | | | | |
% 59.22/8.78 | | | | | | GROUND_INST: instantiating (8) with all_32_6, all_32_4, all_32_3,
% 59.22/8.78 | | | | | | all_57_2, all_57_1, all_68_0, simplifying with (19),
% 59.22/8.78 | | | | | | (21), (22), (32), (137), (138), (140), (141), (159),
% 59.22/8.78 | | | | | | (160) gives:
% 59.22/8.78 | | | | | | (180) all_57_1 = all_57_2 | ? [v0: any] : ? [v1: any] :
% 59.22/8.78 | | | | | | (apply(all_32_6, all_57_1, all_68_0) = v1 & apply(all_32_6,
% 59.22/8.78 | | | | | | all_57_2, all_68_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.78 | | | | | |
% 59.22/8.78 | | | | | | GROUND_INST: instantiating (8) with all_32_6, all_32_4, all_32_3,
% 59.22/8.78 | | | | | | all_57_1, all_57_2, all_68_0, simplifying with (19),
% 59.22/8.78 | | | | | | (21), (22), (32), (137), (138), (140), (141), (159),
% 59.22/8.78 | | | | | | (160) gives:
% 59.22/8.78 | | | | | | (181) all_57_1 = all_57_2 | ? [v0: any] : ? [v1: any] :
% 59.22/8.78 | | | | | | (apply(all_32_6, all_57_1, all_68_0) = v0 & apply(all_32_6,
% 59.22/8.78 | | | | | | all_57_2, all_68_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.78 | | | | | |
% 59.22/8.78 | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_3,
% 59.22/8.78 | | | | | | all_57_1, all_68_0, all_70_0, simplifying with (19),
% 59.22/8.78 | | | | | | (21), (22), (25), (138), (141), (159), (160), (163),
% 59.22/8.78 | | | | | | (164) gives:
% 59.22/8.78 | | | | | | (182) all_70_0 = all_68_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.78 | | | | | | (apply(all_32_6, all_57_1, all_70_0) = v1 & apply(all_32_6,
% 59.22/8.78 | | | | | | all_57_1, all_68_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.78 | | | | | |
% 59.22/8.78 | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_3,
% 59.22/8.78 | | | | | | all_57_2, all_68_0, all_70_0, simplifying with (19),
% 59.22/8.78 | | | | | | (21), (22), (25), (137), (140), (159), (160), (163),
% 59.22/8.78 | | | | | | (164) gives:
% 59.22/8.78 | | | | | | (183) all_70_0 = all_68_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.78 | | | | | | (apply(all_32_6, all_57_2, all_70_0) = v1 & apply(all_32_6,
% 59.22/8.78 | | | | | | all_57_2, all_68_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.78 | | | | | |
% 59.22/8.78 | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_3,
% 59.22/8.78 | | | | | | all_57_2, all_70_0, all_68_0, simplifying with (19),
% 59.22/8.78 | | | | | | (21), (22), (25), (137), (140), (159), (160), (163),
% 59.22/8.78 | | | | | | (164) gives:
% 59.22/8.78 | | | | | | (184) all_70_0 = all_68_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.78 | | | | | | (apply(all_32_6, all_57_2, all_70_0) = v0 & apply(all_32_6,
% 59.22/8.78 | | | | | | all_57_2, all_68_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.78 | | | | | |
% 59.22/8.78 | | | | | | GROUND_INST: instantiating (8) with all_32_5, all_32_3, all_32_2,
% 59.22/8.78 | | | | | | all_70_0, all_66_0, all_57_0, simplifying with (20),
% 59.22/8.78 | | | | | | (22), (23), (35), (139), (142), (155), (156), (163),
% 59.22/8.78 | | | | | | (164) gives:
% 59.22/8.78 | | | | | | (185) all_70_0 = all_66_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.78 | | | | | | (apply(all_32_5, all_70_0, all_57_0) = v0 & apply(all_32_5,
% 59.22/8.78 | | | | | | all_66_0, all_57_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.78 | | | | | |
% 59.22/8.78 | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_3,
% 59.22/8.78 | | | | | | all_57_2, all_72_3, all_70_0, simplifying with (19),
% 59.22/8.78 | | | | | | (21), (22), (25), (137), (140), (163), (164), (167),
% 59.22/8.78 | | | | | | (177) gives:
% 59.22/8.78 | | | | | | (186) all_72_3 = all_70_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.78 | | | | | | (apply(all_32_6, all_57_2, all_72_3) = v0 & apply(all_32_6,
% 59.22/8.78 | | | | | | all_57_2, all_70_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.78 | | | | | |
% 59.22/8.78 | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_3,
% 59.22/8.78 | | | | | | all_64_0, all_70_0, all_72_3, simplifying with (19),
% 59.22/8.78 | | | | | | (21), (22), (25), (152), (153), (163), (164), (167),
% 59.22/8.78 | | | | | | (177) gives:
% 59.22/8.79 | | | | | | (187) all_72_3 = all_70_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.79 | | | | | | (apply(all_32_6, all_64_0, all_72_3) = v1 & apply(all_32_6,
% 59.22/8.79 | | | | | | all_64_0, all_70_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.79 | | | | | |
% 59.22/8.79 | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_3,
% 59.22/8.79 | | | | | | all_57_1, all_72_3, all_68_0, simplifying with (19),
% 59.22/8.79 | | | | | | (21), (22), (25), (138), (141), (159), (160), (167),
% 59.22/8.79 | | | | | | (177) gives:
% 59.22/8.79 | | | | | | (188) all_72_3 = all_68_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.79 | | | | | | (apply(all_32_6, all_57_1, all_72_3) = v0 & apply(all_32_6,
% 59.22/8.79 | | | | | | all_57_1, all_68_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.79 | | | | | |
% 59.22/8.79 | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_3,
% 59.22/8.79 | | | | | | all_57_2, all_68_0, all_72_3, simplifying with (19),
% 59.22/8.79 | | | | | | (21), (22), (25), (137), (140), (159), (160), (167),
% 59.22/8.79 | | | | | | (177) gives:
% 59.22/8.79 | | | | | | (189) all_72_3 = all_68_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.79 | | | | | | (apply(all_32_6, all_57_2, all_72_3) = v1 & apply(all_32_6,
% 59.22/8.79 | | | | | | all_57_2, all_68_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.79 | | | | | |
% 59.22/8.79 | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_3,
% 59.22/8.79 | | | | | | all_57_1, all_72_3, all_66_0, simplifying with (19),
% 59.22/8.79 | | | | | | (21), (22), (25), (138), (141), (155), (156), (167),
% 59.22/8.79 | | | | | | (177) gives:
% 59.22/8.79 | | | | | | (190) all_72_3 = all_66_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.79 | | | | | | (apply(all_32_6, all_57_1, all_72_3) = v0 & apply(all_32_6,
% 59.22/8.79 | | | | | | all_57_1, all_66_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.79 | | | | | |
% 59.22/8.79 | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_3,
% 59.22/8.79 | | | | | | all_57_2, all_66_0, all_72_3, simplifying with (19),
% 59.22/8.79 | | | | | | (21), (22), (25), (137), (140), (155), (156), (167),
% 59.22/8.79 | | | | | | (177) gives:
% 59.22/8.79 | | | | | | (191) all_72_3 = all_66_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.79 | | | | | | (apply(all_32_6, all_57_2, all_72_3) = v1 & apply(all_32_6,
% 59.22/8.79 | | | | | | all_57_2, all_66_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.79 | | | | | |
% 59.22/8.79 | | | | | | GROUND_INST: instantiating (8) with all_32_5, all_32_3, all_32_2,
% 59.22/8.79 | | | | | | all_72_3, all_66_0, all_57_0, simplifying with (20),
% 59.22/8.79 | | | | | | (22), (23), (35), (139), (142), (155), (156), (167),
% 59.22/8.79 | | | | | | (177) gives:
% 59.22/8.79 | | | | | | (192) all_72_3 = all_66_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.79 | | | | | | (apply(all_32_5, all_72_3, all_57_0) = v0 & apply(all_32_5,
% 59.22/8.79 | | | | | | all_66_0, all_57_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.79 | | | | | |
% 59.22/8.79 | | | | | | GROUND_INST: instantiating (8) with all_32_6, all_32_4, all_32_3,
% 59.22/8.79 | | | | | | all_57_1, all_57_2, all_72_3, simplifying with (19),
% 59.22/8.79 | | | | | | (21), (22), (32), (137), (138), (140), (141), (167),
% 59.22/8.79 | | | | | | (177) gives:
% 59.22/8.79 | | | | | | (193) all_57_1 = all_57_2 | ? [v0: any] : ? [v1: any] :
% 59.22/8.79 | | | | | | (apply(all_32_6, all_57_1, all_72_3) = v0 & apply(all_32_6,
% 59.22/8.79 | | | | | | all_57_2, all_72_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.79 | | | | | |
% 59.22/8.79 | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_3,
% 59.22/8.79 | | | | | | all_64_0, all_68_0, all_74_3, simplifying with (19),
% 59.22/8.79 | | | | | | (21), (22), (25), (152), (153), (159), (160), (170),
% 59.22/8.79 | | | | | | (173) gives:
% 59.22/8.79 | | | | | | (194) all_74_3 = all_68_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.79 | | | | | | (apply(all_32_6, all_64_0, all_74_3) = v1 & apply(all_32_6,
% 59.22/8.79 | | | | | | all_64_0, all_68_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.79 | | | | | |
% 59.22/8.79 | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4, all_32_3,
% 59.22/8.79 | | | | | | all_57_1, all_66_0, all_74_3, simplifying with (19),
% 59.22/8.79 | | | | | | (21), (22), (25), (138), (141), (155), (156), (170),
% 59.22/8.79 | | | | | | (173) gives:
% 59.22/8.79 | | | | | | (195) all_74_3 = all_66_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.79 | | | | | | (apply(all_32_6, all_57_1, all_74_3) = v1 & apply(all_32_6,
% 59.22/8.79 | | | | | | all_57_1, all_66_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.79 | | | | | |
% 59.22/8.79 | | | | | | GROUND_INST: instantiating (8) with all_32_5, all_32_3, all_32_2,
% 59.22/8.79 | | | | | | all_74_3, all_72_3, all_57_0, simplifying with (20),
% 59.22/8.79 | | | | | | (22), (23), (35), (139), (142), (167), (170), (173),
% 59.22/8.79 | | | | | | (177) gives:
% 59.22/8.79 | | | | | | (196) all_74_3 = all_72_3 | ? [v0: any] : ? [v1: any] :
% 59.22/8.79 | | | | | | (apply(all_32_5, all_74_3, all_57_0) = v0 & apply(all_32_5,
% 59.22/8.79 | | | | | | all_72_3, all_57_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.79 | | | | | |
% 59.22/8.79 | | | | | | GROUND_INST: instantiating (8) with all_32_5, all_32_3, all_32_2,
% 59.22/8.79 | | | | | | all_74_3, all_70_0, all_57_0, simplifying with (20),
% 59.22/8.79 | | | | | | (22), (23), (35), (139), (142), (163), (164), (170),
% 59.22/8.79 | | | | | | (173) gives:
% 59.22/8.79 | | | | | | (197) all_74_3 = all_70_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.79 | | | | | | (apply(all_32_5, all_74_3, all_57_0) = v0 & apply(all_32_5,
% 59.22/8.79 | | | | | | all_70_0, all_57_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.79 | | | | | |
% 59.22/8.79 | | | | | | GROUND_INST: instantiating (8) with all_32_5, all_32_3, all_32_2,
% 59.22/8.79 | | | | | | all_68_0, all_74_3, all_57_0, simplifying with (20),
% 59.22/8.79 | | | | | | (22), (23), (35), (139), (142), (159), (160), (170),
% 59.22/8.79 | | | | | | (173) gives:
% 59.22/8.79 | | | | | | (198) all_74_3 = all_68_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.79 | | | | | | (apply(all_32_5, all_74_3, all_57_0) = v1 & apply(all_32_5,
% 59.22/8.79 | | | | | | all_68_0, all_57_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.79 | | | | | |
% 59.22/8.79 | | | | | | GROUND_INST: instantiating (8) with all_32_5, all_32_3, all_32_2,
% 59.22/8.79 | | | | | | all_74_3, all_68_0, all_57_0, simplifying with (20),
% 59.22/8.79 | | | | | | (22), (23), (35), (139), (142), (159), (160), (170),
% 59.22/8.79 | | | | | | (173) gives:
% 59.22/8.80 | | | | | | (199) all_74_3 = all_68_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.80 | | | | | | (apply(all_32_5, all_74_3, all_57_0) = v0 & apply(all_32_5,
% 59.22/8.80 | | | | | | all_68_0, all_57_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.80 | | | | | |
% 59.22/8.80 | | | | | | GROUND_INST: instantiating (8) with all_32_5, all_32_3, all_32_2,
% 59.22/8.80 | | | | | | all_74_3, all_66_0, all_57_0, simplifying with (20),
% 59.22/8.80 | | | | | | (22), (23), (35), (139), (142), (155), (156), (170),
% 59.22/8.80 | | | | | | (173) gives:
% 59.22/8.80 | | | | | | (200) all_74_3 = all_66_0 | ? [v0: any] : ? [v1: any] :
% 59.22/8.80 | | | | | | (apply(all_32_5, all_74_3, all_57_0) = v0 & apply(all_32_5,
% 59.22/8.80 | | | | | | all_66_0, all_57_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.22/8.80 | | | | | |
% 59.22/8.80 | | | | | | GROUND_INST: instantiating (9) with all_32_6, all_32_4, all_32_3,
% 59.22/8.80 | | | | | | all_57_1, all_57_2, all_70_0, simplifying with (19),
% 59.22/8.80 | | | | | | (21), (22), (32), (137), (138), (141), (163), (165)
% 59.22/8.80 | | | | | | gives:
% 59.22/8.80 | | | | | | (201) all_57_1 = all_57_2 | ? [v0: any] : ? [v1: any] : ? [v2:
% 59.22/8.80 | | | | | | any] : (apply(all_32_6, all_57_1, all_70_0) = v2 &
% 59.22/8.80 | | | | | | member(all_70_0, all_32_3) = v1 & member(all_57_2,
% 59.22/8.80 | | | | | | all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 59.22/8.80 | | | | | | 0)))
% 59.22/8.80 | | | | | |
% 59.22/8.80 | | | | | | GROUND_INST: instantiating (4) with all_32_6, all_32_4, all_32_3,
% 59.22/8.80 | | | | | | all_57_2, all_70_0, all_72_3, simplifying with (19),
% 59.22/8.80 | | | | | | (21), (22), (25), (137), (163), (165), (167), (178)
% 59.22/8.80 | | | | | | gives:
% 59.22/8.80 | | | | | | (202) all_72_3 = all_70_0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 59.22/8.80 | | | | | | any] : (member(all_72_3, all_32_3) = v2 &
% 59.22/8.80 | | | | | | member(all_70_0, all_32_3) = v1 & member(all_57_2,
% 59.22/8.80 | | | | | | all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 59.22/8.80 | | | | | | 0)))
% 59.22/8.80 | | | | | |
% 59.22/8.80 | | | | | | GROUND_INST: instantiating (3) with all_32_6, all_32_4, all_32_3,
% 59.22/8.80 | | | | | | all_57_1, all_74_3, all_68_0, simplifying with (19),
% 59.22/8.80 | | | | | | (21), (22), (25), (138), (159), (161), (170), (173)
% 59.22/8.80 | | | | | | gives:
% 59.22/8.80 | | | | | | (203) all_74_3 = all_68_0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 59.22/8.80 | | | | | | any] : (apply(all_32_6, all_57_1, all_74_3) = v2 &
% 59.22/8.80 | | | | | | member(all_68_0, all_32_3) = v1 & member(all_57_1,
% 59.22/8.80 | | | | | | all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 59.22/8.80 | | | | | | 0)))
% 59.22/8.80 | | | | | |
% 59.22/8.80 | | | | | | GROUND_INST: instantiating (4) with all_32_6, all_32_4, all_32_3,
% 59.22/8.80 | | | | | | all_57_1, all_68_0, all_74_3, simplifying with (19),
% 59.22/8.80 | | | | | | (21), (22), (25), (138), (159), (161), (170), (174)
% 59.22/8.80 | | | | | | gives:
% 59.22/8.80 | | | | | | (204) all_74_3 = all_68_0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 59.22/8.80 | | | | | | any] : (member(all_74_3, all_32_3) = v2 &
% 59.22/8.80 | | | | | | member(all_68_0, all_32_3) = v1 & member(all_57_1,
% 59.22/8.80 | | | | | | all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 59.22/8.80 | | | | | | 0)))
% 59.22/8.80 | | | | | |
% 59.22/8.80 | | | | | | GROUND_INST: instantiating (9) with all_32_6, all_32_4, all_32_3,
% 59.22/8.80 | | | | | | all_57_2, all_57_1, all_74_3, simplifying with (19),
% 59.22/8.80 | | | | | | (21), (22), (32), (137), (138), (140), (170), (174)
% 59.22/8.80 | | | | | | gives:
% 59.22/8.80 | | | | | | (205) all_57_1 = all_57_2 | ? [v0: any] : ? [v1: any] : ? [v2:
% 59.22/8.80 | | | | | | any] : (apply(all_32_6, all_57_2, all_74_3) = v2 &
% 59.22/8.80 | | | | | | member(all_74_3, all_32_3) = v1 & member(all_57_1,
% 59.22/8.80 | | | | | | all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 59.22/8.80 | | | | | | 0)))
% 59.22/8.80 | | | | | |
% 59.22/8.80 | | | | | | GROUND_INST: instantiating (9) with all_32_5, all_32_3, all_32_2,
% 59.22/8.80 | | | | | | all_70_0, all_72_3, all_57_0, simplifying with (20),
% 59.22/8.80 | | | | | | (22), (23), (35), (139), (163), (164), (167), (179)
% 59.22/8.80 | | | | | | gives:
% 59.22/8.80 | | | | | | (206) all_72_3 = all_70_0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 59.22/8.80 | | | | | | any] : (apply(all_32_5, all_70_0, all_57_0) = v2 &
% 59.22/8.80 | | | | | | member(all_72_3, all_32_3) = v0 & member(all_57_0,
% 59.22/8.80 | | | | | | all_32_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 59.22/8.80 | | | | | | 0)))
% 59.22/8.80 | | | | | |
% 59.22/8.80 | | | | | | GROUND_INST: instantiating (10) with all_32_5, all_32_3, all_32_2,
% 59.22/8.80 | | | | | | all_72_3, all_74_3, all_57_0, simplifying with (20),
% 59.22/8.80 | | | | | | (22), (23), (35), (139), (167), (170), (175), (179)
% 59.22/8.80 | | | | | | gives:
% 59.58/8.80 | | | | | | (207) all_74_3 = all_72_3 | ? [v0: any] : ? [v1: any] : ? [v2:
% 59.58/8.80 | | | | | | any] : (member(all_74_3, all_32_3) = v1 &
% 59.58/8.80 | | | | | | member(all_72_3, all_32_3) = v0 & member(all_57_0,
% 59.58/8.80 | | | | | | all_32_2) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 59.58/8.80 | | | | | | 0)))
% 59.58/8.80 | | | | | |
% 59.58/8.80 | | | | | | GROUND_INST: instantiating (9) with all_32_5, all_32_3, all_32_2,
% 59.58/8.80 | | | | | | all_66_0, all_74_3, all_57_0, simplifying with (20),
% 59.58/8.80 | | | | | | (22), (23), (35), (139), (155), (156), (170), (175)
% 59.58/8.80 | | | | | | gives:
% 59.58/8.80 | | | | | | (208) all_74_3 = all_66_0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 59.58/8.80 | | | | | | any] : (apply(all_32_5, all_66_0, all_57_0) = v2 &
% 59.58/8.80 | | | | | | member(all_74_3, all_32_3) = v0 & member(all_57_0,
% 59.58/8.80 | | | | | | all_32_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 59.58/8.80 | | | | | | 0)))
% 59.58/8.80 | | | | | |
% 59.58/8.80 | | | | | | BETA: splitting (202) gives:
% 59.58/8.80 | | | | | |
% 59.58/8.80 | | | | | | Case 1:
% 59.58/8.80 | | | | | | |
% 59.58/8.80 | | | | | | | (209) all_72_3 = all_70_0
% 59.58/8.80 | | | | | | |
% 59.58/8.80 | | | | | | | REDUCE: (179), (209) imply:
% 59.58/8.80 | | | | | | | (210) apply(all_32_5, all_70_0, all_57_0) = 0
% 59.58/8.80 | | | | | | |
% 59.58/8.80 | | | | | | | BETA: splitting (208) gives:
% 59.58/8.80 | | | | | | |
% 59.58/8.80 | | | | | | | Case 1:
% 59.58/8.80 | | | | | | | |
% 59.58/8.80 | | | | | | | | (211) all_74_3 = all_66_0
% 59.58/8.80 | | | | | | | |
% 59.58/8.80 | | | | | | | | REDUCE: (174), (211) imply:
% 59.58/8.80 | | | | | | | | (212) apply(all_32_6, all_57_1, all_66_0) = 0
% 59.58/8.80 | | | | | | | |
% 59.58/8.80 | | | | | | | | BETA: splitting (193) gives:
% 59.58/8.80 | | | | | | | |
% 59.58/8.80 | | | | | | | | Case 1:
% 59.58/8.80 | | | | | | | | |
% 59.58/8.80 | | | | | | | | | (213) all_57_1 = all_57_2
% 59.58/8.80 | | | | | | | | |
% 59.58/8.80 | | | | | | | | | REDUCE: (136), (213) imply:
% 59.58/8.80 | | | | | | | | | (214) $false
% 59.58/8.80 | | | | | | | | |
% 59.58/8.80 | | | | | | | | | CLOSE: (214) is inconsistent.
% 59.58/8.80 | | | | | | | | |
% 59.58/8.80 | | | | | | | | Case 2:
% 59.58/8.80 | | | | | | | | |
% 59.58/8.80 | | | | | | | | | (215) ? [v0: any] : ? [v1: any] : (apply(all_32_6,
% 59.58/8.80 | | | | | | | | | all_57_1, all_72_3) = v0 & apply(all_32_6,
% 59.58/8.80 | | | | | | | | | all_57_2, all_72_3) = v1 & ( ~ (v1 = 0) | ~ (v0
% 59.58/8.80 | | | | | | | | | = 0)))
% 59.58/8.80 | | | | | | | | |
% 59.58/8.80 | | | | | | | | | DELTA: instantiating (215) with fresh symbols all_138_0,
% 59.58/8.80 | | | | | | | | | all_138_1 gives:
% 59.58/8.80 | | | | | | | | | (216) apply(all_32_6, all_57_1, all_72_3) = all_138_1 &
% 59.58/8.80 | | | | | | | | | apply(all_32_6, all_57_2, all_72_3) = all_138_0 & ( ~
% 59.58/8.80 | | | | | | | | | (all_138_0 = 0) | ~ (all_138_1 = 0))
% 59.58/8.80 | | | | | | | | |
% 59.58/8.80 | | | | | | | | | ALPHA: (216) implies:
% 59.58/8.80 | | | | | | | | | (217) apply(all_32_6, all_57_2, all_72_3) = all_138_0
% 59.58/8.80 | | | | | | | | | (218) apply(all_32_6, all_57_1, all_72_3) = all_138_1
% 59.58/8.80 | | | | | | | | | (219) ~ (all_138_0 = 0) | ~ (all_138_1 = 0)
% 59.58/8.80 | | | | | | | | |
% 59.58/8.80 | | | | | | | | | REDUCE: (209), (218) imply:
% 59.58/8.80 | | | | | | | | | (220) apply(all_32_6, all_57_1, all_70_0) = all_138_1
% 59.58/8.80 | | | | | | | | |
% 59.58/8.80 | | | | | | | | | REDUCE: (209), (217) imply:
% 59.58/8.80 | | | | | | | | | (221) apply(all_32_6, all_57_2, all_70_0) = all_138_0
% 59.58/8.80 | | | | | | | | |
% 59.58/8.80 | | | | | | | | | BETA: splitting (201) gives:
% 59.58/8.80 | | | | | | | | |
% 59.58/8.80 | | | | | | | | | Case 1:
% 59.58/8.80 | | | | | | | | | |
% 59.58/8.80 | | | | | | | | | | (222) all_57_1 = all_57_2
% 59.58/8.80 | | | | | | | | | |
% 59.58/8.80 | | | | | | | | | | REDUCE: (136), (222) imply:
% 59.58/8.80 | | | | | | | | | | (223) $false
% 59.58/8.80 | | | | | | | | | |
% 59.58/8.80 | | | | | | | | | | CLOSE: (223) is inconsistent.
% 59.58/8.80 | | | | | | | | | |
% 59.58/8.80 | | | | | | | | | Case 2:
% 59.58/8.80 | | | | | | | | | |
% 59.58/8.80 | | | | | | | | | | (224) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 59.58/8.80 | | | | | | | | | | (apply(all_32_6, all_57_1, all_70_0) = v2 &
% 59.58/8.80 | | | | | | | | | | member(all_70_0, all_32_3) = v1 &
% 59.58/8.80 | | | | | | | | | | member(all_57_2, all_32_4) = v0 & ( ~ (v2 = 0) |
% 59.58/8.80 | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 59.58/8.80 | | | | | | | | | |
% 59.58/8.80 | | | | | | | | | | DELTA: instantiating (224) with fresh symbols all_144_0,
% 59.58/8.80 | | | | | | | | | | all_144_1, all_144_2 gives:
% 59.58/8.80 | | | | | | | | | | (225) apply(all_32_6, all_57_1, all_70_0) = all_144_0 &
% 59.58/8.80 | | | | | | | | | | member(all_70_0, all_32_3) = all_144_1 &
% 59.58/8.80 | | | | | | | | | | member(all_57_2, all_32_4) = all_144_2 & ( ~
% 59.58/8.80 | | | | | | | | | | (all_144_0 = 0) | ~ (all_144_1 = 0) | ~
% 59.58/8.80 | | | | | | | | | | (all_144_2 = 0))
% 59.58/8.80 | | | | | | | | | |
% 59.58/8.80 | | | | | | | | | | ALPHA: (225) implies:
% 59.58/8.80 | | | | | | | | | | (226) apply(all_32_6, all_57_1, all_70_0) = all_144_0
% 59.58/8.80 | | | | | | | | | |
% 59.58/8.80 | | | | | | | | | | BETA: splitting (192) gives:
% 59.58/8.80 | | | | | | | | | |
% 59.58/8.80 | | | | | | | | | | Case 1:
% 59.58/8.80 | | | | | | | | | | |
% 59.58/8.80 | | | | | | | | | | | (227) all_72_3 = all_66_0
% 59.58/8.80 | | | | | | | | | | |
% 59.58/8.80 | | | | | | | | | | | COMBINE_EQS: (209), (227) imply:
% 59.58/8.80 | | | | | | | | | | | (228) all_70_0 = all_66_0
% 59.58/8.80 | | | | | | | | | | |
% 59.58/8.80 | | | | | | | | | | | SIMP: (228) implies:
% 59.58/8.81 | | | | | | | | | | | (229) all_70_0 = all_66_0
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | REDUCE: (226), (229) imply:
% 59.58/8.81 | | | | | | | | | | | (230) apply(all_32_6, all_57_1, all_66_0) = all_144_0
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | REDUCE: (220), (229) imply:
% 59.58/8.81 | | | | | | | | | | | (231) apply(all_32_6, all_57_1, all_66_0) = all_138_1
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | REDUCE: (221), (229) imply:
% 59.58/8.81 | | | | | | | | | | | (232) apply(all_32_6, all_57_2, all_66_0) = all_138_0
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | REDUCE: (165), (229) imply:
% 59.58/8.81 | | | | | | | | | | | (233) apply(all_32_6, all_57_2, all_66_0) = 0
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_138_0, all_66_0,
% 59.58/8.81 | | | | | | | | | | | all_57_2, all_32_6, simplifying with (232), (233)
% 59.58/8.81 | | | | | | | | | | | gives:
% 59.58/8.81 | | | | | | | | | | | (234) all_138_0 = 0
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | GROUND_INST: instantiating (16) with all_138_1, all_144_0,
% 59.58/8.81 | | | | | | | | | | | all_66_0, all_57_1, all_32_6, simplifying with
% 59.58/8.81 | | | | | | | | | | | (230), (231) gives:
% 59.58/8.81 | | | | | | | | | | | (235) all_144_0 = all_138_1
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_144_0, all_66_0,
% 59.58/8.81 | | | | | | | | | | | all_57_1, all_32_6, simplifying with (212), (230)
% 59.58/8.81 | | | | | | | | | | | gives:
% 59.58/8.81 | | | | | | | | | | | (236) all_144_0 = 0
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | COMBINE_EQS: (235), (236) imply:
% 59.58/8.81 | | | | | | | | | | | (237) all_138_1 = 0
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | SIMP: (237) implies:
% 59.58/8.81 | | | | | | | | | | | (238) all_138_1 = 0
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | BETA: splitting (219) gives:
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | Case 1:
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | (239) ~ (all_138_0 = 0)
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | REDUCE: (234), (239) imply:
% 59.58/8.81 | | | | | | | | | | | | (240) $false
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | CLOSE: (240) is inconsistent.
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | Case 2:
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | (241) ~ (all_138_1 = 0)
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | REDUCE: (238), (241) imply:
% 59.58/8.81 | | | | | | | | | | | | (242) $false
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | CLOSE: (242) is inconsistent.
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | End of split
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | Case 2:
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | (243) ~ (all_72_3 = all_66_0)
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | REDUCE: (209), (243) imply:
% 59.58/8.81 | | | | | | | | | | | (244) ~ (all_70_0 = all_66_0)
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | REF_CLOSE: (16), (157), (185), (191), (209), (210), (244) are
% 59.58/8.81 | | | | | | | | | | | inconsistent by sub-proof #3.
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | End of split
% 59.58/8.81 | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | End of split
% 59.58/8.81 | | | | | | | | |
% 59.58/8.81 | | | | | | | | End of split
% 59.58/8.81 | | | | | | | |
% 59.58/8.81 | | | | | | | Case 2:
% 59.58/8.81 | | | | | | | |
% 59.58/8.81 | | | | | | | | (245) ~ (all_74_3 = all_66_0)
% 59.58/8.81 | | | | | | | |
% 59.58/8.81 | | | | | | | | BETA: splitting (197) gives:
% 59.58/8.81 | | | | | | | |
% 59.58/8.81 | | | | | | | | Case 1:
% 59.58/8.81 | | | | | | | | |
% 59.58/8.81 | | | | | | | | | (246) all_74_3 = all_70_0
% 59.58/8.81 | | | | | | | | |
% 59.58/8.81 | | | | | | | | | REDUCE: (245), (246) imply:
% 59.58/8.81 | | | | | | | | | (247) ~ (all_70_0 = all_66_0)
% 59.58/8.81 | | | | | | | | |
% 59.58/8.81 | | | | | | | | | REF_CLOSE: (16), (157), (185), (191), (209), (210), (247) are
% 59.58/8.81 | | | | | | | | | inconsistent by sub-proof #3.
% 59.58/8.81 | | | | | | | | |
% 59.58/8.81 | | | | | | | | Case 2:
% 59.58/8.81 | | | | | | | | |
% 59.58/8.81 | | | | | | | | | (248) ~ (all_74_3 = all_70_0)
% 59.58/8.81 | | | | | | | | | (249) ? [v0: any] : ? [v1: any] : (apply(all_32_5,
% 59.58/8.81 | | | | | | | | | all_74_3, all_57_0) = v0 & apply(all_32_5,
% 59.58/8.81 | | | | | | | | | all_70_0, all_57_0) = v1 & ( ~ (v1 = 0) | ~ (v0
% 59.58/8.81 | | | | | | | | | = 0)))
% 59.58/8.81 | | | | | | | | |
% 59.58/8.81 | | | | | | | | | DELTA: instantiating (249) with fresh symbols all_137_0,
% 59.58/8.81 | | | | | | | | | all_137_1 gives:
% 59.58/8.81 | | | | | | | | | (250) apply(all_32_5, all_74_3, all_57_0) = all_137_1 &
% 59.58/8.81 | | | | | | | | | apply(all_32_5, all_70_0, all_57_0) = all_137_0 & ( ~
% 59.58/8.81 | | | | | | | | | (all_137_0 = 0) | ~ (all_137_1 = 0))
% 59.58/8.81 | | | | | | | | |
% 59.58/8.81 | | | | | | | | | ALPHA: (250) implies:
% 59.58/8.81 | | | | | | | | | (251) apply(all_32_5, all_70_0, all_57_0) = all_137_0
% 59.58/8.81 | | | | | | | | | (252) apply(all_32_5, all_74_3, all_57_0) = all_137_1
% 59.58/8.81 | | | | | | | | | (253) ~ (all_137_0 = 0) | ~ (all_137_1 = 0)
% 59.58/8.81 | | | | | | | | |
% 59.58/8.81 | | | | | | | | | BETA: splitting (203) gives:
% 59.58/8.81 | | | | | | | | |
% 59.58/8.81 | | | | | | | | | Case 1:
% 59.58/8.81 | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | (254) all_74_3 = all_68_0
% 59.58/8.81 | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | REDUCE: (248), (254) imply:
% 59.58/8.81 | | | | | | | | | | (255) ~ (all_70_0 = all_68_0)
% 59.58/8.81 | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | SIMP: (255) implies:
% 59.58/8.81 | | | | | | | | | | (256) ~ (all_70_0 = all_68_0)
% 59.58/8.81 | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | REDUCE: (252), (254) imply:
% 59.58/8.81 | | | | | | | | | | (257) apply(all_32_5, all_68_0, all_57_0) = all_137_1
% 59.58/8.81 | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | REDUCE: (175), (254) imply:
% 59.58/8.81 | | | | | | | | | | (258) apply(all_32_5, all_68_0, all_57_0) = 0
% 59.58/8.81 | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | BETA: splitting (189) gives:
% 59.58/8.81 | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | Case 1:
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | (259) all_72_3 = all_68_0
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | COMBINE_EQS: (209), (259) imply:
% 59.58/8.81 | | | | | | | | | | | (260) all_70_0 = all_68_0
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | SIMP: (260) implies:
% 59.58/8.81 | | | | | | | | | | | (261) all_70_0 = all_68_0
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | REDUCE: (256), (261) imply:
% 59.58/8.81 | | | | | | | | | | | (262) $false
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | CLOSE: (262) is inconsistent.
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | Case 2:
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_137_1, all_57_0,
% 59.58/8.81 | | | | | | | | | | | all_68_0, all_32_5, simplifying with (257), (258)
% 59.58/8.81 | | | | | | | | | | | gives:
% 59.58/8.81 | | | | | | | | | | | (263) all_137_1 = 0
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_137_0, all_57_0,
% 59.58/8.81 | | | | | | | | | | | all_70_0, all_32_5, simplifying with (210), (251)
% 59.58/8.81 | | | | | | | | | | | gives:
% 59.58/8.81 | | | | | | | | | | | (264) all_137_0 = 0
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | REF_CLOSE: (253), (263), (264) are inconsistent by sub-proof
% 59.58/8.81 | | | | | | | | | | | #2.
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | End of split
% 59.58/8.81 | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | Case 2:
% 59.58/8.81 | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | (265) ~ (all_74_3 = all_68_0)
% 59.58/8.81 | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | BETA: splitting (199) gives:
% 59.58/8.81 | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | Case 1:
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | (266) all_74_3 = all_68_0
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | REDUCE: (265), (266) imply:
% 59.58/8.81 | | | | | | | | | | | (267) $false
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | CLOSE: (267) is inconsistent.
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | Case 2:
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | (268) ? [v0: any] : ? [v1: any] : (apply(all_32_5,
% 59.58/8.81 | | | | | | | | | | | all_74_3, all_57_0) = v0 & apply(all_32_5,
% 59.58/8.81 | | | | | | | | | | | all_68_0, all_57_0) = v1 & ( ~ (v1 = 0) | ~
% 59.58/8.81 | | | | | | | | | | | (v0 = 0)))
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | DELTA: instantiating (268) with fresh symbols all_190_0,
% 59.58/8.81 | | | | | | | | | | | all_190_1 gives:
% 59.58/8.81 | | | | | | | | | | | (269) apply(all_32_5, all_74_3, all_57_0) = all_190_1 &
% 59.58/8.81 | | | | | | | | | | | apply(all_32_5, all_68_0, all_57_0) = all_190_0 &
% 59.58/8.81 | | | | | | | | | | | ( ~ (all_190_0 = 0) | ~ (all_190_1 = 0))
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | ALPHA: (269) implies:
% 59.58/8.81 | | | | | | | | | | | (270) apply(all_32_5, all_74_3, all_57_0) = all_190_1
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | BETA: splitting (198) gives:
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | Case 1:
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | (271) all_74_3 = all_68_0
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | REDUCE: (265), (271) imply:
% 59.58/8.81 | | | | | | | | | | | | (272) $false
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | CLOSE: (272) is inconsistent.
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | Case 2:
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | (273) ? [v0: any] : ? [v1: any] : (apply(all_32_5,
% 59.58/8.81 | | | | | | | | | | | | all_74_3, all_57_0) = v1 & apply(all_32_5,
% 59.58/8.81 | | | | | | | | | | | | all_68_0, all_57_0) = v0 & ( ~ (v1 = 0) | ~
% 59.58/8.81 | | | | | | | | | | | | (v0 = 0)))
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | DELTA: instantiating (273) with fresh symbols all_195_0,
% 59.58/8.81 | | | | | | | | | | | | all_195_1 gives:
% 59.58/8.81 | | | | | | | | | | | | (274) apply(all_32_5, all_74_3, all_57_0) = all_195_0 &
% 59.58/8.81 | | | | | | | | | | | | apply(all_32_5, all_68_0, all_57_0) = all_195_1 &
% 59.58/8.81 | | | | | | | | | | | | ( ~ (all_195_0 = 0) | ~ (all_195_1 = 0))
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | ALPHA: (274) implies:
% 59.58/8.81 | | | | | | | | | | | | (275) apply(all_32_5, all_74_3, all_57_0) = all_195_0
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | BETA: splitting (194) gives:
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | Case 1:
% 59.58/8.81 | | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | | (276) all_74_3 = all_68_0
% 59.58/8.81 | | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | | REDUCE: (265), (276) imply:
% 59.58/8.81 | | | | | | | | | | | | | (277) $false
% 59.58/8.81 | | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | | CLOSE: (277) is inconsistent.
% 59.58/8.81 | | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | Case 2:
% 59.58/8.81 | | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_137_0, all_57_0,
% 59.58/8.81 | | | | | | | | | | | | | all_70_0, all_32_5, simplifying with (210), (251)
% 59.58/8.81 | | | | | | | | | | | | | gives:
% 59.58/8.81 | | | | | | | | | | | | | (278) all_137_0 = 0
% 59.58/8.81 | | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_190_1, all_57_0,
% 59.58/8.81 | | | | | | | | | | | | | all_74_3, all_32_5, simplifying with (175), (270)
% 59.58/8.81 | | | | | | | | | | | | | gives:
% 59.58/8.81 | | | | | | | | | | | | | (279) all_190_1 = 0
% 59.58/8.81 | | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_190_1, all_195_0,
% 59.58/8.81 | | | | | | | | | | | | | all_57_0, all_74_3, all_32_5, simplifying with
% 59.58/8.81 | | | | | | | | | | | | | (270), (275) gives:
% 59.58/8.81 | | | | | | | | | | | | | (280) all_195_0 = all_190_1
% 59.58/8.81 | | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_137_1, all_195_0,
% 59.58/8.81 | | | | | | | | | | | | | all_57_0, all_74_3, all_32_5, simplifying with
% 59.58/8.81 | | | | | | | | | | | | | (252), (275) gives:
% 59.58/8.81 | | | | | | | | | | | | | (281) all_195_0 = all_137_1
% 59.58/8.81 | | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | | COMBINE_EQS: (280), (281) imply:
% 59.58/8.81 | | | | | | | | | | | | | (282) all_190_1 = all_137_1
% 59.58/8.81 | | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | | SIMP: (282) implies:
% 59.58/8.81 | | | | | | | | | | | | | (283) all_190_1 = all_137_1
% 59.58/8.81 | | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | | COMBINE_EQS: (279), (283) imply:
% 59.58/8.81 | | | | | | | | | | | | | (284) all_137_1 = 0
% 59.58/8.81 | | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | | SIMP: (284) implies:
% 59.58/8.81 | | | | | | | | | | | | | (285) all_137_1 = 0
% 59.58/8.81 | | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | | REF_CLOSE: (253), (278), (285) are inconsistent by sub-proof
% 59.58/8.81 | | | | | | | | | | | | | #2.
% 59.58/8.81 | | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | | End of split
% 59.58/8.81 | | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | | End of split
% 59.58/8.81 | | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | | End of split
% 59.58/8.81 | | | | | | | | | |
% 59.58/8.81 | | | | | | | | | End of split
% 59.58/8.81 | | | | | | | | |
% 59.58/8.81 | | | | | | | | End of split
% 59.58/8.81 | | | | | | | |
% 59.58/8.81 | | | | | | | End of split
% 59.58/8.81 | | | | | | |
% 59.58/8.81 | | | | | | Case 2:
% 59.58/8.81 | | | | | | |
% 59.58/8.81 | | | | | | | (286) ~ (all_72_3 = all_70_0)
% 59.58/8.81 | | | | | | |
% 59.58/8.81 | | | | | | | BETA: splitting (196) gives:
% 59.58/8.81 | | | | | | |
% 59.58/8.81 | | | | | | | Case 1:
% 59.58/8.81 | | | | | | | |
% 59.58/8.81 | | | | | | | | (287) all_74_3 = all_72_3
% 59.58/8.81 | | | | | | | |
% 59.58/8.81 | | | | | | | | REDUCE: (174), (287) imply:
% 59.58/8.81 | | | | | | | | (288) apply(all_32_6, all_57_1, all_72_3) = 0
% 59.58/8.81 | | | | | | | |
% 59.58/8.81 | | | | | | | | BETA: splitting (188) gives:
% 59.58/8.81 | | | | | | | |
% 59.58/8.81 | | | | | | | | Case 1:
% 59.58/8.81 | | | | | | | | |
% 59.58/8.82 | | | | | | | | | (289) all_72_3 = all_68_0
% 59.58/8.82 | | | | | | | | |
% 59.58/8.82 | | | | | | | | | COMBINE_EQS: (287), (289) imply:
% 59.58/8.82 | | | | | | | | | (290) all_74_3 = all_68_0
% 59.58/8.82 | | | | | | | | |
% 59.58/8.82 | | | | | | | | | REDUCE: (286), (289) imply:
% 59.58/8.82 | | | | | | | | | (291) ~ (all_70_0 = all_68_0)
% 59.58/8.82 | | | | | | | | |
% 59.58/8.82 | | | | | | | | | SIMP: (291) implies:
% 59.58/8.82 | | | | | | | | | (292) ~ (all_70_0 = all_68_0)
% 59.58/8.82 | | | | | | | | |
% 59.58/8.82 | | | | | | | | | REDUCE: (178), (289) imply:
% 59.58/8.82 | | | | | | | | | (293) apply(all_32_6, all_57_2, all_68_0) = 0
% 59.58/8.82 | | | | | | | | |
% 59.58/8.82 | | | | | | | | | BETA: splitting (186) gives:
% 59.58/8.82 | | | | | | | | |
% 59.58/8.82 | | | | | | | | | Case 1:
% 59.58/8.82 | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | (294) all_72_3 = all_70_0
% 59.58/8.82 | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | COMBINE_EQS: (289), (294) imply:
% 59.58/8.82 | | | | | | | | | | (295) all_70_0 = all_68_0
% 59.58/8.82 | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | REDUCE: (292), (295) imply:
% 59.58/8.82 | | | | | | | | | | (296) $false
% 59.58/8.82 | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | CLOSE: (296) is inconsistent.
% 59.58/8.82 | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | Case 2:
% 59.58/8.82 | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | (297) ? [v0: any] : ? [v1: any] : (apply(all_32_6,
% 59.58/8.82 | | | | | | | | | | all_57_2, all_72_3) = v0 & apply(all_32_6,
% 59.58/8.82 | | | | | | | | | | all_57_2, all_70_0) = v1 & ( ~ (v1 = 0) | ~
% 59.58/8.82 | | | | | | | | | | (v0 = 0)))
% 59.58/8.82 | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | DELTA: instantiating (297) with fresh symbols all_146_0,
% 59.58/8.82 | | | | | | | | | | all_146_1 gives:
% 59.58/8.82 | | | | | | | | | | (298) apply(all_32_6, all_57_2, all_72_3) = all_146_1 &
% 59.58/8.82 | | | | | | | | | | apply(all_32_6, all_57_2, all_70_0) = all_146_0 & (
% 59.58/8.82 | | | | | | | | | | ~ (all_146_0 = 0) | ~ (all_146_1 = 0))
% 59.58/8.82 | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | ALPHA: (298) implies:
% 59.58/8.82 | | | | | | | | | | (299) apply(all_32_6, all_57_2, all_70_0) = all_146_0
% 59.58/8.82 | | | | | | | | | | (300) apply(all_32_6, all_57_2, all_72_3) = all_146_1
% 59.58/8.82 | | | | | | | | | | (301) ~ (all_146_0 = 0) | ~ (all_146_1 = 0)
% 59.58/8.82 | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | REDUCE: (289), (300) imply:
% 59.58/8.82 | | | | | | | | | | (302) apply(all_32_6, all_57_2, all_68_0) = all_146_1
% 59.58/8.82 | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | BETA: splitting (200) gives:
% 59.58/8.82 | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | Case 1:
% 59.58/8.82 | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | (303) all_74_3 = all_66_0
% 59.58/8.82 | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | COMBINE_EQS: (290), (303) imply:
% 59.58/8.82 | | | | | | | | | | | (304) all_68_0 = all_66_0
% 59.58/8.82 | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | REDUCE: (292), (304) imply:
% 59.58/8.82 | | | | | | | | | | | (305) ~ (all_70_0 = all_66_0)
% 59.58/8.82 | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | REDUCE: (293), (304) imply:
% 59.58/8.82 | | | | | | | | | | | (306) apply(all_32_6, all_57_2, all_66_0) = 0
% 59.58/8.82 | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | BETA: splitting (184) gives:
% 59.58/8.82 | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | Case 1:
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | (307) all_70_0 = all_68_0
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | COMBINE_EQS: (304), (307) imply:
% 59.58/8.82 | | | | | | | | | | | | (308) all_70_0 = all_66_0
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | REDUCE: (305), (308) imply:
% 59.58/8.82 | | | | | | | | | | | | (309) $false
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | CLOSE: (309) is inconsistent.
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | Case 2:
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | (310) ? [v0: any] : ? [v1: any] : (apply(all_32_6,
% 59.58/8.82 | | | | | | | | | | | | all_57_2, all_70_0) = v0 & apply(all_32_6,
% 59.58/8.82 | | | | | | | | | | | | all_57_2, all_68_0) = v1 & ( ~ (v1 = 0) | ~
% 59.58/8.82 | | | | | | | | | | | | (v0 = 0)))
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | DELTA: instantiating (310) with fresh symbols all_202_0,
% 59.58/8.82 | | | | | | | | | | | | all_202_1 gives:
% 59.58/8.82 | | | | | | | | | | | | (311) apply(all_32_6, all_57_2, all_70_0) = all_202_1 &
% 59.58/8.82 | | | | | | | | | | | | apply(all_32_6, all_57_2, all_68_0) = all_202_0 &
% 59.58/8.82 | | | | | | | | | | | | ( ~ (all_202_0 = 0) | ~ (all_202_1 = 0))
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | ALPHA: (311) implies:
% 59.58/8.82 | | | | | | | | | | | | (312) apply(all_32_6, all_57_2, all_70_0) = all_202_1
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | BETA: splitting (183) gives:
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | Case 1:
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | (313) all_70_0 = all_68_0
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | COMBINE_EQS: (304), (313) imply:
% 59.58/8.82 | | | | | | | | | | | | | (314) all_70_0 = all_66_0
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | REDUCE: (305), (314) imply:
% 59.58/8.82 | | | | | | | | | | | | | (315) $false
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | CLOSE: (315) is inconsistent.
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | Case 2:
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | (316) ? [v0: any] : ? [v1: any] : (apply(all_32_6,
% 59.58/8.82 | | | | | | | | | | | | | all_57_2, all_70_0) = v1 & apply(all_32_6,
% 59.58/8.82 | | | | | | | | | | | | | all_57_2, all_68_0) = v0 & ( ~ (v1 = 0) | ~
% 59.58/8.82 | | | | | | | | | | | | | (v0 = 0)))
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | DELTA: instantiating (316) with fresh symbols all_208_0,
% 59.58/8.82 | | | | | | | | | | | | | all_208_1 gives:
% 59.58/8.82 | | | | | | | | | | | | | (317) apply(all_32_6, all_57_2, all_70_0) = all_208_0 &
% 59.58/8.82 | | | | | | | | | | | | | apply(all_32_6, all_57_2, all_68_0) = all_208_1 &
% 59.58/8.82 | | | | | | | | | | | | | ( ~ (all_208_0 = 0) | ~ (all_208_1 = 0))
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | ALPHA: (317) implies:
% 59.58/8.82 | | | | | | | | | | | | | (318) apply(all_32_6, all_57_2, all_68_0) = all_208_1
% 59.58/8.82 | | | | | | | | | | | | | (319) apply(all_32_6, all_57_2, all_70_0) = all_208_0
% 59.58/8.82 | | | | | | | | | | | | | (320) ~ (all_208_0 = 0) | ~ (all_208_1 = 0)
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | REDUCE: (304), (318) imply:
% 59.58/8.82 | | | | | | | | | | | | | (321) apply(all_32_6, all_57_2, all_66_0) = all_208_1
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | BETA: splitting (182) gives:
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | Case 1:
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | (322) all_70_0 = all_68_0
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | COMBINE_EQS: (304), (322) imply:
% 59.58/8.82 | | | | | | | | | | | | | | (323) all_70_0 = all_66_0
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | REDUCE: (305), (323) imply:
% 59.58/8.82 | | | | | | | | | | | | | | (324) $false
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | CLOSE: (324) is inconsistent.
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | Case 2:
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_208_1, all_66_0,
% 59.58/8.82 | | | | | | | | | | | | | | all_57_2, all_32_6, simplifying with (306), (321)
% 59.58/8.82 | | | | | | | | | | | | | | gives:
% 59.58/8.82 | | | | | | | | | | | | | | (325) all_208_1 = 0
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_202_1, all_70_0,
% 59.58/8.82 | | | | | | | | | | | | | | all_57_2, all_32_6, simplifying with (165), (312)
% 59.58/8.82 | | | | | | | | | | | | | | gives:
% 59.58/8.82 | | | | | | | | | | | | | | (326) all_202_1 = 0
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_202_1, all_208_0,
% 59.58/8.82 | | | | | | | | | | | | | | all_70_0, all_57_2, all_32_6, simplifying with
% 59.58/8.82 | | | | | | | | | | | | | | (312), (319) gives:
% 59.58/8.82 | | | | | | | | | | | | | | (327) all_208_0 = all_202_1
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_146_0, all_208_0,
% 59.58/8.82 | | | | | | | | | | | | | | all_70_0, all_57_2, all_32_6, simplifying with
% 59.58/8.82 | | | | | | | | | | | | | | (299), (319) gives:
% 59.58/8.82 | | | | | | | | | | | | | | (328) all_208_0 = all_146_0
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | COMBINE_EQS: (327), (328) imply:
% 59.58/8.82 | | | | | | | | | | | | | | (329) all_202_1 = all_146_0
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | SIMP: (329) implies:
% 59.58/8.82 | | | | | | | | | | | | | | (330) all_202_1 = all_146_0
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | COMBINE_EQS: (326), (330) imply:
% 59.58/8.82 | | | | | | | | | | | | | | (331) all_146_0 = 0
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | COMBINE_EQS: (328), (331) imply:
% 59.58/8.82 | | | | | | | | | | | | | | (332) all_208_0 = 0
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | BETA: splitting (320) gives:
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | Case 1:
% 59.58/8.82 | | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | | (333) ~ (all_208_0 = 0)
% 59.58/8.82 | | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | | REDUCE: (332), (333) imply:
% 59.58/8.82 | | | | | | | | | | | | | | | (334) $false
% 59.58/8.82 | | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | | CLOSE: (334) is inconsistent.
% 59.58/8.82 | | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | Case 2:
% 59.58/8.82 | | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | | (335) ~ (all_208_1 = 0)
% 59.58/8.82 | | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | | REDUCE: (325), (335) imply:
% 59.58/8.82 | | | | | | | | | | | | | | | (336) $false
% 59.58/8.82 | | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | | CLOSE: (336) is inconsistent.
% 59.58/8.82 | | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | End of split
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | End of split
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | End of split
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | End of split
% 59.58/8.82 | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | Case 2:
% 59.58/8.82 | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | (337) ~ (all_74_3 = all_66_0)
% 59.58/8.82 | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | REDUCE: (290), (337) imply:
% 59.58/8.82 | | | | | | | | | | | (338) ~ (all_68_0 = all_66_0)
% 59.58/8.82 | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | BETA: splitting (190) gives:
% 59.58/8.82 | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | Case 1:
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | (339) all_72_3 = all_66_0
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | COMBINE_EQS: (289), (339) imply:
% 59.58/8.82 | | | | | | | | | | | | (340) all_68_0 = all_66_0
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | SIMP: (340) implies:
% 59.58/8.82 | | | | | | | | | | | | (341) all_68_0 = all_66_0
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | REDUCE: (338), (341) imply:
% 59.58/8.82 | | | | | | | | | | | | (342) $false
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | CLOSE: (342) is inconsistent.
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | Case 2:
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | (343) ~ (all_72_3 = all_66_0)
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | BETA: splitting (184) gives:
% 59.58/8.82 | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | Case 1:
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | (344) all_70_0 = all_68_0
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | REDUCE: (292), (344) imply:
% 59.58/8.82 | | | | | | | | | | | | | (345) $false
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | CLOSE: (345) is inconsistent.
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | Case 2:
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | (346) ? [v0: any] : ? [v1: any] : (apply(all_32_6,
% 59.58/8.82 | | | | | | | | | | | | | all_57_2, all_70_0) = v0 & apply(all_32_6,
% 59.58/8.82 | | | | | | | | | | | | | all_57_2, all_68_0) = v1 & ( ~ (v1 = 0) | ~
% 59.58/8.82 | | | | | | | | | | | | | (v0 = 0)))
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | DELTA: instantiating (346) with fresh symbols all_207_0,
% 59.58/8.82 | | | | | | | | | | | | | all_207_1 gives:
% 59.58/8.82 | | | | | | | | | | | | | (347) apply(all_32_6, all_57_2, all_70_0) = all_207_1 &
% 59.58/8.82 | | | | | | | | | | | | | apply(all_32_6, all_57_2, all_68_0) = all_207_0 &
% 59.58/8.82 | | | | | | | | | | | | | ( ~ (all_207_0 = 0) | ~ (all_207_1 = 0))
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | ALPHA: (347) implies:
% 59.58/8.82 | | | | | | | | | | | | | (348) apply(all_32_6, all_57_2, all_68_0) = all_207_0
% 59.58/8.82 | | | | | | | | | | | | | (349) apply(all_32_6, all_57_2, all_70_0) = all_207_1
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | BETA: splitting (183) gives:
% 59.58/8.82 | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | Case 1:
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | (350) all_70_0 = all_68_0
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | REDUCE: (292), (350) imply:
% 59.58/8.82 | | | | | | | | | | | | | | (351) $false
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | CLOSE: (351) is inconsistent.
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | Case 2:
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | (352) ? [v0: any] : ? [v1: any] : (apply(all_32_6,
% 59.58/8.82 | | | | | | | | | | | | | | all_57_2, all_70_0) = v1 & apply(all_32_6,
% 59.58/8.82 | | | | | | | | | | | | | | all_57_2, all_68_0) = v0 & ( ~ (v1 = 0) | ~
% 59.58/8.82 | | | | | | | | | | | | | | (v0 = 0)))
% 59.58/8.82 | | | | | | | | | | | | | |
% 59.58/8.82 | | | | | | | | | | | | | | DELTA: instantiating (352) with fresh symbols all_245_0,
% 59.58/8.82 | | | | | | | | | | | | | | all_245_1 gives:
% 59.58/8.82 | | | | | | | | | | | | | | (353) apply(all_32_6, all_57_2, all_70_0) = all_245_0 &
% 59.58/8.82 | | | | | | | | | | | | | | apply(all_32_6, all_57_2, all_68_0) = all_245_1 &
% 59.58/8.82 | | | | | | | | | | | | | | ( ~ (all_245_0 = 0) | ~ (all_245_1 = 0))
% 59.58/8.83 | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | ALPHA: (353) implies:
% 59.58/8.83 | | | | | | | | | | | | | | (354) apply(all_32_6, all_57_2, all_68_0) = all_245_1
% 59.58/8.83 | | | | | | | | | | | | | | (355) apply(all_32_6, all_57_2, all_70_0) = all_245_0
% 59.58/8.83 | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 59.58/8.83 | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | Case 1:
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | (356) all_74_3 = all_66_0
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | REF_CLOSE: (15), (136), (142), (156), (177), (187), (205),
% 59.58/8.83 | | | | | | | | | | | | | | | (206), (207), (286), (343), (356) are inconsistent
% 59.58/8.83 | | | | | | | | | | | | | | | by sub-proof #1.
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | Case 2:
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_146_1, all_207_0,
% 59.58/8.83 | | | | | | | | | | | | | | | all_68_0, all_57_2, all_32_6, simplifying with
% 59.58/8.83 | | | | | | | | | | | | | | | (302), (348) gives:
% 59.58/8.83 | | | | | | | | | | | | | | | (357) all_207_0 = all_146_1
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_207_0, all_245_1,
% 59.58/8.83 | | | | | | | | | | | | | | | all_68_0, all_57_2, all_32_6, simplifying with
% 59.58/8.83 | | | | | | | | | | | | | | | (348), (354) gives:
% 59.58/8.83 | | | | | | | | | | | | | | | (358) all_245_1 = all_207_0
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_245_1, all_68_0,
% 59.58/8.83 | | | | | | | | | | | | | | | all_57_2, all_32_6, simplifying with (293), (354)
% 59.58/8.83 | | | | | | | | | | | | | | | gives:
% 59.58/8.83 | | | | | | | | | | | | | | | (359) all_245_1 = 0
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_146_0, all_207_1,
% 59.58/8.83 | | | | | | | | | | | | | | | all_70_0, all_57_2, all_32_6, simplifying with
% 59.58/8.83 | | | | | | | | | | | | | | | (299), (349) gives:
% 59.58/8.83 | | | | | | | | | | | | | | | (360) all_207_1 = all_146_0
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_245_0, all_70_0,
% 59.58/8.83 | | | | | | | | | | | | | | | all_57_2, all_32_6, simplifying with (165), (355)
% 59.58/8.83 | | | | | | | | | | | | | | | gives:
% 59.58/8.83 | | | | | | | | | | | | | | | (361) all_245_0 = 0
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_207_1, all_245_0,
% 59.58/8.83 | | | | | | | | | | | | | | | all_70_0, all_57_2, all_32_6, simplifying with
% 59.58/8.83 | | | | | | | | | | | | | | | (349), (355) gives:
% 59.58/8.83 | | | | | | | | | | | | | | | (362) all_245_0 = all_207_1
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | COMBINE_EQS: (361), (362) imply:
% 59.58/8.83 | | | | | | | | | | | | | | | (363) all_207_1 = 0
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | SIMP: (363) implies:
% 59.58/8.83 | | | | | | | | | | | | | | | (364) all_207_1 = 0
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | COMBINE_EQS: (358), (359) imply:
% 59.58/8.83 | | | | | | | | | | | | | | | (365) all_207_0 = 0
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | SIMP: (365) implies:
% 59.58/8.83 | | | | | | | | | | | | | | | (366) all_207_0 = 0
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | COMBINE_EQS: (357), (366) imply:
% 59.58/8.83 | | | | | | | | | | | | | | | (367) all_146_1 = 0
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | SIMP: (367) implies:
% 59.58/8.83 | | | | | | | | | | | | | | | (368) all_146_1 = 0
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | COMBINE_EQS: (360), (364) imply:
% 59.58/8.83 | | | | | | | | | | | | | | | (369) all_146_0 = 0
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | SIMP: (369) implies:
% 59.58/8.83 | | | | | | | | | | | | | | | (370) all_146_0 = 0
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | Case 1:
% 59.58/8.83 | | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | | (371) ~ (all_146_0 = 0)
% 59.58/8.83 | | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | | REDUCE: (370), (371) imply:
% 59.58/8.83 | | | | | | | | | | | | | | | | (372) $false
% 59.58/8.83 | | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | | CLOSE: (372) is inconsistent.
% 59.58/8.83 | | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | Case 2:
% 59.58/8.83 | | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | | (373) ~ (all_146_1 = 0)
% 59.58/8.83 | | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | | REDUCE: (368), (373) imply:
% 59.58/8.83 | | | | | | | | | | | | | | | | (374) $false
% 59.58/8.83 | | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | | CLOSE: (374) is inconsistent.
% 59.58/8.83 | | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | | End of split
% 59.58/8.83 | | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | End of split
% 59.58/8.83 | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | End of split
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | End of split
% 59.58/8.83 | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | End of split
% 59.58/8.83 | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | End of split
% 59.58/8.83 | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | End of split
% 59.58/8.83 | | | | | | | | |
% 59.58/8.83 | | | | | | | | Case 2:
% 59.58/8.83 | | | | | | | | |
% 59.58/8.83 | | | | | | | | | (375) ~ (all_72_3 = all_68_0)
% 59.58/8.83 | | | | | | | | | (376) ? [v0: any] : ? [v1: any] : (apply(all_32_6,
% 59.58/8.83 | | | | | | | | | all_57_1, all_72_3) = v0 & apply(all_32_6,
% 59.58/8.83 | | | | | | | | | all_57_1, all_68_0) = v1 & ( ~ (v1 = 0) | ~ (v0
% 59.58/8.83 | | | | | | | | | = 0)))
% 59.58/8.83 | | | | | | | | |
% 59.58/8.83 | | | | | | | | | DELTA: instantiating (376) with fresh symbols all_132_0,
% 59.58/8.83 | | | | | | | | | all_132_1 gives:
% 59.58/8.83 | | | | | | | | | (377) apply(all_32_6, all_57_1, all_72_3) = all_132_1 &
% 59.58/8.83 | | | | | | | | | apply(all_32_6, all_57_1, all_68_0) = all_132_0 & ( ~
% 59.58/8.83 | | | | | | | | | (all_132_0 = 0) | ~ (all_132_1 = 0))
% 59.58/8.83 | | | | | | | | |
% 59.58/8.83 | | | | | | | | | ALPHA: (377) implies:
% 59.58/8.83 | | | | | | | | | (378) apply(all_32_6, all_57_1, all_68_0) = all_132_0
% 59.58/8.83 | | | | | | | | | (379) apply(all_32_6, all_57_1, all_72_3) = all_132_1
% 59.58/8.83 | | | | | | | | | (380) ~ (all_132_0 = 0) | ~ (all_132_1 = 0)
% 59.58/8.83 | | | | | | | | |
% 59.58/8.83 | | | | | | | | | BETA: splitting (180) gives:
% 59.58/8.83 | | | | | | | | |
% 59.58/8.83 | | | | | | | | | Case 1:
% 59.58/8.83 | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | (381) all_57_1 = all_57_2
% 59.58/8.83 | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | REDUCE: (136), (381) imply:
% 59.58/8.83 | | | | | | | | | | (382) $false
% 59.58/8.83 | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | CLOSE: (382) is inconsistent.
% 59.58/8.83 | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | Case 2:
% 59.58/8.83 | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | (383) ? [v0: any] : ? [v1: any] : (apply(all_32_6,
% 59.58/8.83 | | | | | | | | | | all_57_1, all_68_0) = v1 & apply(all_32_6,
% 59.58/8.83 | | | | | | | | | | all_57_2, all_68_0) = v0 & ( ~ (v1 = 0) | ~
% 59.58/8.83 | | | | | | | | | | (v0 = 0)))
% 59.58/8.83 | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | DELTA: instantiating (383) with fresh symbols all_137_0,
% 59.58/8.83 | | | | | | | | | | all_137_1 gives:
% 59.58/8.83 | | | | | | | | | | (384) apply(all_32_6, all_57_1, all_68_0) = all_137_0 &
% 59.58/8.83 | | | | | | | | | | apply(all_32_6, all_57_2, all_68_0) = all_137_1 & (
% 59.58/8.83 | | | | | | | | | | ~ (all_137_0 = 0) | ~ (all_137_1 = 0))
% 59.58/8.83 | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | ALPHA: (384) implies:
% 59.58/8.83 | | | | | | | | | | (385) apply(all_32_6, all_57_1, all_68_0) = all_137_0
% 59.58/8.83 | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | BETA: splitting (181) gives:
% 59.58/8.83 | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | Case 1:
% 59.58/8.83 | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | (386) all_57_1 = all_57_2
% 59.58/8.83 | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | REDUCE: (136), (386) imply:
% 59.58/8.83 | | | | | | | | | | | (387) $false
% 59.58/8.83 | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | CLOSE: (387) is inconsistent.
% 59.58/8.83 | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | Case 2:
% 59.58/8.83 | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | (388) ? [v0: any] : ? [v1: any] : (apply(all_32_6,
% 59.58/8.83 | | | | | | | | | | | all_57_1, all_68_0) = v0 & apply(all_32_6,
% 59.58/8.83 | | | | | | | | | | | all_57_2, all_68_0) = v1 & ( ~ (v1 = 0) | ~
% 59.58/8.83 | | | | | | | | | | | (v0 = 0)))
% 59.58/8.83 | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | DELTA: instantiating (388) with fresh symbols all_142_0,
% 59.58/8.83 | | | | | | | | | | | all_142_1 gives:
% 59.58/8.83 | | | | | | | | | | | (389) apply(all_32_6, all_57_1, all_68_0) = all_142_1 &
% 59.58/8.83 | | | | | | | | | | | apply(all_32_6, all_57_2, all_68_0) = all_142_0 &
% 59.58/8.83 | | | | | | | | | | | ( ~ (all_142_0 = 0) | ~ (all_142_1 = 0))
% 59.58/8.83 | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | ALPHA: (389) implies:
% 59.58/8.83 | | | | | | | | | | | (390) apply(all_32_6, all_57_1, all_68_0) = all_142_1
% 59.58/8.83 | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | BETA: splitting (193) gives:
% 59.58/8.83 | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | Case 1:
% 59.58/8.83 | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | (391) all_57_1 = all_57_2
% 59.58/8.83 | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | REDUCE: (136), (391) imply:
% 59.58/8.83 | | | | | | | | | | | | (392) $false
% 59.58/8.83 | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | CLOSE: (392) is inconsistent.
% 59.58/8.83 | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | Case 2:
% 59.58/8.83 | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | (393) ? [v0: any] : ? [v1: any] : (apply(all_32_6,
% 59.58/8.83 | | | | | | | | | | | | all_57_1, all_72_3) = v0 & apply(all_32_6,
% 59.58/8.83 | | | | | | | | | | | | all_57_2, all_72_3) = v1 & ( ~ (v1 = 0) | ~
% 59.58/8.83 | | | | | | | | | | | | (v0 = 0)))
% 59.58/8.83 | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | DELTA: instantiating (393) with fresh symbols all_148_0,
% 59.58/8.83 | | | | | | | | | | | | all_148_1 gives:
% 59.58/8.83 | | | | | | | | | | | | (394) apply(all_32_6, all_57_1, all_72_3) = all_148_1 &
% 59.58/8.83 | | | | | | | | | | | | apply(all_32_6, all_57_2, all_72_3) = all_148_0 &
% 59.58/8.83 | | | | | | | | | | | | ( ~ (all_148_0 = 0) | ~ (all_148_1 = 0))
% 59.58/8.83 | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | ALPHA: (394) implies:
% 59.58/8.83 | | | | | | | | | | | | (395) apply(all_32_6, all_57_1, all_72_3) = all_148_1
% 59.58/8.83 | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | BETA: splitting (204) gives:
% 59.58/8.83 | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | Case 1:
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | (396) all_74_3 = all_68_0
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | COMBINE_EQS: (287), (396) imply:
% 59.58/8.83 | | | | | | | | | | | | | (397) all_72_3 = all_68_0
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | REDUCE: (375), (397) imply:
% 59.58/8.83 | | | | | | | | | | | | | (398) $false
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | CLOSE: (398) is inconsistent.
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | Case 2:
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_137_0, all_68_0,
% 59.58/8.83 | | | | | | | | | | | | | all_57_1, all_32_6, simplifying with (161), (385)
% 59.58/8.83 | | | | | | | | | | | | | gives:
% 59.58/8.83 | | | | | | | | | | | | | (399) all_137_0 = 0
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_137_0, all_142_1,
% 59.58/8.83 | | | | | | | | | | | | | all_68_0, all_57_1, all_32_6, simplifying with
% 59.58/8.83 | | | | | | | | | | | | | (385), (390) gives:
% 59.58/8.83 | | | | | | | | | | | | | (400) all_142_1 = all_137_0
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_132_0, all_142_1,
% 59.58/8.83 | | | | | | | | | | | | | all_68_0, all_57_1, all_32_6, simplifying with
% 59.58/8.83 | | | | | | | | | | | | | (378), (390) gives:
% 59.58/8.83 | | | | | | | | | | | | | (401) all_142_1 = all_132_0
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_132_1, all_148_1,
% 59.58/8.83 | | | | | | | | | | | | | all_72_3, all_57_1, all_32_6, simplifying with
% 59.58/8.83 | | | | | | | | | | | | | (379), (395) gives:
% 59.58/8.83 | | | | | | | | | | | | | (402) all_148_1 = all_132_1
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_148_1, all_72_3,
% 59.58/8.83 | | | | | | | | | | | | | all_57_1, all_32_6, simplifying with (288), (395)
% 59.58/8.83 | | | | | | | | | | | | | gives:
% 59.58/8.83 | | | | | | | | | | | | | (403) all_148_1 = 0
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | COMBINE_EQS: (402), (403) imply:
% 59.58/8.83 | | | | | | | | | | | | | (404) all_132_1 = 0
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | COMBINE_EQS: (400), (401) imply:
% 59.58/8.83 | | | | | | | | | | | | | (405) all_137_0 = all_132_0
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | SIMP: (405) implies:
% 59.58/8.83 | | | | | | | | | | | | | (406) all_137_0 = all_132_0
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | COMBINE_EQS: (399), (406) imply:
% 59.58/8.83 | | | | | | | | | | | | | (407) all_132_0 = 0
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | BETA: splitting (380) gives:
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | Case 1:
% 59.58/8.83 | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | (408) ~ (all_132_0 = 0)
% 59.58/8.83 | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | REDUCE: (407), (408) imply:
% 59.58/8.83 | | | | | | | | | | | | | | (409) $false
% 59.58/8.83 | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | CLOSE: (409) is inconsistent.
% 59.58/8.83 | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | Case 2:
% 59.58/8.83 | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | (410) ~ (all_132_1 = 0)
% 59.58/8.83 | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | REDUCE: (404), (410) imply:
% 59.58/8.83 | | | | | | | | | | | | | | (411) $false
% 59.58/8.83 | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | | CLOSE: (411) is inconsistent.
% 59.58/8.83 | | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | | End of split
% 59.58/8.83 | | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | | End of split
% 59.58/8.83 | | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | | End of split
% 59.58/8.83 | | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | | End of split
% 59.58/8.83 | | | | | | | | | |
% 59.58/8.83 | | | | | | | | | End of split
% 59.58/8.83 | | | | | | | | |
% 59.58/8.83 | | | | | | | | End of split
% 59.58/8.83 | | | | | | | |
% 59.58/8.83 | | | | | | | Case 2:
% 59.58/8.83 | | | | | | | |
% 59.58/8.83 | | | | | | | | (412) ~ (all_74_3 = all_72_3)
% 59.58/8.83 | | | | | | | |
% 59.58/8.83 | | | | | | | | BETA: splitting (208) gives:
% 59.58/8.83 | | | | | | | |
% 59.58/8.83 | | | | | | | | Case 1:
% 59.58/8.83 | | | | | | | | |
% 59.58/8.83 | | | | | | | | | (413) all_74_3 = all_66_0
% 59.58/8.83 | | | | | | | | |
% 59.58/8.83 | | | | | | | | | REDUCE: (412), (413) imply:
% 59.58/8.83 | | | | | | | | | (414) ~ (all_72_3 = all_66_0)
% 59.58/8.83 | | | | | | | | |
% 59.58/8.83 | | | | | | | | | SIMP: (414) implies:
% 59.58/8.83 | | | | | | | | | (415) ~ (all_72_3 = all_66_0)
% 59.58/8.83 | | | | | | | | |
% 59.58/8.84 | | | | | | | | | REF_CLOSE: (15), (136), (142), (156), (177), (187), (205),
% 59.58/8.84 | | | | | | | | | (206), (207), (286), (413), (415) are inconsistent
% 59.58/8.84 | | | | | | | | | by sub-proof #1.
% 59.58/8.84 | | | | | | | | |
% 59.58/8.84 | | | | | | | | Case 2:
% 59.58/8.84 | | | | | | | | |
% 59.58/8.84 | | | | | | | | | (416) ~ (all_74_3 = all_66_0)
% 59.58/8.84 | | | | | | | | | (417) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 59.58/8.84 | | | | | | | | | (apply(all_32_5, all_66_0, all_57_0) = v2 &
% 59.58/8.84 | | | | | | | | | member(all_74_3, all_32_3) = v0 & member(all_57_0,
% 59.58/8.84 | | | | | | | | | all_32_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 59.58/8.84 | | | | | | | | | (v0 = 0)))
% 59.58/8.84 | | | | | | | | |
% 59.58/8.84 | | | | | | | | | DELTA: instantiating (417) with fresh symbols all_134_0,
% 59.58/8.84 | | | | | | | | | all_134_1, all_134_2 gives:
% 59.58/8.84 | | | | | | | | | (418) apply(all_32_5, all_66_0, all_57_0) = all_134_0 &
% 59.58/8.84 | | | | | | | | | member(all_74_3, all_32_3) = all_134_2 &
% 59.58/8.84 | | | | | | | | | member(all_57_0, all_32_2) = all_134_1 & ( ~
% 59.58/8.84 | | | | | | | | | (all_134_0 = 0) | ~ (all_134_1 = 0) | ~
% 59.58/8.84 | | | | | | | | | (all_134_2 = 0))
% 59.58/8.84 | | | | | | | | |
% 59.58/8.84 | | | | | | | | | ALPHA: (418) implies:
% 59.58/8.84 | | | | | | | | | (419) member(all_57_0, all_32_2) = all_134_1
% 59.58/8.84 | | | | | | | | | (420) member(all_74_3, all_32_3) = all_134_2
% 59.58/8.84 | | | | | | | | | (421) apply(all_32_5, all_66_0, all_57_0) = all_134_0
% 59.58/8.84 | | | | | | | | | (422) ~ (all_134_0 = 0) | ~ (all_134_1 = 0) | ~
% 59.58/8.84 | | | | | | | | | (all_134_2 = 0)
% 59.58/8.84 | | | | | | | | |
% 59.58/8.84 | | | | | | | | | BETA: splitting (206) gives:
% 59.58/8.84 | | | | | | | | |
% 59.58/8.84 | | | | | | | | | Case 1:
% 59.58/8.84 | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | (423) all_72_3 = all_70_0
% 59.58/8.84 | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | REDUCE: (286), (423) imply:
% 59.58/8.84 | | | | | | | | | | (424) $false
% 59.58/8.84 | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | CLOSE: (424) is inconsistent.
% 59.58/8.84 | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | Case 2:
% 59.58/8.84 | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | (425) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 59.58/8.84 | | | | | | | | | | (apply(all_32_5, all_70_0, all_57_0) = v2 &
% 59.58/8.84 | | | | | | | | | | member(all_72_3, all_32_3) = v0 &
% 59.58/8.84 | | | | | | | | | | member(all_57_0, all_32_2) = v1 & ( ~ (v2 = 0) |
% 59.58/8.84 | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 59.58/8.84 | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | DELTA: instantiating (425) with fresh symbols all_223_0,
% 59.58/8.84 | | | | | | | | | | all_223_1, all_223_2 gives:
% 59.58/8.84 | | | | | | | | | | (426) apply(all_32_5, all_70_0, all_57_0) = all_223_0 &
% 59.58/8.84 | | | | | | | | | | member(all_72_3, all_32_3) = all_223_2 &
% 59.58/8.84 | | | | | | | | | | member(all_57_0, all_32_2) = all_223_1 & ( ~
% 59.58/8.84 | | | | | | | | | | (all_223_0 = 0) | ~ (all_223_1 = 0) | ~
% 59.58/8.84 | | | | | | | | | | (all_223_2 = 0))
% 59.58/8.84 | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | ALPHA: (426) implies:
% 59.58/8.84 | | | | | | | | | | (427) member(all_57_0, all_32_2) = all_223_1
% 59.58/8.84 | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | BETA: splitting (195) gives:
% 59.58/8.84 | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | Case 1:
% 59.58/8.84 | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | (428) all_74_3 = all_66_0
% 59.58/8.84 | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | REDUCE: (416), (428) imply:
% 59.58/8.84 | | | | | | | | | | | (429) $false
% 59.58/8.84 | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | CLOSE: (429) is inconsistent.
% 59.58/8.84 | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | Case 2:
% 59.58/8.84 | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_223_1, all_32_2,
% 59.58/8.84 | | | | | | | | | | | all_57_0, simplifying with (142), (427) gives:
% 59.58/8.84 | | | | | | | | | | | (430) all_223_1 = 0
% 59.58/8.84 | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | GROUND_INST: instantiating (15) with all_134_1, all_223_1,
% 59.58/8.84 | | | | | | | | | | | all_32_2, all_57_0, simplifying with (419), (427)
% 59.58/8.84 | | | | | | | | | | | gives:
% 59.58/8.84 | | | | | | | | | | | (431) all_223_1 = all_134_1
% 59.58/8.84 | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_134_2, all_32_3,
% 59.58/8.84 | | | | | | | | | | | all_74_3, simplifying with (173), (420) gives:
% 59.58/8.84 | | | | | | | | | | | (432) all_134_2 = 0
% 59.58/8.84 | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | GROUND_INST: instantiating (16) with 0, all_134_0, all_57_0,
% 59.58/8.84 | | | | | | | | | | | all_66_0, all_32_5, simplifying with (157), (421)
% 59.58/8.84 | | | | | | | | | | | gives:
% 59.58/8.84 | | | | | | | | | | | (433) all_134_0 = 0
% 59.58/8.84 | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | COMBINE_EQS: (430), (431) imply:
% 59.58/8.84 | | | | | | | | | | | (434) all_134_1 = 0
% 59.58/8.84 | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | BETA: splitting (422) gives:
% 59.58/8.84 | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | Case 1:
% 59.58/8.84 | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | | (435) ~ (all_134_0 = 0)
% 59.58/8.84 | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | | REDUCE: (433), (435) imply:
% 59.58/8.84 | | | | | | | | | | | | (436) $false
% 59.58/8.84 | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | | CLOSE: (436) is inconsistent.
% 59.58/8.84 | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | Case 2:
% 59.58/8.84 | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | | (437) ~ (all_134_1 = 0) | ~ (all_134_2 = 0)
% 59.58/8.84 | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | | BETA: splitting (437) gives:
% 59.58/8.84 | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | | Case 1:
% 59.58/8.84 | | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | | | (438) ~ (all_134_1 = 0)
% 59.58/8.84 | | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | | | REDUCE: (434), (438) imply:
% 59.58/8.84 | | | | | | | | | | | | | (439) $false
% 59.58/8.84 | | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | | | CLOSE: (439) is inconsistent.
% 59.58/8.84 | | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | | Case 2:
% 59.58/8.84 | | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | | | (440) ~ (all_134_2 = 0)
% 59.58/8.84 | | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | | | REDUCE: (432), (440) imply:
% 59.58/8.84 | | | | | | | | | | | | | (441) $false
% 59.58/8.84 | | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | | | CLOSE: (441) is inconsistent.
% 59.58/8.84 | | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | | End of split
% 59.58/8.84 | | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | | End of split
% 59.58/8.84 | | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | | End of split
% 59.58/8.84 | | | | | | | | | |
% 59.58/8.84 | | | | | | | | | End of split
% 59.58/8.84 | | | | | | | | |
% 59.58/8.84 | | | | | | | | End of split
% 59.58/8.84 | | | | | | | |
% 59.58/8.84 | | | | | | | End of split
% 59.58/8.84 | | | | | | |
% 59.58/8.84 | | | | | | End of split
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | Case 2:
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | | (442) member(all_57_0, all_32_2) = all_72_4 & member(all_57_2,
% 59.58/8.84 | | | | | | all_32_4) = all_72_5 & ( ~ (all_72_4 = 0) | ~ (all_72_5
% 59.58/8.84 | | | | | | = 0))
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | | ALPHA: (442) implies:
% 59.58/8.84 | | | | | | (443) member(all_57_2, all_32_4) = all_72_5
% 59.58/8.84 | | | | | | (444) member(all_57_0, all_32_2) = all_72_4
% 59.58/8.84 | | | | | | (445) ~ (all_72_4 = 0) | ~ (all_72_5 = 0)
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | | GROUND_INST: instantiating (15) with 0, all_72_5, all_32_4,
% 59.58/8.84 | | | | | | all_57_2, simplifying with (140), (443) gives:
% 59.58/8.84 | | | | | | (446) all_72_5 = 0
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | | GROUND_INST: instantiating (15) with 0, all_72_4, all_32_2,
% 59.58/8.84 | | | | | | all_57_0, simplifying with (142), (444) gives:
% 59.58/8.84 | | | | | | (447) all_72_4 = 0
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | | BETA: splitting (445) gives:
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | | Case 1:
% 59.58/8.84 | | | | | | |
% 59.58/8.84 | | | | | | | (448) ~ (all_72_4 = 0)
% 59.58/8.84 | | | | | | |
% 59.58/8.84 | | | | | | | REDUCE: (447), (448) imply:
% 59.58/8.84 | | | | | | | (449) $false
% 59.58/8.84 | | | | | | |
% 59.58/8.84 | | | | | | | CLOSE: (449) is inconsistent.
% 59.58/8.84 | | | | | | |
% 59.58/8.84 | | | | | | Case 2:
% 59.58/8.84 | | | | | | |
% 59.58/8.84 | | | | | | | (450) ~ (all_72_5 = 0)
% 59.58/8.84 | | | | | | |
% 59.58/8.84 | | | | | | | REDUCE: (446), (450) imply:
% 59.58/8.84 | | | | | | | (451) $false
% 59.58/8.84 | | | | | | |
% 59.58/8.84 | | | | | | | CLOSE: (451) is inconsistent.
% 59.58/8.84 | | | | | | |
% 59.58/8.84 | | | | | | End of split
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | End of split
% 59.58/8.84 | | | | |
% 59.58/8.84 | | | | Case 2:
% 59.58/8.84 | | | | |
% 59.58/8.84 | | | | | (452) member(all_57_0, all_32_2) = all_74_4 & member(all_57_1,
% 59.58/8.84 | | | | | all_32_4) = all_74_5 & ( ~ (all_74_4 = 0) | ~ (all_74_5 =
% 59.58/8.84 | | | | | 0))
% 59.58/8.84 | | | | |
% 59.58/8.84 | | | | | ALPHA: (452) implies:
% 59.58/8.84 | | | | | (453) member(all_57_1, all_32_4) = all_74_5
% 59.58/8.84 | | | | | (454) member(all_57_0, all_32_2) = all_74_4
% 59.58/8.84 | | | | | (455) ~ (all_74_4 = 0) | ~ (all_74_5 = 0)
% 59.58/8.84 | | | | |
% 59.58/8.84 | | | | | GROUND_INST: instantiating (15) with 0, all_74_5, all_32_4, all_57_1,
% 59.58/8.84 | | | | | simplifying with (141), (453) gives:
% 59.58/8.84 | | | | | (456) all_74_5 = 0
% 59.58/8.84 | | | | |
% 59.58/8.84 | | | | | GROUND_INST: instantiating (15) with 0, all_74_4, all_32_2, all_57_0,
% 59.58/8.84 | | | | | simplifying with (142), (454) gives:
% 59.58/8.84 | | | | | (457) all_74_4 = 0
% 59.58/8.84 | | | | |
% 59.58/8.84 | | | | | BETA: splitting (455) gives:
% 59.58/8.84 | | | | |
% 59.58/8.84 | | | | | Case 1:
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | | (458) ~ (all_74_4 = 0)
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | | REDUCE: (457), (458) imply:
% 59.58/8.84 | | | | | | (459) $false
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | | CLOSE: (459) is inconsistent.
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | Case 2:
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | | (460) ~ (all_74_5 = 0)
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | | REDUCE: (456), (460) imply:
% 59.58/8.84 | | | | | | (461) $false
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | | CLOSE: (461) is inconsistent.
% 59.58/8.84 | | | | | |
% 59.58/8.84 | | | | | End of split
% 59.58/8.84 | | | | |
% 59.58/8.85 | | | | End of split
% 59.58/8.85 | | | |
% 59.58/8.85 | | | End of split
% 59.58/8.85 | | |
% 59.58/8.85 | | End of split
% 59.58/8.85 | |
% 59.58/8.85 | End of split
% 59.58/8.85 |
% 59.58/8.85 End of proof
% 59.58/8.85
% 59.58/8.85 Sub-proof #1 shows that the following formulas are inconsistent:
% 59.58/8.85 ----------------------------------------------------------------
% 59.58/8.85 (1) member(all_72_3, all_32_3) = 0
% 59.58/8.85 (2) all_74_3 = all_66_0
% 59.58/8.85 (3) ~ (all_72_3 = all_66_0)
% 59.58/8.85 (4) all_57_1 = all_57_2 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 59.58/8.85 (apply(all_32_6, all_57_2, all_74_3) = v2 & member(all_74_3, all_32_3) =
% 59.58/8.85 v1 & member(all_57_1, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 59.58/8.85 (v0 = 0)))
% 59.58/8.85 (5) ~ (all_57_1 = all_57_2)
% 59.58/8.85 (6) all_72_3 = all_70_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 59.58/8.85 (apply(all_32_5, all_70_0, all_57_0) = v2 & member(all_72_3, all_32_3) =
% 59.58/8.85 v0 & member(all_57_0, all_32_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 59.58/8.85 (v0 = 0)))
% 59.58/8.85 (7) ~ (all_72_3 = all_70_0)
% 59.58/8.85 (8) member(all_66_0, all_32_3) = 0
% 59.58/8.85 (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 59.58/8.85 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) =
% 59.58/8.85 v0))
% 59.58/8.85 (10) member(all_57_0, all_32_2) = 0
% 59.58/8.85 (11) all_72_3 = all_70_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_6,
% 59.58/8.85 all_64_0, all_72_3) = v1 & apply(all_32_6, all_64_0, all_70_0) = v0
% 59.58/8.85 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.58/8.85 (12) all_74_3 = all_72_3 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 59.58/8.85 (member(all_74_3, all_32_3) = v1 & member(all_72_3, all_32_3) = v0 &
% 59.58/8.85 member(all_57_0, all_32_2) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0
% 59.58/8.85 = 0)))
% 59.58/8.85
% 59.58/8.85 Begin of proof
% 59.58/8.85 |
% 59.58/8.85 | BETA: splitting (12) gives:
% 59.58/8.85 |
% 59.58/8.85 | Case 1:
% 59.58/8.85 | |
% 59.58/8.85 | | (13) all_74_3 = all_72_3
% 59.58/8.85 | |
% 59.58/8.85 | | COMBINE_EQS: (2), (13) imply:
% 59.58/8.85 | | (14) all_72_3 = all_66_0
% 59.58/8.85 | |
% 59.58/8.85 | | SIMP: (14) implies:
% 59.58/8.85 | | (15) all_72_3 = all_66_0
% 59.58/8.85 | |
% 59.58/8.85 | | REDUCE: (3), (15) imply:
% 59.58/8.85 | | (16) $false
% 59.58/8.85 | |
% 59.58/8.85 | | CLOSE: (16) is inconsistent.
% 59.58/8.85 | |
% 59.58/8.85 | Case 2:
% 59.58/8.85 | |
% 59.58/8.85 | | (17) ? [v0: any] : ? [v1: any] : ? [v2: any] : (member(all_74_3,
% 59.58/8.85 | | all_32_3) = v1 & member(all_72_3, all_32_3) = v0 &
% 59.58/8.85 | | member(all_57_0, all_32_2) = v2 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 59.58/8.85 | | (v0 = 0)))
% 59.58/8.85 | |
% 59.58/8.85 | | DELTA: instantiating (17) with fresh symbols all_159_0, all_159_1, all_159_2
% 59.58/8.85 | | gives:
% 59.58/8.85 | | (18) member(all_74_3, all_32_3) = all_159_1 & member(all_72_3, all_32_3)
% 59.58/8.85 | | = all_159_2 & member(all_57_0, all_32_2) = all_159_0 & ( ~
% 59.58/8.85 | | (all_159_0 = 0) | ~ (all_159_1 = 0) | ~ (all_159_2 = 0))
% 59.58/8.85 | |
% 59.58/8.85 | | ALPHA: (18) implies:
% 59.58/8.85 | | (19) member(all_57_0, all_32_2) = all_159_0
% 59.58/8.85 | | (20) member(all_72_3, all_32_3) = all_159_2
% 59.58/8.85 | | (21) member(all_74_3, all_32_3) = all_159_1
% 59.58/8.85 | | (22) ~ (all_159_0 = 0) | ~ (all_159_1 = 0) | ~ (all_159_2 = 0)
% 59.58/8.85 | |
% 59.58/8.85 | | REDUCE: (2), (21) imply:
% 59.58/8.85 | | (23) member(all_66_0, all_32_3) = all_159_1
% 59.58/8.85 | |
% 59.58/8.85 | | BETA: splitting (4) gives:
% 59.58/8.85 | |
% 59.58/8.85 | | Case 1:
% 59.58/8.85 | | |
% 59.58/8.85 | | | (24) all_57_1 = all_57_2
% 59.58/8.85 | | |
% 59.58/8.85 | | | REDUCE: (5), (24) imply:
% 59.58/8.85 | | | (25) $false
% 59.58/8.85 | | |
% 59.58/8.85 | | | CLOSE: (25) is inconsistent.
% 59.58/8.85 | | |
% 59.58/8.85 | | Case 2:
% 59.58/8.85 | | |
% 59.58/8.85 | | | (26) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_6,
% 59.58/8.85 | | | all_57_2, all_74_3) = v2 & member(all_74_3, all_32_3) = v1 &
% 59.58/8.85 | | | member(all_57_1, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) |
% 59.58/8.85 | | | ~ (v0 = 0)))
% 59.58/8.85 | | |
% 59.58/8.85 | | | DELTA: instantiating (26) with fresh symbols all_170_0, all_170_1,
% 59.58/8.85 | | | all_170_2 gives:
% 59.58/8.85 | | | (27) apply(all_32_6, all_57_2, all_74_3) = all_170_0 & member(all_74_3,
% 59.58/8.85 | | | all_32_3) = all_170_1 & member(all_57_1, all_32_4) = all_170_2 &
% 59.58/8.85 | | | ( ~ (all_170_0 = 0) | ~ (all_170_1 = 0) | ~ (all_170_2 = 0))
% 59.58/8.85 | | |
% 59.58/8.85 | | | ALPHA: (27) implies:
% 59.58/8.85 | | | (28) member(all_74_3, all_32_3) = all_170_1
% 59.58/8.85 | | |
% 59.58/8.85 | | | REDUCE: (2), (28) imply:
% 59.58/8.86 | | | (29) member(all_66_0, all_32_3) = all_170_1
% 59.58/8.86 | | |
% 59.58/8.86 | | | BETA: splitting (6) gives:
% 59.58/8.86 | | |
% 59.58/8.86 | | | Case 1:
% 59.58/8.86 | | | |
% 59.58/8.86 | | | | (30) all_72_3 = all_70_0
% 59.58/8.86 | | | |
% 59.58/8.86 | | | | REDUCE: (7), (30) imply:
% 59.58/8.86 | | | | (31) $false
% 59.58/8.86 | | | |
% 59.58/8.86 | | | | CLOSE: (31) is inconsistent.
% 59.58/8.86 | | | |
% 59.58/8.86 | | | Case 2:
% 59.58/8.86 | | | |
% 59.58/8.86 | | | | (32) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_5,
% 59.58/8.86 | | | | all_70_0, all_57_0) = v2 & member(all_72_3, all_32_3) = v0 &
% 59.58/8.86 | | | | member(all_57_0, all_32_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) |
% 59.58/8.86 | | | | ~ (v0 = 0)))
% 59.58/8.86 | | | |
% 59.58/8.86 | | | | DELTA: instantiating (32) with fresh symbols all_180_0, all_180_1,
% 59.58/8.86 | | | | all_180_2 gives:
% 59.58/8.86 | | | | (33) apply(all_32_5, all_70_0, all_57_0) = all_180_0 &
% 59.58/8.86 | | | | member(all_72_3, all_32_3) = all_180_2 & member(all_57_0,
% 59.58/8.86 | | | | all_32_2) = all_180_1 & ( ~ (all_180_0 = 0) | ~ (all_180_1 =
% 59.58/8.86 | | | | 0) | ~ (all_180_2 = 0))
% 59.58/8.86 | | | |
% 59.58/8.86 | | | | ALPHA: (33) implies:
% 59.58/8.86 | | | | (34) member(all_57_0, all_32_2) = all_180_1
% 59.58/8.86 | | | | (35) member(all_72_3, all_32_3) = all_180_2
% 59.58/8.86 | | | |
% 59.58/8.86 | | | | BETA: splitting (11) gives:
% 59.58/8.86 | | | |
% 59.58/8.86 | | | | Case 1:
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | | (36) all_72_3 = all_70_0
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | | REDUCE: (7), (36) imply:
% 59.58/8.86 | | | | | (37) $false
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | | CLOSE: (37) is inconsistent.
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | Case 2:
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | | GROUND_INST: instantiating (9) with 0, all_180_1, all_32_2, all_57_0,
% 59.58/8.86 | | | | | simplifying with (10), (34) gives:
% 59.58/8.86 | | | | | (38) all_180_1 = 0
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | | GROUND_INST: instantiating (9) with all_159_0, all_180_1, all_32_2,
% 59.58/8.86 | | | | | all_57_0, simplifying with (19), (34) gives:
% 59.58/8.86 | | | | | (39) all_180_1 = all_159_0
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | | GROUND_INST: instantiating (9) with 0, all_170_1, all_32_3, all_66_0,
% 59.58/8.86 | | | | | simplifying with (8), (29) gives:
% 59.58/8.86 | | | | | (40) all_170_1 = 0
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | | GROUND_INST: instantiating (9) with all_159_1, all_170_1, all_32_3,
% 59.58/8.86 | | | | | all_66_0, simplifying with (23), (29) gives:
% 59.58/8.86 | | | | | (41) all_170_1 = all_159_1
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | | GROUND_INST: instantiating (9) with 0, all_180_2, all_32_3, all_72_3,
% 59.58/8.86 | | | | | simplifying with (1), (35) gives:
% 59.58/8.86 | | | | | (42) all_180_2 = 0
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | | GROUND_INST: instantiating (9) with all_159_2, all_180_2, all_32_3,
% 59.58/8.86 | | | | | all_72_3, simplifying with (20), (35) gives:
% 59.58/8.86 | | | | | (43) all_180_2 = all_159_2
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | | COMBINE_EQS: (38), (39) imply:
% 59.58/8.86 | | | | | (44) all_159_0 = 0
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | | SIMP: (44) implies:
% 59.58/8.86 | | | | | (45) all_159_0 = 0
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | | COMBINE_EQS: (42), (43) imply:
% 59.58/8.86 | | | | | (46) all_159_2 = 0
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | | COMBINE_EQS: (40), (41) imply:
% 59.58/8.86 | | | | | (47) all_159_1 = 0
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | | BETA: splitting (22) gives:
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | | Case 1:
% 59.58/8.86 | | | | | |
% 59.58/8.86 | | | | | | (48) ~ (all_159_0 = 0)
% 59.58/8.86 | | | | | |
% 59.58/8.86 | | | | | | REDUCE: (45), (48) imply:
% 59.58/8.86 | | | | | | (49) $false
% 59.58/8.86 | | | | | |
% 59.58/8.86 | | | | | | CLOSE: (49) is inconsistent.
% 59.58/8.86 | | | | | |
% 59.58/8.86 | | | | | Case 2:
% 59.58/8.86 | | | | | |
% 59.58/8.86 | | | | | | (50) ~ (all_159_1 = 0) | ~ (all_159_2 = 0)
% 59.58/8.86 | | | | | |
% 59.58/8.86 | | | | | | BETA: splitting (50) gives:
% 59.58/8.86 | | | | | |
% 59.58/8.86 | | | | | | Case 1:
% 59.58/8.86 | | | | | | |
% 59.58/8.86 | | | | | | | (51) ~ (all_159_1 = 0)
% 59.58/8.86 | | | | | | |
% 59.58/8.86 | | | | | | | REDUCE: (47), (51) imply:
% 59.58/8.86 | | | | | | | (52) $false
% 59.58/8.86 | | | | | | |
% 59.58/8.86 | | | | | | | CLOSE: (52) is inconsistent.
% 59.58/8.86 | | | | | | |
% 59.58/8.86 | | | | | | Case 2:
% 59.58/8.86 | | | | | | |
% 59.58/8.86 | | | | | | | (53) ~ (all_159_2 = 0)
% 59.58/8.86 | | | | | | |
% 59.58/8.86 | | | | | | | REDUCE: (46), (53) imply:
% 59.58/8.86 | | | | | | | (54) $false
% 59.58/8.86 | | | | | | |
% 59.58/8.86 | | | | | | | CLOSE: (54) is inconsistent.
% 59.58/8.86 | | | | | | |
% 59.58/8.86 | | | | | | End of split
% 59.58/8.86 | | | | | |
% 59.58/8.86 | | | | | End of split
% 59.58/8.86 | | | | |
% 59.58/8.86 | | | | End of split
% 59.58/8.86 | | | |
% 59.58/8.86 | | | End of split
% 59.58/8.86 | | |
% 59.58/8.86 | | End of split
% 59.58/8.86 | |
% 59.58/8.86 | End of split
% 59.58/8.86 |
% 59.58/8.86 End of proof
% 59.58/8.86
% 59.58/8.86 Sub-proof #2 shows that the following formulas are inconsistent:
% 59.58/8.86 ----------------------------------------------------------------
% 59.58/8.86 (1) ~ (all_137_0 = 0) | ~ (all_137_1 = 0)
% 59.58/8.86 (2) all_137_0 = 0
% 59.58/8.86 (3) all_137_1 = 0
% 59.58/8.86
% 59.58/8.86 Begin of proof
% 59.58/8.86 |
% 59.58/8.86 | BETA: splitting (1) gives:
% 59.58/8.86 |
% 59.58/8.86 | Case 1:
% 59.58/8.86 | |
% 59.58/8.86 | | (4) ~ (all_137_0 = 0)
% 59.58/8.86 | |
% 59.58/8.86 | | REDUCE: (2), (4) imply:
% 59.58/8.86 | | (5) $false
% 59.58/8.86 | |
% 59.58/8.86 | | CLOSE: (5) is inconsistent.
% 59.58/8.86 | |
% 59.58/8.86 | Case 2:
% 59.58/8.86 | |
% 59.58/8.86 | | (6) ~ (all_137_1 = 0)
% 59.58/8.86 | |
% 59.58/8.86 | | REDUCE: (3), (6) imply:
% 59.58/8.86 | | (7) $false
% 59.58/8.86 | |
% 59.58/8.86 | | CLOSE: (7) is inconsistent.
% 59.58/8.86 | |
% 59.58/8.86 | End of split
% 59.58/8.86 |
% 59.58/8.86 End of proof
% 59.58/8.86
% 59.58/8.86 Sub-proof #3 shows that the following formulas are inconsistent:
% 59.58/8.86 ----------------------------------------------------------------
% 59.58/8.86 (1) apply(all_32_5, all_66_0, all_57_0) = 0
% 59.58/8.86 (2) all_70_0 = all_66_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_5,
% 59.58/8.86 all_70_0, all_57_0) = v0 & apply(all_32_5, all_66_0, all_57_0) = v1 &
% 59.58/8.86 ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.58/8.86 (3) ~ (all_70_0 = all_66_0)
% 59.58/8.86 (4) all_72_3 = all_70_0
% 59.58/8.86 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 59.58/8.86 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~
% 59.58/8.86 (apply(v4, v3, v2) = v0))
% 59.58/8.86 (6) apply(all_32_5, all_70_0, all_57_0) = 0
% 59.58/8.86 (7) all_72_3 = all_66_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_6,
% 59.58/8.86 all_57_2, all_72_3) = v1 & apply(all_32_6, all_57_2, all_66_0) = v0 &
% 59.58/8.86 ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.58/8.86
% 59.58/8.86 Begin of proof
% 59.58/8.86 |
% 59.58/8.86 | BETA: splitting (2) gives:
% 59.58/8.86 |
% 59.58/8.86 | Case 1:
% 59.58/8.86 | |
% 59.58/8.86 | | (8) all_70_0 = all_66_0
% 59.58/8.86 | |
% 59.58/8.86 | | REDUCE: (3), (8) imply:
% 59.58/8.86 | | (9) $false
% 59.58/8.86 | |
% 59.58/8.86 | | CLOSE: (9) is inconsistent.
% 59.58/8.86 | |
% 59.58/8.86 | Case 2:
% 59.58/8.86 | |
% 59.58/8.86 | | (10) ? [v0: any] : ? [v1: any] : (apply(all_32_5, all_70_0, all_57_0) =
% 59.58/8.86 | | v0 & apply(all_32_5, all_66_0, all_57_0) = v1 & ( ~ (v1 = 0) | ~
% 59.58/8.86 | | (v0 = 0)))
% 59.58/8.86 | |
% 59.58/8.86 | | DELTA: instantiating (10) with fresh symbols all_151_0, all_151_1 gives:
% 59.58/8.87 | | (11) apply(all_32_5, all_70_0, all_57_0) = all_151_1 & apply(all_32_5,
% 59.58/8.87 | | all_66_0, all_57_0) = all_151_0 & ( ~ (all_151_0 = 0) | ~
% 59.58/8.87 | | (all_151_1 = 0))
% 59.58/8.87 | |
% 59.58/8.87 | | ALPHA: (11) implies:
% 59.58/8.87 | | (12) apply(all_32_5, all_66_0, all_57_0) = all_151_0
% 59.58/8.87 | | (13) apply(all_32_5, all_70_0, all_57_0) = all_151_1
% 59.58/8.87 | | (14) ~ (all_151_0 = 0) | ~ (all_151_1 = 0)
% 59.58/8.87 | |
% 59.58/8.87 | | BETA: splitting (7) gives:
% 59.58/8.87 | |
% 59.58/8.87 | | Case 1:
% 59.58/8.87 | | |
% 59.58/8.87 | | | (15) all_72_3 = all_66_0
% 59.58/8.87 | | |
% 59.58/8.87 | | | COMBINE_EQS: (4), (15) imply:
% 59.58/8.87 | | | (16) all_70_0 = all_66_0
% 59.58/8.87 | | |
% 59.58/8.87 | | | SIMP: (16) implies:
% 59.58/8.87 | | | (17) all_70_0 = all_66_0
% 59.58/8.87 | | |
% 59.58/8.87 | | | REDUCE: (3), (17) imply:
% 59.58/8.87 | | | (18) $false
% 59.58/8.87 | | |
% 59.58/8.87 | | | CLOSE: (18) is inconsistent.
% 59.58/8.87 | | |
% 59.58/8.87 | | Case 2:
% 59.58/8.87 | | |
% 59.58/8.87 | | |
% 59.58/8.87 | | | GROUND_INST: instantiating (5) with 0, all_151_0, all_57_0, all_66_0,
% 59.58/8.87 | | | all_32_5, simplifying with (1), (12) gives:
% 59.58/8.87 | | | (19) all_151_0 = 0
% 59.58/8.87 | | |
% 59.58/8.87 | | | GROUND_INST: instantiating (5) with 0, all_151_1, all_57_0, all_70_0,
% 59.58/8.87 | | | all_32_5, simplifying with (6), (13) gives:
% 59.58/8.87 | | | (20) all_151_1 = 0
% 59.58/8.87 | | |
% 59.58/8.87 | | | BETA: splitting (14) gives:
% 59.58/8.87 | | |
% 59.58/8.87 | | | Case 1:
% 59.58/8.87 | | | |
% 59.58/8.87 | | | | (21) ~ (all_151_0 = 0)
% 59.58/8.87 | | | |
% 59.58/8.87 | | | | REDUCE: (19), (21) imply:
% 59.58/8.87 | | | | (22) $false
% 59.58/8.87 | | | |
% 59.58/8.87 | | | | CLOSE: (22) is inconsistent.
% 59.58/8.87 | | | |
% 59.58/8.87 | | | Case 2:
% 59.58/8.87 | | | |
% 59.58/8.87 | | | | (23) ~ (all_151_1 = 0)
% 59.58/8.87 | | | |
% 59.58/8.87 | | | | REDUCE: (20), (23) imply:
% 59.58/8.87 | | | | (24) $false
% 59.58/8.87 | | | |
% 59.58/8.87 | | | | CLOSE: (24) is inconsistent.
% 59.58/8.87 | | | |
% 59.58/8.87 | | | End of split
% 59.58/8.87 | | |
% 59.58/8.87 | | End of split
% 59.58/8.87 | |
% 59.58/8.87 | End of split
% 59.58/8.87 |
% 59.58/8.87 End of proof
% 59.58/8.87
% 59.58/8.87 Sub-proof #4 shows that the following formulas are inconsistent:
% 59.58/8.87 ----------------------------------------------------------------
% 59.58/8.87 (1) ~ (all_117_0 = 0) | ~ (all_117_1 = 0)
% 59.58/8.87 (2) all_117_0 = 0
% 59.58/8.87 (3) all_117_1 = 0
% 59.58/8.87
% 59.58/8.87 Begin of proof
% 59.58/8.87 |
% 59.58/8.87 | BETA: splitting (1) gives:
% 59.58/8.87 |
% 59.58/8.87 | Case 1:
% 59.58/8.87 | |
% 59.58/8.87 | | (4) ~ (all_117_0 = 0)
% 59.58/8.87 | |
% 59.58/8.87 | | REDUCE: (2), (4) imply:
% 59.58/8.87 | | (5) $false
% 59.58/8.87 | |
% 59.58/8.87 | | CLOSE: (5) is inconsistent.
% 59.58/8.87 | |
% 59.58/8.87 | Case 2:
% 59.58/8.87 | |
% 59.58/8.87 | | (6) ~ (all_117_1 = 0)
% 59.58/8.87 | |
% 59.58/8.87 | | REDUCE: (3), (6) imply:
% 59.58/8.87 | | (7) $false
% 59.58/8.87 | |
% 59.58/8.87 | | CLOSE: (7) is inconsistent.
% 59.58/8.87 | |
% 59.58/8.87 | End of split
% 59.58/8.87 |
% 59.58/8.87 End of proof
% 59.58/8.87
% 59.58/8.87 Sub-proof #5 shows that the following formulas are inconsistent:
% 59.58/8.87 ----------------------------------------------------------------
% 59.58/8.87 (1) member(all_57_0, all_32_2) = 0
% 59.58/8.87 (2) apply(all_32_5, all_65_0, all_57_0) = 0
% 59.58/8.87 (3) member(all_72_0, all_32_4) = 0
% 59.58/8.87 (4) all_85_0 = all_83_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_5,
% 59.58/8.87 all_85_0, all_57_0) = v0 & apply(all_32_5, all_83_0, all_57_0) = v1 &
% 59.58/8.87 ( ~ (v1 = 0) | ~ (v0 = 0)))
% 59.58/8.87 (5) (apply(all_32_6, all_72_0, all_85_0) = all_133_0 & member(all_85_0,
% 59.58/8.87 all_32_3) = all_133_1 & ( ~ (all_133_0 = 0) | ~ (all_133_1 = 0))) |
% 59.58/8.87 (member(all_72_0, all_32_4) = all_133_1 & member(all_57_0, all_32_2) =
% 59.58/8.87 all_133_0 & ( ~ (all_133_0 = 0) | ~ (all_133_1 = 0)))
% 59.58/8.87 (6) apply(all_32_6, all_72_0, all_65_0) = 0
% 59.58/8.87 (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 59.58/8.87 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~
% 59.58/8.87 (apply(v4, v3, v2) = v0))
% 59.58/8.87 (8) all_83_0 = all_65_0
% 59.58/8.87 (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 59.58/8.87 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) =
% 59.58/8.87 v0))
% 59.58/8.87 (10) apply(all_32_5, all_85_0, all_57_0) = 0
% 59.58/8.87 (11) all_81_0 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_6, all_72_0,
% 59.58/8.87 all_65_0) = v1 & member(all_65_0, all_32_3) = v0 & ( ~ (v1 = 0) |
% 59.58/8.87 ~ (v0 = 0))) | (member(all_72_0, all_32_4) = v0 & member(all_57_0,
% 59.58/8.87 all_32_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 59.58/8.87 (12) ~ (all_81_0 = 0)
% 59.90/8.87 (13) member(all_85_0, all_32_3) = 0
% 59.90/8.87
% 59.90/8.87 Begin of proof
% 59.90/8.87 |
% 59.90/8.87 | BETA: splitting (4) gives:
% 59.90/8.87 |
% 59.90/8.87 | Case 1:
% 59.90/8.87 | |
% 59.90/8.87 | | (14) all_85_0 = all_83_0
% 59.90/8.87 | |
% 59.90/8.87 | | COMBINE_EQS: (8), (14) imply:
% 59.90/8.87 | | (15) all_85_0 = all_65_0
% 59.90/8.87 | |
% 59.90/8.87 | | REDUCE: (13), (15) imply:
% 59.90/8.87 | | (16) member(all_65_0, all_32_3) = 0
% 59.90/8.87 | |
% 59.90/8.87 | | BETA: splitting (5) gives:
% 59.90/8.87 | |
% 59.90/8.87 | | Case 1:
% 59.90/8.87 | | |
% 59.90/8.87 | | | (17) apply(all_32_6, all_72_0, all_85_0) = all_133_0 & member(all_85_0,
% 59.90/8.87 | | | all_32_3) = all_133_1 & ( ~ (all_133_0 = 0) | ~ (all_133_1 =
% 59.90/8.87 | | | 0))
% 59.90/8.87 | | |
% 59.90/8.87 | | | ALPHA: (17) implies:
% 59.90/8.87 | | | (18) member(all_85_0, all_32_3) = all_133_1
% 59.90/8.87 | | | (19) apply(all_32_6, all_72_0, all_85_0) = all_133_0
% 59.90/8.87 | | | (20) ~ (all_133_0 = 0) | ~ (all_133_1 = 0)
% 59.90/8.87 | | |
% 59.90/8.87 | | | REDUCE: (15), (19) imply:
% 59.90/8.87 | | | (21) apply(all_32_6, all_72_0, all_65_0) = all_133_0
% 59.90/8.87 | | |
% 59.90/8.87 | | | REDUCE: (15), (18) imply:
% 59.90/8.87 | | | (22) member(all_65_0, all_32_3) = all_133_1
% 59.90/8.87 | | |
% 59.90/8.87 | | | GROUND_INST: instantiating (9) with 0, all_133_1, all_32_3, all_65_0,
% 59.90/8.87 | | | simplifying with (16), (22) gives:
% 59.90/8.87 | | | (23) all_133_1 = 0
% 59.90/8.87 | | |
% 59.90/8.87 | | | GROUND_INST: instantiating (7) with 0, all_133_0, all_65_0, all_72_0,
% 59.90/8.87 | | | all_32_6, simplifying with (6), (21) gives:
% 59.90/8.87 | | | (24) all_133_0 = 0
% 59.90/8.87 | | |
% 59.90/8.87 | | | REF_CLOSE: (20), (23), (24) are inconsistent by sub-proof #6.
% 59.90/8.87 | | |
% 59.90/8.87 | | Case 2:
% 59.90/8.87 | | |
% 59.90/8.88 | | | (25) member(all_72_0, all_32_4) = all_133_1 & member(all_57_0,
% 59.90/8.88 | | | all_32_2) = all_133_0 & ( ~ (all_133_0 = 0) | ~ (all_133_1 =
% 59.90/8.88 | | | 0))
% 59.90/8.88 | | |
% 59.90/8.88 | | | ALPHA: (25) implies:
% 59.90/8.88 | | | (26) member(all_57_0, all_32_2) = all_133_0
% 59.90/8.88 | | | (27) member(all_72_0, all_32_4) = all_133_1
% 59.90/8.88 | | | (28) ~ (all_133_0 = 0) | ~ (all_133_1 = 0)
% 59.90/8.88 | | |
% 59.90/8.88 | | | BETA: splitting (11) gives:
% 59.90/8.88 | | |
% 59.90/8.88 | | | Case 1:
% 59.90/8.88 | | | |
% 59.90/8.88 | | | | (29) all_81_0 = 0
% 59.90/8.88 | | | |
% 59.90/8.88 | | | | REDUCE: (12), (29) imply:
% 59.90/8.88 | | | | (30) $false
% 59.90/8.88 | | | |
% 59.90/8.88 | | | | CLOSE: (30) is inconsistent.
% 59.90/8.88 | | | |
% 59.90/8.88 | | | Case 2:
% 59.90/8.88 | | | |
% 59.90/8.88 | | | | (31) ? [v0: any] : ? [v1: any] : ((apply(all_32_6, all_72_0,
% 59.90/8.88 | | | | all_65_0) = v1 & member(all_65_0, all_32_3) = v0 & ( ~ (v1
% 59.90/8.88 | | | | = 0) | ~ (v0 = 0))) | (member(all_72_0, all_32_4) = v0
% 59.90/8.88 | | | | & member(all_57_0, all_32_2) = v1 & ( ~ (v1 = 0) | ~ (v0 =
% 59.90/8.88 | | | | 0))))
% 59.90/8.88 | | | |
% 59.90/8.88 | | | | DELTA: instantiating (31) with fresh symbols all_150_0, all_150_1 gives:
% 59.90/8.88 | | | | (32) (apply(all_32_6, all_72_0, all_65_0) = all_150_0 &
% 59.90/8.88 | | | | member(all_65_0, all_32_3) = all_150_1 & ( ~ (all_150_0 = 0) |
% 59.90/8.88 | | | | ~ (all_150_1 = 0))) | (member(all_72_0, all_32_4) =
% 59.90/8.88 | | | | all_150_1 & member(all_57_0, all_32_2) = all_150_0 & ( ~
% 59.90/8.88 | | | | (all_150_0 = 0) | ~ (all_150_1 = 0)))
% 59.90/8.88 | | | |
% 59.90/8.88 | | | | BETA: splitting (32) gives:
% 59.90/8.88 | | | |
% 59.90/8.88 | | | | Case 1:
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | | GROUND_INST: instantiating (9) with 0, all_133_0, all_32_2, all_57_0,
% 59.90/8.88 | | | | | simplifying with (1), (26) gives:
% 59.90/8.88 | | | | | (33) all_133_0 = 0
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | | GROUND_INST: instantiating (9) with 0, all_133_1, all_32_4, all_72_0,
% 59.90/8.88 | | | | | simplifying with (3), (27) gives:
% 59.90/8.88 | | | | | (34) all_133_1 = 0
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | | REF_CLOSE: (28), (33), (34) are inconsistent by sub-proof #6.
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | Case 2:
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | | (35) member(all_72_0, all_32_4) = all_150_1 & member(all_57_0,
% 59.90/8.88 | | | | | all_32_2) = all_150_0 & ( ~ (all_150_0 = 0) | ~ (all_150_1
% 59.90/8.88 | | | | | = 0))
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | | ALPHA: (35) implies:
% 59.90/8.88 | | | | | (36) member(all_57_0, all_32_2) = all_150_0
% 59.90/8.88 | | | | | (37) member(all_72_0, all_32_4) = all_150_1
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | | GROUND_INST: instantiating (9) with 0, all_150_0, all_32_2, all_57_0,
% 59.90/8.88 | | | | | simplifying with (1), (36) gives:
% 59.90/8.88 | | | | | (38) all_150_0 = 0
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | | GROUND_INST: instantiating (9) with all_133_0, all_150_0, all_32_2,
% 59.90/8.88 | | | | | all_57_0, simplifying with (26), (36) gives:
% 59.90/8.88 | | | | | (39) all_150_0 = all_133_0
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | | GROUND_INST: instantiating (9) with 0, all_150_1, all_32_4, all_72_0,
% 59.90/8.88 | | | | | simplifying with (3), (37) gives:
% 59.90/8.88 | | | | | (40) all_150_1 = 0
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | | GROUND_INST: instantiating (9) with all_133_1, all_150_1, all_32_4,
% 59.90/8.88 | | | | | all_72_0, simplifying with (27), (37) gives:
% 59.90/8.88 | | | | | (41) all_150_1 = all_133_1
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | | COMBINE_EQS: (38), (39) imply:
% 59.90/8.88 | | | | | (42) all_133_0 = 0
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | | COMBINE_EQS: (40), (41) imply:
% 59.90/8.88 | | | | | (43) all_133_1 = 0
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | | SIMP: (43) implies:
% 59.90/8.88 | | | | | (44) all_133_1 = 0
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | | REF_CLOSE: (28), (42), (44) are inconsistent by sub-proof #6.
% 59.90/8.88 | | | | |
% 59.90/8.88 | | | | End of split
% 59.90/8.88 | | | |
% 59.90/8.88 | | | End of split
% 59.90/8.88 | | |
% 59.90/8.88 | | End of split
% 59.90/8.88 | |
% 59.90/8.88 | Case 2:
% 59.90/8.88 | |
% 59.90/8.88 | | (45) ? [v0: any] : ? [v1: any] : (apply(all_32_5, all_85_0, all_57_0) =
% 59.90/8.88 | | v0 & apply(all_32_5, all_83_0, all_57_0) = v1 & ( ~ (v1 = 0) | ~
% 59.90/8.88 | | (v0 = 0)))
% 59.90/8.88 | |
% 59.90/8.88 | | DELTA: instantiating (45) with fresh symbols all_138_0, all_138_1 gives:
% 59.90/8.88 | | (46) apply(all_32_5, all_85_0, all_57_0) = all_138_1 & apply(all_32_5,
% 59.90/8.88 | | all_83_0, all_57_0) = all_138_0 & ( ~ (all_138_0 = 0) | ~
% 59.90/8.88 | | (all_138_1 = 0))
% 59.90/8.88 | |
% 59.90/8.88 | | ALPHA: (46) implies:
% 59.90/8.88 | | (47) apply(all_32_5, all_83_0, all_57_0) = all_138_0
% 59.90/8.88 | | (48) apply(all_32_5, all_85_0, all_57_0) = all_138_1
% 59.90/8.88 | | (49) ~ (all_138_0 = 0) | ~ (all_138_1 = 0)
% 59.90/8.88 | |
% 59.90/8.88 | | REDUCE: (8), (47) imply:
% 59.90/8.88 | | (50) apply(all_32_5, all_65_0, all_57_0) = all_138_0
% 59.90/8.88 | |
% 59.90/8.88 | | BETA: splitting (11) gives:
% 59.90/8.88 | |
% 59.90/8.88 | | Case 1:
% 59.90/8.88 | | |
% 59.90/8.88 | | | (51) all_81_0 = 0
% 59.90/8.88 | | |
% 59.90/8.88 | | | REDUCE: (12), (51) imply:
% 59.90/8.89 | | | (52) $false
% 59.90/8.89 | | |
% 59.90/8.89 | | | CLOSE: (52) is inconsistent.
% 59.90/8.89 | | |
% 59.90/8.89 | | Case 2:
% 59.90/8.89 | | |
% 59.90/8.89 | | |
% 59.90/8.89 | | | GROUND_INST: instantiating (7) with 0, all_138_0, all_57_0, all_65_0,
% 59.90/8.89 | | | all_32_5, simplifying with (2), (50) gives:
% 59.90/8.89 | | | (53) all_138_0 = 0
% 59.90/8.89 | | |
% 59.90/8.89 | | | GROUND_INST: instantiating (7) with 0, all_138_1, all_57_0, all_85_0,
% 59.90/8.89 | | | all_32_5, simplifying with (10), (48) gives:
% 59.90/8.89 | | | (54) all_138_1 = 0
% 59.90/8.89 | | |
% 59.90/8.89 | | | BETA: splitting (49) gives:
% 59.90/8.89 | | |
% 59.90/8.89 | | | Case 1:
% 59.90/8.89 | | | |
% 59.90/8.89 | | | | (55) ~ (all_138_0 = 0)
% 59.90/8.89 | | | |
% 59.90/8.89 | | | | REDUCE: (53), (55) imply:
% 59.90/8.89 | | | | (56) $false
% 59.90/8.89 | | | |
% 59.90/8.89 | | | | CLOSE: (56) is inconsistent.
% 59.90/8.89 | | | |
% 59.90/8.89 | | | Case 2:
% 59.90/8.89 | | | |
% 59.90/8.89 | | | | (57) ~ (all_138_1 = 0)
% 59.90/8.89 | | | |
% 59.90/8.89 | | | | REDUCE: (54), (57) imply:
% 59.90/8.89 | | | | (58) $false
% 59.90/8.89 | | | |
% 59.90/8.89 | | | | CLOSE: (58) is inconsistent.
% 59.90/8.89 | | | |
% 59.90/8.89 | | | End of split
% 59.90/8.89 | | |
% 59.90/8.89 | | End of split
% 59.90/8.89 | |
% 59.90/8.89 | End of split
% 59.90/8.89 |
% 59.90/8.89 End of proof
% 59.90/8.89
% 59.90/8.89 Sub-proof #6 shows that the following formulas are inconsistent:
% 59.90/8.89 ----------------------------------------------------------------
% 59.90/8.89 (1) ~ (all_133_0 = 0) | ~ (all_133_1 = 0)
% 59.90/8.89 (2) all_133_0 = 0
% 59.90/8.89 (3) all_133_1 = 0
% 59.90/8.89
% 59.90/8.89 Begin of proof
% 59.90/8.89 |
% 59.90/8.89 | BETA: splitting (1) gives:
% 59.90/8.89 |
% 59.90/8.89 | Case 1:
% 59.90/8.89 | |
% 59.90/8.89 | | (4) ~ (all_133_0 = 0)
% 59.90/8.89 | |
% 59.90/8.89 | | REDUCE: (2), (4) imply:
% 59.90/8.89 | | (5) $false
% 59.90/8.89 | |
% 59.90/8.89 | | CLOSE: (5) is inconsistent.
% 59.90/8.89 | |
% 59.90/8.89 | Case 2:
% 59.90/8.89 | |
% 59.90/8.89 | | (6) ~ (all_133_1 = 0)
% 59.90/8.89 | |
% 59.90/8.89 | | REDUCE: (3), (6) imply:
% 59.90/8.89 | | (7) $false
% 59.90/8.89 | |
% 59.90/8.89 | | CLOSE: (7) is inconsistent.
% 59.90/8.89 | |
% 59.90/8.89 | End of split
% 59.90/8.89 |
% 59.90/8.89 End of proof
% 59.90/8.89 % SZS output end Proof for theBenchmark
% 59.90/8.89
% 59.90/8.89 8259ms
%------------------------------------------------------------------------------