TSTP Solution File: SET726+4 by Princess---230619
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- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET726+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 : n031.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 15:26:10 EDT 2023
% Result : Theorem 29.85s 4.77s
% Output : Proof 107.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET726+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.12/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.34 % Computer : n031.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Sat Aug 26 12:17:08 EDT 2023
% 0.19/0.35 % CPUTime :
% 0.20/0.61 ________ _____
% 0.20/0.61 ___ __ \_________(_)________________________________
% 0.20/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.61
% 0.20/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.61 (2023-06-19)
% 0.20/0.61
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.64 Running up to 7 provers in parallel.
% 0.20/0.66 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.66 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.66 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.66 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.66 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.66 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.66 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 3.71/1.24 Prover 1: Preprocessing ...
% 3.71/1.24 Prover 4: Preprocessing ...
% 4.36/1.28 Prover 5: Preprocessing ...
% 4.36/1.28 Prover 3: Preprocessing ...
% 4.36/1.28 Prover 0: Preprocessing ...
% 4.36/1.28 Prover 2: Preprocessing ...
% 4.36/1.28 Prover 6: Preprocessing ...
% 9.83/2.06 Prover 2: Proving ...
% 9.83/2.06 Prover 5: Proving ...
% 10.68/2.15 Prover 6: Proving ...
% 11.04/2.20 Prover 3: Constructing countermodel ...
% 11.04/2.21 Prover 1: Constructing countermodel ...
% 14.36/2.74 Prover 4: Constructing countermodel ...
% 15.19/2.76 Prover 0: Proving ...
% 29.85/4.77 Prover 0: proved (4119ms)
% 29.85/4.77
% 29.85/4.77 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 29.85/4.77
% 29.85/4.77 Prover 3: stopped
% 29.85/4.78 Prover 5: stopped
% 29.85/4.78 Prover 2: stopped
% 29.85/4.79 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 29.85/4.79 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 29.85/4.79 Prover 6: stopped
% 29.85/4.80 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 29.85/4.80 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 29.85/4.81 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 30.88/4.85 Prover 10: Preprocessing ...
% 31.07/4.86 Prover 7: Preprocessing ...
% 31.09/4.90 Prover 13: Preprocessing ...
% 31.38/4.90 Prover 11: Preprocessing ...
% 31.38/4.90 Prover 8: Preprocessing ...
% 31.68/4.98 Prover 10: Warning: ignoring some quantifiers
% 31.68/4.99 Prover 7: Warning: ignoring some quantifiers
% 31.68/4.99 Prover 10: Constructing countermodel ...
% 31.68/5.00 Prover 7: Constructing countermodel ...
% 32.91/5.11 Prover 13: Warning: ignoring some quantifiers
% 32.91/5.12 Prover 10: gave up
% 32.91/5.13 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 32.91/5.13 Prover 13: Constructing countermodel ...
% 33.73/5.20 Prover 8: Warning: ignoring some quantifiers
% 33.73/5.20 Prover 16: Preprocessing ...
% 33.73/5.21 Prover 8: Constructing countermodel ...
% 34.03/5.39 Prover 16: Warning: ignoring some quantifiers
% 34.03/5.41 Prover 16: Constructing countermodel ...
% 38.76/5.90 Prover 11: Constructing countermodel ...
% 69.81/9.97 Prover 13: stopped
% 69.81/9.99 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 70.66/10.04 Prover 19: Preprocessing ...
% 72.29/10.26 Prover 19: Warning: ignoring some quantifiers
% 72.29/10.28 Prover 19: Constructing countermodel ...
% 83.62/11.74 Prover 16: stopped
% 100.40/13.91 Prover 19: stopped
% 106.02/14.65 Prover 4: Found proof (size 633)
% 106.02/14.65 Prover 4: proved (13999ms)
% 106.02/14.65 Prover 1: stopped
% 106.02/14.65 Prover 7: stopped
% 106.02/14.65 Prover 11: stopped
% 106.02/14.65 Prover 8: stopped
% 106.02/14.65
% 106.02/14.65 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 106.02/14.65
% 106.02/14.67 % SZS output start Proof for theBenchmark
% 106.02/14.67 Assumptions after simplification:
% 106.02/14.67 ---------------------------------
% 106.02/14.67
% 106.02/14.67 (compose_function)
% 106.20/14.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 106.20/14.71 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~
% 106.20/14.71 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) |
% 106.20/14.71 ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) |
% 106.20/14.71 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any]
% 106.20/14.71 : ((apply(v0, v9, v6) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10
% 106.20/14.71 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 =
% 106.20/14.71 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 106.20/14.71 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 106.20/14.71 int] : ! [v9: $i] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) =
% 106.20/14.71 v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9)
% 106.20/14.71 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 106.20/14.71 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v11 &
% 106.20/14.71 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4)
% 106.20/14.71 = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & !
% 106.20/14.71 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 106.20/14.71 : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~
% 106.20/14.71 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) |
% 106.20/14.71 ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~
% 106.20/14.71 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] :
% 106.20/14.71 ((apply(v1, v5, v9) = v10 & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~
% 106.20/14.71 (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11
% 106.20/14.71 = 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 106.20/14.71 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 106.20/14.71 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) |
% 106.20/14.71 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 106.20/14.71 $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ?
% 106.20/14.71 [v12: int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 &
% 106.20/14.71 apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, v3) = 0)
% 106.20/14.71 | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 =
% 106.20/14.71 0))))))
% 106.20/14.71
% 106.20/14.71 (equal_maps)
% 106.20/14.72 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 106.20/14.72 $i] : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~
% 106.20/14.72 (apply(v1, v4, v6) = 0) | ~ (apply(v0, v4, v5) = 0) | ~ $i(v6) | ~ $i(v5)
% 106.20/14.72 | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] :
% 106.20/14.72 ? [v8: any] : ? [v9: any] : (member(v6, v3) = v9 & member(v5, v3) = v8 &
% 106.20/14.72 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & !
% 106.20/14.72 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 106.20/14.72 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v1,
% 106.20/14.72 v4, v6) = 0) | ~ (member(v5, v3) = 0) | ~ $i(v6) | ~ $i(v5) | ~
% 106.20/14.72 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ?
% 106.20/14.72 [v8: any] : ? [v9: any] : (apply(v0, v4, v5) = v9 & member(v6, v3) = v8 &
% 106.20/14.72 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & !
% 106.20/14.72 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 106.20/14.72 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~ (apply(v0,
% 106.20/14.72 v4, v5) = 0) | ~ (member(v6, v3) = 0) | ~ $i(v6) | ~ $i(v5) | ~
% 106.20/14.72 $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v7: any] : ?
% 106.20/14.72 [v8: any] : ? [v9: any] : (apply(v1, v4, v6) = v9 & member(v5, v3) = v8 &
% 106.20/14.72 member(v4, v2) = v7 & ( ~ (v9 = 0) | ~ (v8 = 0) | ~ (v7 = 0)))) & !
% 106.20/14.72 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 106.20/14.72 : ! [v6: $i] : (v6 = v5 | ~ (equal_maps(v0, v1, v2, v3) = 0) | ~
% 106.20/14.72 (member(v6, v3) = 0) | ~ (member(v5, v3) = 0) | ~ (member(v4, v2) = 0) |
% 106.20/14.72 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 106.20/14.72 $i(v0) | ? [v7: any] : ? [v8: any] : (apply(v1, v4, v6) = v8 & apply(v0,
% 106.20/14.72 v4, v5) = v7 & ( ~ (v8 = 0) | ~ (v7 = 0)))) & ! [v0: $i] : ! [v1: $i]
% 106.20/14.73 : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0 | ~ (equal_maps(v0, v1,
% 106.20/14.73 v2, v3) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 106.20/14.73 $i] : ? [v6: $i] : ? [v7: $i] : ( ~ (v7 = v6) & apply(v1, v5, v7) = 0 &
% 106.20/14.73 apply(v0, v5, v6) = 0 & member(v7, v3) = 0 & member(v6, v3) = 0 &
% 106.20/14.73 member(v5, v2) = 0 & $i(v7) & $i(v6) & $i(v5)))
% 106.20/14.73
% 106.20/14.73 (identity)
% 106.20/14.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 106.20/14.73 (identity(v0, v1) = 0) | ~ (apply(v0, v2, v2) = v3) | ~ $i(v2) | ~ $i(v1)
% 106.20/14.73 | ~ $i(v0) | ? [v4: int] : ( ~ (v4 = 0) & member(v2, v1) = v4)) & ! [v0:
% 106.20/14.73 $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (identity(v0, v1) = v2) | ~
% 106.20/14.73 $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & apply(v0,
% 106.20/14.73 v3, v3) = v4 & member(v3, v1) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i]
% 106.20/14.73 : ! [v2: $i] : ( ~ (identity(v0, v1) = 0) | ~ (member(v2, v1) = 0) | ~
% 106.20/14.73 $i(v2) | ~ $i(v1) | ~ $i(v0) | apply(v0, v2, v2) = 0)
% 106.20/14.73
% 106.20/14.73 (inverse_function)
% 106.20/14.73 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 106.20/14.73 $i] : ! [v6: any] : ( ~ (inverse_function(v0, v1, v2) = v5) | ~ (apply(v5,
% 106.20/14.73 v4, v3) = v6) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 106.20/14.73 $i(v0) | ? [v7: any] : ? [v8: any] : ? [v9: any] : (apply(v0, v3, v4) =
% 106.20/14.73 v9 & member(v4, v2) = v8 & member(v3, v1) = v7 & ( ~ (v8 = 0) | ~ (v7 =
% 106.20/14.73 0) | (( ~ (v9 = 0) | v6 = 0) & ( ~ (v6 = 0) | v9 = 0)))))
% 106.20/14.73
% 106.20/14.73 (maps)
% 106.46/14.74 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 106.46/14.74 $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~
% 106.46/14.74 (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 106.46/14.74 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 106.46/14.74 (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 =
% 106.46/14.74 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 106.46/14.74 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0,
% 106.46/14.74 v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ~
% 106.46/14.74 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 106.46/14.74 any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5,
% 106.46/14.74 v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 =
% 106.46/14.74 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 106.46/14.74 [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0,
% 106.46/14.74 v3, v4) = 0) | ~ (member(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 106.46/14.74 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 106.46/14.74 ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v4, v2) = v7 & member(v3, v1)
% 106.46/14.74 = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1:
% 106.46/14.74 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 106.46/14.74 (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) |
% 106.46/14.74 ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 106.46/14.74 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 &
% 106.46/14.74 apply(v0, v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : !
% 106.46/14.74 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) |
% 106.46/14.74 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 106.46/14.74 : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int]
% 106.46/14.74 : ? [v12: $i] : ? [v13: int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13
% 106.46/14.74 = 0 & member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) =
% 106.46/14.74 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & member(v14, v2)
% 106.46/14.74 = v15)) & ! [v14: $i] : ( ~ (member(v14, v2) = 0) | ~ $i(v14) |
% 106.46/14.74 ? [v15: int] : ( ~ (v15 = 0) & apply(v0, v12, v14) = v15))) | (v11 =
% 106.46/14.74 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4,
% 106.46/14.74 v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5,
% 106.46/14.74 v2) = 0 & member(v4, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 106.46/14.74 [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0)
% 106.46/14.74 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0,
% 106.46/14.74 v3, v4) = 0 & member(v4, v2) = 0 & $i(v4)))
% 106.46/14.74
% 106.46/14.74 (thII17)
% 106.46/14.74 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 106.46/14.74 $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: int] : ( ~ (v8 = 0) &
% 106.46/14.74 inverse_function(v0, v3, v4) = v7 & identity(v6, v4) = 0 & identity(v5, v3)
% 106.46/14.74 = 0 & equal_maps(v7, v1, v4, v3) = v8 & compose_function(v1, v0, v3, v4, v3)
% 106.46/14.74 = v5 & compose_function(v0, v2, v4, v3, v4) = v6 & maps(v2, v4, v3) = 0 &
% 106.46/14.74 maps(v1, v4, v3) = 0 & maps(v0, v3, v4) = 0 & $i(v7) & $i(v6) & $i(v5) &
% 106.46/14.74 $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 106.46/14.74
% 106.46/14.74 (function-axioms)
% 106.54/14.75 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 106.54/14.75 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 106.54/14.75 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~
% 106.54/14.75 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 106.54/14.75 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 106.54/14.75 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5,
% 106.54/14.75 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 106.54/14.75 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 106.54/14.75 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5,
% 106.54/14.75 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 106.54/14.75 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 106.54/14.75 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5,
% 106.54/14.75 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 106.54/14.75 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 106.54/14.75 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~
% 106.54/14.75 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 106.54/14.75 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 106.54/14.75 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~
% 106.54/14.75 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 106.54/14.75 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 106.54/14.75 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5,
% 106.54/14.75 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 106.54/14.75 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~
% 106.54/14.75 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 106.54/14.75 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~
% 106.54/14.75 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 106.54/14.75 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) |
% 106.54/14.75 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 106.54/14.75 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 106.54/14.75 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & !
% 106.54/14.75 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 106.54/14.75 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~
% 106.54/14.75 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 106.54/14.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 106.54/14.75 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0:
% 106.54/14.75 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 106.54/14.75 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) =
% 106.54/14.75 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 106.54/14.75 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 106.54/14.75 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 106.54/14.75 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~
% 106.54/14.75 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 106.54/14.75 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) &
% 106.54/14.75 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 106.54/14.75 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 106.54/14.75 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 106.54/14.75 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 106.54/14.75 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 106.54/14.75 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 106.54/14.75 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 106.54/14.75 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 106.54/14.75 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 106.54/14.75 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 106.54/14.75 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 106.54/14.75 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 106.54/14.75 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 106.54/14.75 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 106.54/14.75 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 106.54/14.75 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 106.54/14.75 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 106.54/14.75 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 106.54/14.75 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 106.54/14.75 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 106.54/14.75 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 106.54/14.75 (power_set(v2) = v0))
% 106.54/14.75
% 106.54/14.75 Further assumptions not needed in the proof:
% 106.54/14.75 --------------------------------------------
% 106.54/14.75 compose_predicate, decreasing_function, difference, empty_set, equal_set,
% 106.54/14.75 image2, image3, increasing_function, injective, intersection, inverse_image2,
% 106.54/14.75 inverse_image3, inverse_predicate, isomorphism, one_to_one, power_set, product,
% 106.54/14.75 singleton, subset, sum, surjective, union, unordered_pair
% 106.54/14.76
% 106.54/14.76 Those formulas are unsatisfiable:
% 106.54/14.76 ---------------------------------
% 106.54/14.76
% 106.54/14.76 Begin of proof
% 106.54/14.76 |
% 106.54/14.76 | ALPHA: (maps) implies:
% 106.54/14.76 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (maps(v0,
% 106.54/14.76 | v1, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) |
% 106.54/14.76 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v3, v4) = 0 &
% 106.54/14.76 | member(v4, v2) = 0 & $i(v4)))
% 106.54/14.76 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 106.54/14.76 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2)
% 106.54/14.76 | = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~
% 106.54/14.76 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 106.54/14.76 | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & apply(v0, v3,
% 106.54/14.76 | v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 106.54/14.76 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 106.54/14.76 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3,
% 106.54/14.76 | v5) = 0) | ~ (member(v4, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 106.54/14.76 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 106.54/14.76 | any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, v2) = v7
% 106.54/14.76 | & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 106.54/14.76 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 106.54/14.76 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3,
% 106.54/14.76 | v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) |
% 106.54/14.76 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 106.54/14.76 | any] : ? [v8: any] : (member(v5, v2) = v8 & member(v4, v2) = v7 &
% 106.54/14.76 | member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 106.54/14.76 |
% 106.54/14.76 | ALPHA: (compose_function) implies:
% 106.54/14.76 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 106.54/14.76 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (compose_function(v0, v1,
% 106.54/14.76 | v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | ~ $i(v6) | ~
% 106.54/14.76 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 106.54/14.76 | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ? [v12:
% 106.54/14.76 | int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 &
% 106.54/14.76 | apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10,
% 106.54/14.76 | v3) = 0) | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~
% 106.54/14.76 | (v9 = 0) | ~ (v8 = 0))))))
% 106.54/14.76 |
% 106.54/14.76 | ALPHA: (equal_maps) implies:
% 106.54/14.76 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 106.54/14.76 | (v4 = 0 | ~ (equal_maps(v0, v1, v2, v3) = v4) | ~ $i(v3) | ~ $i(v2)
% 106.54/14.76 | | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : (
% 106.54/14.76 | ~ (v7 = v6) & apply(v1, v5, v7) = 0 & apply(v0, v5, v6) = 0 &
% 106.54/14.76 | member(v7, v3) = 0 & member(v6, v3) = 0 & member(v5, v2) = 0 &
% 106.54/14.76 | $i(v7) & $i(v6) & $i(v5)))
% 106.54/14.76 |
% 106.54/14.76 | ALPHA: (identity) implies:
% 106.54/14.77 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (identity(v0, v1) = 0) |
% 106.54/14.77 | ~ (member(v2, v1) = 0) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 106.54/14.77 | apply(v0, v2, v2) = 0)
% 106.54/14.77 |
% 106.54/14.77 | ALPHA: (function-axioms) implies:
% 106.54/14.77 | (8) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 106.54/14.77 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 106.54/14.77 | = v0))
% 106.54/14.77 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 106.54/14.77 | ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~
% 106.54/14.77 | (apply(v4, v3, v2) = v0))
% 106.54/14.77 |
% 106.54/14.77 | DELTA: instantiating (thII17) with fresh symbols all_32_0, all_32_1, all_32_2,
% 106.54/14.77 | all_32_3, all_32_4, all_32_5, all_32_6, all_32_7, all_32_8 gives:
% 106.54/14.77 | (10) ~ (all_32_0 = 0) & inverse_function(all_32_8, all_32_5, all_32_4) =
% 106.54/14.77 | all_32_1 & identity(all_32_2, all_32_4) = 0 & identity(all_32_3,
% 106.54/14.77 | all_32_5) = 0 & equal_maps(all_32_1, all_32_7, all_32_4, all_32_5) =
% 106.54/14.77 | all_32_0 & compose_function(all_32_7, all_32_8, all_32_5, all_32_4,
% 106.54/14.77 | all_32_5) = all_32_3 & compose_function(all_32_8, all_32_6,
% 106.54/14.77 | all_32_4, all_32_5, all_32_4) = all_32_2 & maps(all_32_6, all_32_4,
% 106.54/14.77 | all_32_5) = 0 & maps(all_32_7, all_32_4, all_32_5) = 0 &
% 106.54/14.77 | maps(all_32_8, all_32_5, all_32_4) = 0 & $i(all_32_1) & $i(all_32_2) &
% 106.54/14.77 | $i(all_32_3) & $i(all_32_4) & $i(all_32_5) & $i(all_32_6) &
% 106.54/14.77 | $i(all_32_7) & $i(all_32_8)
% 106.54/14.77 |
% 106.54/14.77 | ALPHA: (10) implies:
% 106.54/14.77 | (11) ~ (all_32_0 = 0)
% 106.54/14.77 | (12) $i(all_32_8)
% 106.54/14.77 | (13) $i(all_32_7)
% 106.54/14.77 | (14) $i(all_32_6)
% 106.54/14.77 | (15) $i(all_32_5)
% 106.54/14.77 | (16) $i(all_32_4)
% 106.54/14.77 | (17) $i(all_32_3)
% 106.54/14.77 | (18) $i(all_32_2)
% 106.54/14.77 | (19) $i(all_32_1)
% 106.54/14.77 | (20) maps(all_32_8, all_32_5, all_32_4) = 0
% 106.54/14.77 | (21) maps(all_32_7, all_32_4, all_32_5) = 0
% 106.54/14.77 | (22) maps(all_32_6, all_32_4, all_32_5) = 0
% 106.54/14.77 | (23) compose_function(all_32_8, all_32_6, all_32_4, all_32_5, all_32_4) =
% 106.54/14.77 | all_32_2
% 106.54/14.77 | (24) compose_function(all_32_7, all_32_8, all_32_5, all_32_4, all_32_5) =
% 106.54/14.77 | all_32_3
% 106.54/14.77 | (25) equal_maps(all_32_1, all_32_7, all_32_4, all_32_5) = all_32_0
% 106.54/14.77 | (26) identity(all_32_3, all_32_5) = 0
% 106.54/14.77 | (27) identity(all_32_2, all_32_4) = 0
% 106.54/14.77 | (28) inverse_function(all_32_8, all_32_5, all_32_4) = all_32_1
% 106.54/14.77 |
% 106.54/14.77 | GROUND_INST: instantiating (6) with all_32_1, all_32_7, all_32_4, all_32_5,
% 106.54/14.77 | all_32_0, simplifying with (13), (15), (16), (19), (25) gives:
% 106.54/14.77 | (29) all_32_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1)
% 106.54/14.77 | & apply(all_32_1, v0, v1) = 0 & apply(all_32_7, v0, v2) = 0 &
% 106.54/14.77 | member(v2, all_32_5) = 0 & member(v1, all_32_5) = 0 & member(v0,
% 106.54/14.77 | all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0))
% 106.54/14.77 |
% 106.54/14.77 | BETA: splitting (29) gives:
% 106.54/14.77 |
% 106.54/14.77 | Case 1:
% 106.54/14.77 | |
% 106.54/14.77 | | (30) all_32_0 = 0
% 106.54/14.77 | |
% 106.54/14.77 | | REDUCE: (11), (30) imply:
% 106.54/14.77 | | (31) $false
% 106.54/14.77 | |
% 106.54/14.77 | | CLOSE: (31) is inconsistent.
% 106.54/14.77 | |
% 106.54/14.77 | Case 2:
% 106.54/14.77 | |
% 106.54/14.78 | | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ( ~ (v2 = v1) &
% 106.54/14.78 | | apply(all_32_1, v0, v1) = 0 & apply(all_32_7, v0, v2) = 0 &
% 106.54/14.78 | | member(v2, all_32_5) = 0 & member(v1, all_32_5) = 0 & member(v0,
% 106.54/14.78 | | all_32_4) = 0 & $i(v2) & $i(v1) & $i(v0))
% 106.54/14.78 | |
% 106.54/14.78 | | DELTA: instantiating (32) with fresh symbols all_41_0, all_41_1, all_41_2
% 106.54/14.78 | | gives:
% 106.54/14.78 | | (33) ~ (all_41_0 = all_41_1) & apply(all_32_1, all_41_2, all_41_1) = 0 &
% 106.54/14.78 | | apply(all_32_7, all_41_2, all_41_0) = 0 & member(all_41_0, all_32_5)
% 106.54/14.78 | | = 0 & member(all_41_1, all_32_5) = 0 & member(all_41_2, all_32_4) =
% 106.54/14.78 | | 0 & $i(all_41_0) & $i(all_41_1) & $i(all_41_2)
% 106.54/14.78 | |
% 106.54/14.78 | | ALPHA: (33) implies:
% 106.54/14.78 | | (34) ~ (all_41_0 = all_41_1)
% 106.54/14.78 | | (35) $i(all_41_2)
% 106.54/14.78 | | (36) $i(all_41_1)
% 106.54/14.78 | | (37) $i(all_41_0)
% 106.54/14.78 | | (38) member(all_41_2, all_32_4) = 0
% 106.54/14.78 | | (39) member(all_41_1, all_32_5) = 0
% 106.54/14.78 | | (40) member(all_41_0, all_32_5) = 0
% 106.54/14.78 | | (41) apply(all_32_7, all_41_2, all_41_0) = 0
% 106.54/14.78 | | (42) apply(all_32_1, all_41_2, all_41_1) = 0
% 106.54/14.78 | |
% 106.54/14.78 | | GROUND_INST: instantiating (1) with all_32_6, all_32_4, all_32_5, all_41_2,
% 106.54/14.78 | | simplifying with (14), (15), (16), (22), (35), (38) gives:
% 106.54/14.78 | | (43) ? [v0: $i] : (apply(all_32_6, all_41_2, v0) = 0 & member(v0,
% 106.54/14.78 | | all_32_5) = 0 & $i(v0))
% 106.54/14.78 | |
% 106.54/14.78 | | GROUND_INST: instantiating (1) with all_32_7, all_32_4, all_32_5, all_41_2,
% 106.54/14.78 | | simplifying with (13), (15), (16), (21), (35), (38) gives:
% 106.54/14.78 | | (44) ? [v0: $i] : (apply(all_32_7, all_41_2, v0) = 0 & member(v0,
% 106.54/14.78 | | all_32_5) = 0 & $i(v0))
% 106.54/14.78 | |
% 106.54/14.78 | | GROUND_INST: instantiating (7) with all_32_2, all_32_4, all_41_2,
% 106.54/14.78 | | simplifying with (16), (18), (27), (35), (38) gives:
% 106.54/14.78 | | (45) apply(all_32_2, all_41_2, all_41_2) = 0
% 106.54/14.78 | |
% 106.54/14.78 | | GROUND_INST: instantiating (1) with all_32_8, all_32_5, all_32_4, all_41_1,
% 106.54/14.78 | | simplifying with (12), (15), (16), (20), (36), (39) gives:
% 106.54/14.78 | | (46) ? [v0: $i] : (apply(all_32_8, all_41_1, v0) = 0 & member(v0,
% 106.54/14.78 | | all_32_4) = 0 & $i(v0))
% 106.54/14.78 | |
% 106.54/14.78 | | GROUND_INST: instantiating (7) with all_32_3, all_32_5, all_41_1,
% 106.54/14.78 | | simplifying with (15), (17), (26), (36), (39) gives:
% 106.54/14.78 | | (47) apply(all_32_3, all_41_1, all_41_1) = 0
% 106.54/14.78 | |
% 106.54/14.78 | | GROUND_INST: instantiating (2) with all_32_7, all_32_4, all_32_5, all_41_2,
% 106.54/14.78 | | all_41_1, all_41_0, simplifying with (13), (15), (16), (21),
% 106.54/14.78 | | (35), (36), (37), (38), (39), (40) gives:
% 106.54/14.78 | | (48) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_7,
% 106.54/14.79 | | all_41_2, all_41_0) = v1 & apply(all_32_7, all_41_2, all_41_1) =
% 106.54/14.79 | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 106.54/14.79 | |
% 106.54/14.79 | | GROUND_INST: instantiating (2) with all_32_7, all_32_4, all_32_5, all_41_2,
% 106.54/14.79 | | all_41_0, all_41_1, simplifying with (13), (15), (16), (21),
% 106.54/14.79 | | (35), (36), (37), (38), (39), (40) gives:
% 106.54/14.79 | | (49) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_7,
% 106.54/14.79 | | all_41_2, all_41_0) = v0 & apply(all_32_7, all_41_2, all_41_1) =
% 106.54/14.79 | | v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 106.54/14.79 | |
% 106.54/14.79 | | GROUND_INST: instantiating (3) with all_32_7, all_32_4, all_32_5, all_41_2,
% 106.54/14.79 | | all_41_1, all_41_0, simplifying with (13), (15), (16), (21),
% 106.54/14.79 | | (35), (36), (37), (39), (41) gives:
% 106.54/14.79 | | (50) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 106.54/14.79 | | (apply(all_32_7, all_41_2, all_41_1) = v2 & member(all_41_0,
% 106.54/14.79 | | all_32_5) = v1 & member(all_41_2, all_32_4) = v0 & ( ~ (v2 = 0)
% 106.54/14.79 | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 106.54/14.79 | |
% 106.54/14.79 | | GROUND_INST: instantiating (inverse_function) with all_32_8, all_32_5,
% 106.54/14.79 | | all_32_4, all_41_1, all_41_2, all_32_1, 0, simplifying with
% 106.54/14.79 | | (12), (15), (16), (28), (35), (36), (42) gives:
% 106.54/14.79 | | (51) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_8,
% 106.54/14.79 | | all_41_1, all_41_2) = v2 & member(all_41_1, all_32_5) = v0 &
% 106.54/14.79 | | member(all_41_2, all_32_4) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0) | v2
% 106.54/14.79 | | = 0))
% 106.54/14.79 | |
% 106.54/14.79 | | DELTA: instantiating (46) with fresh symbol all_49_0 gives:
% 106.54/14.79 | | (52) apply(all_32_8, all_41_1, all_49_0) = 0 & member(all_49_0, all_32_4)
% 106.54/14.79 | | = 0 & $i(all_49_0)
% 106.54/14.79 | |
% 106.54/14.79 | | ALPHA: (52) implies:
% 106.54/14.79 | | (53) $i(all_49_0)
% 106.54/14.79 | | (54) member(all_49_0, all_32_4) = 0
% 106.54/14.79 | | (55) apply(all_32_8, all_41_1, all_49_0) = 0
% 106.54/14.79 | |
% 106.54/14.79 | | DELTA: instantiating (44) with fresh symbol all_53_0 gives:
% 106.54/14.79 | | (56) apply(all_32_7, all_41_2, all_53_0) = 0 & member(all_53_0, all_32_5)
% 106.54/14.79 | | = 0 & $i(all_53_0)
% 106.54/14.79 | |
% 106.54/14.79 | | ALPHA: (56) implies:
% 106.54/14.79 | | (57) $i(all_53_0)
% 106.54/14.79 | | (58) member(all_53_0, all_32_5) = 0
% 106.54/14.79 | | (59) apply(all_32_7, all_41_2, all_53_0) = 0
% 106.54/14.79 | |
% 106.54/14.79 | | DELTA: instantiating (43) with fresh symbol all_55_0 gives:
% 106.54/14.79 | | (60) apply(all_32_6, all_41_2, all_55_0) = 0 & member(all_55_0, all_32_5)
% 106.54/14.79 | | = 0 & $i(all_55_0)
% 106.54/14.79 | |
% 106.54/14.79 | | ALPHA: (60) implies:
% 106.54/14.79 | | (61) $i(all_55_0)
% 106.54/14.79 | | (62) member(all_55_0, all_32_5) = 0
% 106.54/14.79 | | (63) apply(all_32_6, all_41_2, all_55_0) = 0
% 106.54/14.79 | |
% 106.54/14.79 | | DELTA: instantiating (51) with fresh symbols all_57_0, all_57_1, all_57_2
% 106.54/14.79 | | gives:
% 106.54/14.79 | | (64) apply(all_32_8, all_41_1, all_41_2) = all_57_0 & member(all_41_1,
% 106.54/14.79 | | all_32_5) = all_57_2 & member(all_41_2, all_32_4) = all_57_1 & ( ~
% 106.54/14.79 | | (all_57_1 = 0) | ~ (all_57_2 = 0) | all_57_0 = 0)
% 106.54/14.79 | |
% 106.54/14.79 | | ALPHA: (64) implies:
% 106.54/14.79 | | (65) member(all_41_2, all_32_4) = all_57_1
% 106.54/14.79 | | (66) member(all_41_1, all_32_5) = all_57_2
% 106.54/14.79 | | (67) apply(all_32_8, all_41_1, all_41_2) = all_57_0
% 106.54/14.79 | | (68) ~ (all_57_1 = 0) | ~ (all_57_2 = 0) | all_57_0 = 0
% 106.54/14.79 | |
% 106.54/14.79 | | BETA: splitting (48) gives:
% 106.54/14.79 | |
% 106.54/14.79 | | Case 1:
% 106.54/14.79 | | |
% 106.54/14.79 | | | (69) all_41_0 = all_41_1
% 106.54/14.79 | | |
% 106.54/14.79 | | | REDUCE: (34), (69) imply:
% 106.54/14.79 | | | (70) $false
% 106.54/14.79 | | |
% 106.54/14.79 | | | CLOSE: (70) is inconsistent.
% 106.54/14.79 | | |
% 106.54/14.79 | | Case 2:
% 106.54/14.79 | | |
% 106.54/14.80 | | | (71) ? [v0: any] : ? [v1: any] : (apply(all_32_7, all_41_2, all_41_0)
% 106.54/14.80 | | | = v1 & apply(all_32_7, all_41_2, all_41_1) = v0 & ( ~ (v1 = 0) |
% 106.54/14.80 | | | ~ (v0 = 0)))
% 106.54/14.80 | | |
% 106.54/14.80 | | | DELTA: instantiating (71) with fresh symbols all_63_0, all_63_1 gives:
% 106.54/14.80 | | | (72) apply(all_32_7, all_41_2, all_41_0) = all_63_0 & apply(all_32_7,
% 106.54/14.80 | | | all_41_2, all_41_1) = all_63_1 & ( ~ (all_63_0 = 0) | ~
% 106.54/14.80 | | | (all_63_1 = 0))
% 106.54/14.80 | | |
% 106.54/14.80 | | | ALPHA: (72) implies:
% 106.54/14.80 | | | (73) apply(all_32_7, all_41_2, all_41_1) = all_63_1
% 106.54/14.80 | | | (74) apply(all_32_7, all_41_2, all_41_0) = all_63_0
% 106.54/14.80 | | |
% 106.54/14.80 | | | BETA: splitting (49) gives:
% 106.54/14.80 | | |
% 106.54/14.80 | | | Case 1:
% 106.54/14.80 | | | |
% 106.54/14.80 | | | | (75) all_41_0 = all_41_1
% 106.54/14.80 | | | |
% 106.54/14.80 | | | | REDUCE: (34), (75) imply:
% 106.54/14.80 | | | | (76) $false
% 106.54/14.80 | | | |
% 106.54/14.80 | | | | CLOSE: (76) is inconsistent.
% 106.54/14.80 | | | |
% 106.54/14.80 | | | Case 2:
% 106.54/14.80 | | | |
% 106.54/14.80 | | | | (77) ? [v0: any] : ? [v1: any] : (apply(all_32_7, all_41_2,
% 106.54/14.80 | | | | all_41_0) = v0 & apply(all_32_7, all_41_2, all_41_1) = v1 &
% 106.54/14.80 | | | | ( ~ (v1 = 0) | ~ (v0 = 0)))
% 106.54/14.80 | | | |
% 106.54/14.80 | | | | DELTA: instantiating (77) with fresh symbols all_68_0, all_68_1 gives:
% 106.54/14.80 | | | | (78) apply(all_32_7, all_41_2, all_41_0) = all_68_1 & apply(all_32_7,
% 106.54/14.80 | | | | all_41_2, all_41_1) = all_68_0 & ( ~ (all_68_0 = 0) | ~
% 106.54/14.80 | | | | (all_68_1 = 0))
% 106.54/14.80 | | | |
% 106.54/14.80 | | | | ALPHA: (78) implies:
% 106.54/14.80 | | | | (79) apply(all_32_7, all_41_2, all_41_1) = all_68_0
% 106.54/14.80 | | | | (80) apply(all_32_7, all_41_2, all_41_0) = all_68_1
% 106.54/14.80 | | | |
% 106.54/14.80 | | | | BETA: splitting (50) gives:
% 106.54/14.80 | | | |
% 106.54/14.80 | | | | Case 1:
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | (81) all_41_0 = all_41_1
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | REDUCE: (34), (81) imply:
% 106.54/14.80 | | | | | (82) $false
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | CLOSE: (82) is inconsistent.
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | Case 2:
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | (83) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_7,
% 106.54/14.80 | | | | | all_41_2, all_41_1) = v2 & member(all_41_0, all_32_5) = v1
% 106.54/14.80 | | | | | & member(all_41_2, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 =
% 106.54/14.80 | | | | | 0) | ~ (v0 = 0)))
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | DELTA: instantiating (83) with fresh symbols all_78_0, all_78_1,
% 106.54/14.80 | | | | | all_78_2 gives:
% 106.54/14.80 | | | | | (84) apply(all_32_7, all_41_2, all_41_1) = all_78_0 &
% 106.54/14.80 | | | | | member(all_41_0, all_32_5) = all_78_1 & member(all_41_2,
% 106.54/14.80 | | | | | all_32_4) = all_78_2 & ( ~ (all_78_0 = 0) | ~ (all_78_1 =
% 106.54/14.80 | | | | | 0) | ~ (all_78_2 = 0))
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | ALPHA: (84) implies:
% 106.54/14.80 | | | | | (85) member(all_41_2, all_32_4) = all_78_2
% 106.54/14.80 | | | | | (86) member(all_41_0, all_32_5) = all_78_1
% 106.54/14.80 | | | | | (87) apply(all_32_7, all_41_2, all_41_1) = all_78_0
% 106.54/14.80 | | | | | (88) ~ (all_78_0 = 0) | ~ (all_78_1 = 0) | ~ (all_78_2 = 0)
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | GROUND_INST: instantiating (8) with 0, all_78_2, all_32_4, all_41_2,
% 106.54/14.80 | | | | | simplifying with (38), (85) gives:
% 106.54/14.80 | | | | | (89) all_78_2 = 0
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | GROUND_INST: instantiating (8) with all_57_1, all_78_2, all_32_4,
% 106.54/14.80 | | | | | all_41_2, simplifying with (65), (85) gives:
% 106.54/14.80 | | | | | (90) all_78_2 = all_57_1
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | GROUND_INST: instantiating (8) with 0, all_57_2, all_32_5, all_41_1,
% 106.54/14.80 | | | | | simplifying with (39), (66) gives:
% 106.54/14.80 | | | | | (91) all_57_2 = 0
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | GROUND_INST: instantiating (8) with 0, all_78_1, all_32_5, all_41_0,
% 106.54/14.80 | | | | | simplifying with (40), (86) gives:
% 106.54/14.80 | | | | | (92) all_78_1 = 0
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | GROUND_INST: instantiating (9) with all_68_0, all_78_0, all_41_1,
% 106.54/14.80 | | | | | all_41_2, all_32_7, simplifying with (79), (87) gives:
% 106.54/14.80 | | | | | (93) all_78_0 = all_68_0
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | GROUND_INST: instantiating (9) with all_63_1, all_78_0, all_41_1,
% 106.54/14.80 | | | | | all_41_2, all_32_7, simplifying with (73), (87) gives:
% 106.54/14.80 | | | | | (94) all_78_0 = all_63_1
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | GROUND_INST: instantiating (9) with 0, all_68_1, all_41_0, all_41_2,
% 106.54/14.80 | | | | | all_32_7, simplifying with (41), (80) gives:
% 106.54/14.80 | | | | | (95) all_68_1 = 0
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | GROUND_INST: instantiating (9) with all_63_0, all_68_1, all_41_0,
% 106.54/14.80 | | | | | all_41_2, all_32_7, simplifying with (74), (80) gives:
% 106.54/14.80 | | | | | (96) all_68_1 = all_63_0
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | COMBINE_EQS: (93), (94) imply:
% 106.54/14.80 | | | | | (97) all_68_0 = all_63_1
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | SIMP: (97) implies:
% 106.54/14.80 | | | | | (98) all_68_0 = all_63_1
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | COMBINE_EQS: (89), (90) imply:
% 106.54/14.80 | | | | | (99) all_57_1 = 0
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | SIMP: (99) implies:
% 106.54/14.80 | | | | | (100) all_57_1 = 0
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | COMBINE_EQS: (95), (96) imply:
% 106.54/14.80 | | | | | (101) all_63_0 = 0
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | SIMP: (101) implies:
% 106.54/14.80 | | | | | (102) all_63_0 = 0
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | BETA: splitting (88) gives:
% 106.54/14.80 | | | | |
% 106.54/14.80 | | | | | Case 1:
% 106.54/14.80 | | | | | |
% 106.54/14.81 | | | | | | (103) ~ (all_78_0 = 0)
% 106.54/14.81 | | | | | |
% 106.54/14.81 | | | | | | REDUCE: (94), (103) imply:
% 106.54/14.81 | | | | | | (104) ~ (all_63_1 = 0)
% 106.54/14.81 | | | | | |
% 106.54/14.81 | | | | | | BETA: splitting (68) gives:
% 106.54/14.81 | | | | | |
% 106.54/14.81 | | | | | | Case 1:
% 106.54/14.81 | | | | | | |
% 106.54/14.81 | | | | | | | (105) ~ (all_57_1 = 0)
% 106.54/14.81 | | | | | | |
% 106.54/14.81 | | | | | | | REDUCE: (100), (105) imply:
% 106.54/14.81 | | | | | | | (106) $false
% 106.54/14.81 | | | | | | |
% 106.54/14.81 | | | | | | | CLOSE: (106) is inconsistent.
% 106.54/14.81 | | | | | | |
% 106.54/14.81 | | | | | | Case 2:
% 106.54/14.81 | | | | | | |
% 106.54/14.81 | | | | | | | (107) ~ (all_57_2 = 0) | all_57_0 = 0
% 106.54/14.81 | | | | | | |
% 106.54/14.81 | | | | | | | BETA: splitting (107) gives:
% 106.54/14.81 | | | | | | |
% 106.54/14.81 | | | | | | | Case 1:
% 106.54/14.81 | | | | | | | |
% 106.54/14.81 | | | | | | | | (108) ~ (all_57_2 = 0)
% 106.54/14.81 | | | | | | | |
% 106.54/14.81 | | | | | | | | REDUCE: (91), (108) imply:
% 106.54/14.81 | | | | | | | | (109) $false
% 106.54/14.81 | | | | | | | |
% 106.54/14.81 | | | | | | | | CLOSE: (109) is inconsistent.
% 106.54/14.81 | | | | | | | |
% 106.54/14.81 | | | | | | | Case 2:
% 106.54/14.81 | | | | | | | |
% 106.54/14.81 | | | | | | | | (110) all_57_0 = 0
% 106.54/14.81 | | | | | | | |
% 106.54/14.81 | | | | | | | | REDUCE: (67), (110) imply:
% 106.54/14.81 | | | | | | | | (111) apply(all_32_8, all_41_1, all_41_2) = 0
% 106.54/14.81 | | | | | | | |
% 106.54/14.81 | | | | | | | | GROUND_INST: instantiating (2) with all_32_6, all_32_4,
% 106.54/14.81 | | | | | | | | all_32_5, all_49_0, all_41_0, all_41_1, simplifying
% 106.54/14.81 | | | | | | | | with (14), (15), (16), (22), (36), (37), (39),
% 106.54/14.81 | | | | | | | | (40), (53), (54) gives:
% 106.54/14.81 | | | | | | | | (112) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] :
% 106.54/14.81 | | | | | | | | (apply(all_32_6, all_49_0, all_41_0) = v0 &
% 106.54/14.81 | | | | | | | | apply(all_32_6, all_49_0, all_41_1) = v1 & ( ~ (v1 =
% 106.54/14.81 | | | | | | | | 0) | ~ (v0 = 0)))
% 106.54/14.81 | | | | | | | |
% 106.54/14.81 | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5,
% 106.54/14.81 | | | | | | | | all_32_4, all_41_1, all_49_0, all_41_2, simplifying
% 106.54/14.81 | | | | | | | | with (12), (15), (16), (20), (35), (36), (38),
% 106.54/14.81 | | | | | | | | (39), (53), (54) gives:
% 106.54/14.81 | | | | | | | | (113) all_49_0 = all_41_2 | ? [v0: any] : ? [v1: any] :
% 106.54/14.81 | | | | | | | | (apply(all_32_8, all_41_1, all_49_0) = v0 &
% 106.54/14.81 | | | | | | | | apply(all_32_8, all_41_1, all_41_2) = v1 & ( ~ (v1 =
% 106.54/14.81 | | | | | | | | 0) | ~ (v0 = 0)))
% 106.54/14.81 | | | | | | | |
% 106.54/14.81 | | | | | | | | GROUND_INST: instantiating (2) with all_32_7, all_32_4,
% 106.54/14.81 | | | | | | | | all_32_5, all_41_2, all_41_0, all_53_0, simplifying
% 106.54/14.81 | | | | | | | | with (13), (15), (16), (21), (35), (37), (38),
% 106.54/14.81 | | | | | | | | (40), (57), (58) gives:
% 106.54/14.81 | | | | | | | | (114) all_53_0 = all_41_0 | ? [v0: any] : ? [v1: any] :
% 106.54/14.81 | | | | | | | | (apply(all_32_7, all_41_2, all_53_0) = v1 &
% 106.54/14.81 | | | | | | | | apply(all_32_7, all_41_2, all_41_0) = v0 & ( ~ (v1 =
% 106.54/14.81 | | | | | | | | 0) | ~ (v0 = 0)))
% 106.54/14.81 | | | | | | | |
% 106.54/14.81 | | | | | | | | GROUND_INST: instantiating (2) with all_32_7, all_32_4,
% 106.54/14.81 | | | | | | | | all_32_5, all_49_0, all_41_0, all_53_0, simplifying
% 106.54/14.81 | | | | | | | | with (13), (15), (16), (21), (37), (40), (53),
% 106.54/14.81 | | | | | | | | (54), (57), (58) gives:
% 106.54/14.82 | | | | | | | | (115) all_53_0 = all_41_0 | ? [v0: any] : ? [v1: any] :
% 106.54/14.82 | | | | | | | | (apply(all_32_7, all_49_0, all_53_0) = v1 &
% 106.54/14.82 | | | | | | | | apply(all_32_7, all_49_0, all_41_0) = v0 & ( ~ (v1 =
% 106.54/14.82 | | | | | | | | 0) | ~ (v0 = 0)))
% 106.54/14.82 | | | | | | | |
% 106.86/14.82 | | | | | | | | GROUND_INST: instantiating (2) with all_32_7, all_32_4,
% 106.86/14.82 | | | | | | | | all_32_5, all_49_0, all_41_1, all_53_0, simplifying
% 106.86/14.82 | | | | | | | | with (13), (15), (16), (21), (36), (39), (53),
% 106.86/14.82 | | | | | | | | (54), (57), (58) gives:
% 106.86/14.82 | | | | | | | | (116) all_53_0 = all_41_1 | ? [v0: any] : ? [v1: any] :
% 106.86/14.82 | | | | | | | | (apply(all_32_7, all_49_0, all_53_0) = v1 &
% 106.86/14.82 | | | | | | | | apply(all_32_7, all_49_0, all_41_1) = v0 & ( ~ (v1 =
% 106.86/14.82 | | | | | | | | 0) | ~ (v0 = 0)))
% 106.86/14.82 | | | | | | | |
% 106.86/14.82 | | | | | | | | GROUND_INST: instantiating (2) with all_32_7, all_32_4,
% 106.86/14.82 | | | | | | | | all_32_5, all_49_0, all_53_0, all_41_1, simplifying
% 106.86/14.82 | | | | | | | | with (13), (15), (16), (21), (36), (39), (53),
% 106.86/14.82 | | | | | | | | (54), (57), (58) gives:
% 106.86/14.82 | | | | | | | | (117) all_53_0 = all_41_1 | ? [v0: any] : ? [v1: any] :
% 106.86/14.82 | | | | | | | | (apply(all_32_7, all_49_0, all_53_0) = v0 &
% 106.86/14.82 | | | | | | | | apply(all_32_7, all_49_0, all_41_1) = v1 & ( ~ (v1 =
% 106.86/14.82 | | | | | | | | 0) | ~ (v0 = 0)))
% 106.86/14.82 | | | | | | | |
% 106.86/14.82 | | | | | | | | GROUND_INST: instantiating (2) with all_32_8, all_32_5,
% 106.86/14.82 | | | | | | | | all_32_4, all_55_0, all_49_0, all_41_2, simplifying
% 106.86/14.82 | | | | | | | | with (12), (15), (16), (20), (35), (38), (53),
% 106.86/14.82 | | | | | | | | (54), (61), (62) gives:
% 106.86/14.82 | | | | | | | | (118) all_49_0 = all_41_2 | ? [v0: any] : ? [v1: any] :
% 106.86/14.82 | | | | | | | | (apply(all_32_8, all_55_0, all_49_0) = v0 &
% 106.86/14.82 | | | | | | | | apply(all_32_8, all_55_0, all_41_2) = v1 & ( ~ (v1 =
% 106.86/14.82 | | | | | | | | 0) | ~ (v0 = 0)))
% 106.86/14.82 | | | | | | | |
% 106.86/14.82 | | | | | | | | GROUND_INST: instantiating (1) with all_32_8, all_32_5,
% 106.86/14.82 | | | | | | | | all_32_4, all_55_0, simplifying with (12), (15),
% 106.86/14.82 | | | | | | | | (16), (20), (61), (62) gives:
% 106.86/14.82 | | | | | | | | (119) ? [v0: $i] : (apply(all_32_8, all_55_0, v0) = 0 &
% 106.86/14.82 | | | | | | | | member(v0, all_32_4) = 0 & $i(v0))
% 106.86/14.82 | | | | | | | |
% 106.86/14.82 | | | | | | | | GROUND_INST: instantiating (5) with all_32_7, all_32_8,
% 106.86/14.82 | | | | | | | | all_32_5, all_32_4, all_32_5, all_41_1, all_41_1,
% 106.86/14.82 | | | | | | | | all_32_3, simplifying with (12), (13), (15), (16),
% 106.86/14.82 | | | | | | | | (24), (36), (47) gives:
% 106.86/14.82 | | | | | | | | (120) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3:
% 106.86/14.82 | | | | | | | | int] : ? [v4: int] : ? [v5: int] : ($i(v2) & ((v5 =
% 106.86/14.82 | | | | | | | | 0 & v4 = 0 & v3 = 0 & apply(all_32_7, v2,
% 106.86/14.82 | | | | | | | | all_41_1) = 0 & apply(all_32_8, all_41_1, v2) =
% 106.86/14.82 | | | | | | | | 0 & member(v2, all_32_4) = 0) | (member(all_41_1,
% 106.86/14.82 | | | | | | | | all_32_5) = v1 & member(all_41_1, all_32_5) =
% 106.86/14.82 | | | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))))
% 106.86/14.82 | | | | | | | |
% 106.86/14.82 | | | | | | | | GROUND_INST: instantiating (5) with all_32_8, all_32_6,
% 106.86/14.82 | | | | | | | | all_32_4, all_32_5, all_32_4, all_41_2, all_41_2,
% 106.86/14.82 | | | | | | | | all_32_2, simplifying with (12), (14), (15), (16),
% 106.86/14.82 | | | | | | | | (23), (35), (45) gives:
% 106.86/14.82 | | | | | | | | (121) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3:
% 106.86/14.82 | | | | | | | | int] : ? [v4: int] : ? [v5: int] : ($i(v2) & ((v5 =
% 106.86/14.82 | | | | | | | | 0 & v4 = 0 & v3 = 0 & apply(all_32_6, all_41_2,
% 106.86/14.82 | | | | | | | | v2) = 0 & apply(all_32_8, v2, all_41_2) = 0 &
% 106.86/14.82 | | | | | | | | member(v2, all_32_5) = 0) | (member(all_41_2,
% 106.86/14.82 | | | | | | | | all_32_4) = v1 & member(all_41_2, all_32_4) =
% 106.86/14.82 | | | | | | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))))
% 106.86/14.82 | | | | | | | |
% 106.86/14.82 | | | | | | | | DELTA: instantiating (119) with fresh symbol all_113_0 gives:
% 106.86/14.82 | | | | | | | | (122) apply(all_32_8, all_55_0, all_113_0) = 0 &
% 106.86/14.82 | | | | | | | | member(all_113_0, all_32_4) = 0 & $i(all_113_0)
% 106.86/14.82 | | | | | | | |
% 106.86/14.82 | | | | | | | | ALPHA: (122) implies:
% 106.86/14.82 | | | | | | | | (123) $i(all_113_0)
% 106.86/14.82 | | | | | | | | (124) member(all_113_0, all_32_4) = 0
% 106.86/14.82 | | | | | | | | (125) apply(all_32_8, all_55_0, all_113_0) = 0
% 106.86/14.82 | | | | | | | |
% 106.86/14.82 | | | | | | | | DELTA: instantiating (121) with fresh symbols all_119_0,
% 106.86/14.82 | | | | | | | | all_119_1, all_119_2, all_119_3, all_119_4, all_119_5
% 106.86/14.82 | | | | | | | | gives:
% 106.86/14.82 | | | | | | | | (126) $i(all_119_3) & ((all_119_0 = 0 & all_119_1 = 0 &
% 106.86/14.82 | | | | | | | | all_119_2 = 0 & apply(all_32_6, all_41_2,
% 106.86/14.82 | | | | | | | | all_119_3) = 0 & apply(all_32_8, all_119_3,
% 106.86/14.82 | | | | | | | | all_41_2) = 0 & member(all_119_3, all_32_5) = 0)
% 106.86/14.82 | | | | | | | | | (member(all_41_2, all_32_4) = all_119_4 &
% 106.86/14.82 | | | | | | | | member(all_41_2, all_32_4) = all_119_5 & ( ~
% 106.86/14.82 | | | | | | | | (all_119_4 = 0) | ~ (all_119_5 = 0))))
% 106.86/14.82 | | | | | | | |
% 106.86/14.82 | | | | | | | | ALPHA: (126) implies:
% 106.86/14.82 | | | | | | | | (127) $i(all_119_3)
% 106.86/14.82 | | | | | | | | (128) (all_119_0 = 0 & all_119_1 = 0 & all_119_2 = 0 &
% 106.86/14.82 | | | | | | | | apply(all_32_6, all_41_2, all_119_3) = 0 &
% 106.86/14.82 | | | | | | | | apply(all_32_8, all_119_3, all_41_2) = 0 &
% 106.86/14.82 | | | | | | | | member(all_119_3, all_32_5) = 0) | (member(all_41_2,
% 106.86/14.82 | | | | | | | | all_32_4) = all_119_4 & member(all_41_2, all_32_4)
% 106.86/14.82 | | | | | | | | = all_119_5 & ( ~ (all_119_4 = 0) | ~ (all_119_5 =
% 106.86/14.82 | | | | | | | | 0)))
% 106.86/14.82 | | | | | | | |
% 106.86/14.82 | | | | | | | | DELTA: instantiating (120) with fresh symbols all_121_0,
% 106.86/14.82 | | | | | | | | all_121_1, all_121_2, all_121_3, all_121_4, all_121_5
% 106.86/14.82 | | | | | | | | gives:
% 106.86/14.82 | | | | | | | | (129) $i(all_121_3) & ((all_121_0 = 0 & all_121_1 = 0 &
% 106.86/14.82 | | | | | | | | all_121_2 = 0 & apply(all_32_7, all_121_3,
% 106.86/14.82 | | | | | | | | all_41_1) = 0 & apply(all_32_8, all_41_1,
% 106.86/14.82 | | | | | | | | all_121_3) = 0 & member(all_121_3, all_32_4) = 0)
% 106.86/14.82 | | | | | | | | | (member(all_41_1, all_32_5) = all_121_4 &
% 106.86/14.82 | | | | | | | | member(all_41_1, all_32_5) = all_121_5 & ( ~
% 106.86/14.82 | | | | | | | | (all_121_4 = 0) | ~ (all_121_5 = 0))))
% 106.86/14.82 | | | | | | | |
% 106.86/14.82 | | | | | | | | ALPHA: (129) implies:
% 106.86/14.82 | | | | | | | | (130) $i(all_121_3)
% 106.86/14.82 | | | | | | | | (131) (all_121_0 = 0 & all_121_1 = 0 & all_121_2 = 0 &
% 106.86/14.82 | | | | | | | | apply(all_32_7, all_121_3, all_41_1) = 0 &
% 106.86/14.82 | | | | | | | | apply(all_32_8, all_41_1, all_121_3) = 0 &
% 106.86/14.82 | | | | | | | | member(all_121_3, all_32_4) = 0) | (member(all_41_1,
% 106.86/14.82 | | | | | | | | all_32_5) = all_121_4 & member(all_41_1, all_32_5)
% 106.86/14.82 | | | | | | | | = all_121_5 & ( ~ (all_121_4 = 0) | ~ (all_121_5 =
% 106.86/14.82 | | | | | | | | 0)))
% 106.86/14.82 | | | | | | | |
% 106.86/14.82 | | | | | | | | BETA: splitting (113) gives:
% 106.86/14.82 | | | | | | | |
% 106.86/14.82 | | | | | | | | Case 1:
% 106.86/14.82 | | | | | | | | |
% 106.86/14.82 | | | | | | | | | (132) all_49_0 = all_41_2
% 106.86/14.83 | | | | | | | | |
% 106.86/14.83 | | | | | | | | | BETA: splitting (115) gives:
% 106.86/14.83 | | | | | | | | |
% 106.86/14.83 | | | | | | | | | Case 1:
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | (133) all_53_0 = all_41_0
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | REF_CLOSE: (2), (3), (4), (8), (9), (12), (14), (15), (16),
% 106.86/14.83 | | | | | | | | | | (20), (22), (34), (35), (36), (37), (38), (39),
% 106.86/14.83 | | | | | | | | | | (40), (61), (62), (63), (73), (104), (111), (116),
% 106.86/14.83 | | | | | | | | | | (117), (123), (124), (125), (127), (128), (130),
% 106.86/14.83 | | | | | | | | | | (131), (132), (133) are inconsistent by sub-proof
% 106.86/14.83 | | | | | | | | | | #1.
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | Case 2:
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | (134) ? [v0: any] : ? [v1: any] : (apply(all_32_7,
% 106.86/14.83 | | | | | | | | | | all_49_0, all_53_0) = v1 & apply(all_32_7,
% 106.86/14.83 | | | | | | | | | | all_49_0, all_41_0) = v0 & ( ~ (v1 = 0) | ~
% 106.86/14.83 | | | | | | | | | | (v0 = 0)))
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | DELTA: instantiating (134) with fresh symbols all_163_0,
% 106.86/14.83 | | | | | | | | | | all_163_1 gives:
% 106.86/14.83 | | | | | | | | | | (135) apply(all_32_7, all_49_0, all_53_0) = all_163_0 &
% 106.86/14.83 | | | | | | | | | | apply(all_32_7, all_49_0, all_41_0) = all_163_1 & (
% 106.86/14.83 | | | | | | | | | | ~ (all_163_0 = 0) | ~ (all_163_1 = 0))
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | ALPHA: (135) implies:
% 106.86/14.83 | | | | | | | | | | (136) apply(all_32_7, all_49_0, all_41_0) = all_163_1
% 106.86/14.83 | | | | | | | | | | (137) apply(all_32_7, all_49_0, all_53_0) = all_163_0
% 106.86/14.83 | | | | | | | | | | (138) ~ (all_163_0 = 0) | ~ (all_163_1 = 0)
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | REDUCE: (132), (137) imply:
% 106.86/14.83 | | | | | | | | | | (139) apply(all_32_7, all_41_2, all_53_0) = all_163_0
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | REDUCE: (132), (136) imply:
% 106.86/14.83 | | | | | | | | | | (140) apply(all_32_7, all_41_2, all_41_0) = all_163_1
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_163_1, all_41_0,
% 106.86/14.83 | | | | | | | | | | all_41_2, all_32_7, simplifying with (41), (140)
% 106.86/14.83 | | | | | | | | | | gives:
% 106.86/14.83 | | | | | | | | | | (141) all_163_1 = 0
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_163_0, all_53_0,
% 106.86/14.83 | | | | | | | | | | all_41_2, all_32_7, simplifying with (59), (139)
% 106.86/14.83 | | | | | | | | | | gives:
% 106.86/14.83 | | | | | | | | | | (142) all_163_0 = 0
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | BETA: splitting (138) gives:
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | Case 1:
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | (143) ~ (all_163_0 = 0)
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | REDUCE: (142), (143) imply:
% 106.86/14.83 | | | | | | | | | | | (144) $false
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | CLOSE: (144) is inconsistent.
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | Case 2:
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | (145) ~ (all_163_1 = 0)
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | REDUCE: (141), (145) imply:
% 106.86/14.83 | | | | | | | | | | | (146) $false
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | CLOSE: (146) is inconsistent.
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | End of split
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | End of split
% 106.86/14.83 | | | | | | | | |
% 106.86/14.83 | | | | | | | | Case 2:
% 106.86/14.83 | | | | | | | | |
% 106.86/14.83 | | | | | | | | | (147) ~ (all_49_0 = all_41_2)
% 106.86/14.83 | | | | | | | | |
% 106.86/14.83 | | | | | | | | | BETA: splitting (114) gives:
% 106.86/14.83 | | | | | | | | |
% 106.86/14.83 | | | | | | | | | Case 1:
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | (148) all_53_0 = all_41_0
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | BETA: splitting (113) gives:
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | Case 1:
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | (149) all_49_0 = all_41_2
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (8), (9), (12), (14), (15), (16),
% 106.86/14.83 | | | | | | | | | | | (20), (22), (34), (35), (36), (37), (38), (39),
% 106.86/14.83 | | | | | | | | | | | (40), (61), (62), (63), (73), (104), (111), (116),
% 106.86/14.83 | | | | | | | | | | | (117), (123), (124), (125), (127), (128), (130),
% 106.86/14.83 | | | | | | | | | | | (131), (148), (149) are inconsistent by sub-proof
% 106.86/14.83 | | | | | | | | | | | #1.
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | Case 2:
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | (150) ? [v0: any] : ? [v1: any] : (apply(all_32_8,
% 106.86/14.83 | | | | | | | | | | | all_41_1, all_49_0) = v0 & apply(all_32_8,
% 106.86/14.83 | | | | | | | | | | | all_41_1, all_41_2) = v1 & ( ~ (v1 = 0) | ~
% 106.86/14.83 | | | | | | | | | | | (v0 = 0)))
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | DELTA: instantiating (150) with fresh symbols all_137_0,
% 106.86/14.83 | | | | | | | | | | | all_137_1 gives:
% 106.86/14.83 | | | | | | | | | | | (151) apply(all_32_8, all_41_1, all_49_0) = all_137_1 &
% 106.86/14.83 | | | | | | | | | | | apply(all_32_8, all_41_1, all_41_2) = all_137_0 &
% 106.86/14.83 | | | | | | | | | | | ( ~ (all_137_0 = 0) | ~ (all_137_1 = 0))
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | ALPHA: (151) implies:
% 106.86/14.83 | | | | | | | | | | | (152) apply(all_32_8, all_41_1, all_41_2) = all_137_0
% 106.86/14.83 | | | | | | | | | | | (153) apply(all_32_8, all_41_1, all_49_0) = all_137_1
% 106.86/14.83 | | | | | | | | | | | (154) ~ (all_137_0 = 0) | ~ (all_137_1 = 0)
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | BETA: splitting (112) gives:
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | Case 1:
% 106.86/14.83 | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | | (155) all_41_0 = all_41_1
% 106.86/14.83 | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | | REDUCE: (34), (155) imply:
% 106.86/14.83 | | | | | | | | | | | | (156) $false
% 106.86/14.83 | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | | CLOSE: (156) is inconsistent.
% 106.86/14.83 | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | Case 2:
% 106.86/14.83 | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_137_0, all_41_2,
% 106.86/14.83 | | | | | | | | | | | | all_41_1, all_32_8, simplifying with (111), (152)
% 106.86/14.83 | | | | | | | | | | | | gives:
% 106.86/14.83 | | | | | | | | | | | | (157) all_137_0 = 0
% 106.86/14.83 | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_137_1, all_49_0,
% 106.86/14.83 | | | | | | | | | | | | all_41_1, all_32_8, simplifying with (55), (153)
% 106.86/14.83 | | | | | | | | | | | | gives:
% 106.86/14.83 | | | | | | | | | | | | (158) all_137_1 = 0
% 106.86/14.83 | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | | BETA: splitting (154) gives:
% 106.86/14.83 | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | | Case 1:
% 106.86/14.83 | | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | | | (159) ~ (all_137_0 = 0)
% 106.86/14.83 | | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | | | REDUCE: (157), (159) imply:
% 106.86/14.83 | | | | | | | | | | | | | (160) $false
% 106.86/14.83 | | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | | | CLOSE: (160) is inconsistent.
% 106.86/14.83 | | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | | Case 2:
% 106.86/14.83 | | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | | | (161) ~ (all_137_1 = 0)
% 106.86/14.83 | | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | | | REDUCE: (158), (161) imply:
% 106.86/14.83 | | | | | | | | | | | | | (162) $false
% 106.86/14.83 | | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | | | CLOSE: (162) is inconsistent.
% 106.86/14.83 | | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | | End of split
% 106.86/14.83 | | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | | End of split
% 106.86/14.83 | | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | End of split
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | Case 2:
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | (163) ? [v0: any] : ? [v1: any] : (apply(all_32_7,
% 106.86/14.83 | | | | | | | | | | all_41_2, all_53_0) = v1 & apply(all_32_7,
% 106.86/14.83 | | | | | | | | | | all_41_2, all_41_0) = v0 & ( ~ (v1 = 0) | ~
% 106.86/14.83 | | | | | | | | | | (v0 = 0)))
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | DELTA: instantiating (163) with fresh symbols all_181_0,
% 106.86/14.83 | | | | | | | | | | all_181_1 gives:
% 106.86/14.83 | | | | | | | | | | (164) apply(all_32_7, all_41_2, all_53_0) = all_181_0 &
% 106.86/14.83 | | | | | | | | | | apply(all_32_7, all_41_2, all_41_0) = all_181_1 & (
% 106.86/14.83 | | | | | | | | | | ~ (all_181_0 = 0) | ~ (all_181_1 = 0))
% 106.86/14.83 | | | | | | | | | |
% 106.86/14.83 | | | | | | | | | | ALPHA: (164) implies:
% 106.86/14.84 | | | | | | | | | | (165) apply(all_32_7, all_41_2, all_41_0) = all_181_1
% 106.86/14.84 | | | | | | | | | | (166) apply(all_32_7, all_41_2, all_53_0) = all_181_0
% 106.86/14.84 | | | | | | | | | | (167) ~ (all_181_0 = 0) | ~ (all_181_1 = 0)
% 106.86/14.84 | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | BETA: splitting (118) gives:
% 106.86/14.84 | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | Case 1:
% 106.86/14.84 | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | | (168) all_49_0 = all_41_2
% 106.86/14.84 | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | | REDUCE: (147), (168) imply:
% 106.86/14.84 | | | | | | | | | | | (169) $false
% 106.86/14.84 | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | | CLOSE: (169) is inconsistent.
% 106.86/14.84 | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | Case 2:
% 106.86/14.84 | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_181_1, all_41_0,
% 106.86/14.84 | | | | | | | | | | | all_41_2, all_32_7, simplifying with (41), (165)
% 106.86/14.84 | | | | | | | | | | | gives:
% 106.86/14.84 | | | | | | | | | | | (170) all_181_1 = 0
% 106.86/14.84 | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | | GROUND_INST: instantiating (9) with 0, all_181_0, all_53_0,
% 106.86/14.84 | | | | | | | | | | | all_41_2, all_32_7, simplifying with (59), (166)
% 106.86/14.84 | | | | | | | | | | | gives:
% 106.86/14.84 | | | | | | | | | | | (171) all_181_0 = 0
% 106.86/14.84 | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | | BETA: splitting (167) gives:
% 106.86/14.84 | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | | Case 1:
% 106.86/14.84 | | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | | | (172) ~ (all_181_0 = 0)
% 106.86/14.84 | | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | | | REDUCE: (171), (172) imply:
% 106.86/14.84 | | | | | | | | | | | | (173) $false
% 106.86/14.84 | | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | | | CLOSE: (173) is inconsistent.
% 106.86/14.84 | | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | | Case 2:
% 106.86/14.84 | | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | | | (174) ~ (all_181_1 = 0)
% 106.86/14.84 | | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | | | REDUCE: (170), (174) imply:
% 106.86/14.84 | | | | | | | | | | | | (175) $false
% 106.86/14.84 | | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | | | CLOSE: (175) is inconsistent.
% 106.86/14.84 | | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | | End of split
% 106.86/14.84 | | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | | End of split
% 106.86/14.84 | | | | | | | | | |
% 106.86/14.84 | | | | | | | | | End of split
% 106.86/14.84 | | | | | | | | |
% 106.86/14.84 | | | | | | | | End of split
% 106.86/14.84 | | | | | | | |
% 106.86/14.84 | | | | | | | End of split
% 106.86/14.84 | | | | | | |
% 106.86/14.84 | | | | | | End of split
% 106.86/14.84 | | | | | |
% 106.86/14.84 | | | | | Case 2:
% 106.86/14.84 | | | | | |
% 106.86/14.84 | | | | | | (176) ~ (all_78_1 = 0) | ~ (all_78_2 = 0)
% 106.86/14.84 | | | | | |
% 106.86/14.84 | | | | | | BETA: splitting (176) gives:
% 106.86/14.84 | | | | | |
% 106.86/14.84 | | | | | | Case 1:
% 106.86/14.84 | | | | | | |
% 106.86/14.84 | | | | | | | (177) ~ (all_78_1 = 0)
% 106.86/14.84 | | | | | | |
% 106.86/14.84 | | | | | | | REDUCE: (92), (177) imply:
% 106.86/14.84 | | | | | | | (178) $false
% 106.86/14.84 | | | | | | |
% 106.86/14.84 | | | | | | | CLOSE: (178) is inconsistent.
% 106.86/14.84 | | | | | | |
% 106.86/14.84 | | | | | | Case 2:
% 106.86/14.84 | | | | | | |
% 106.86/14.84 | | | | | | | (179) ~ (all_78_2 = 0)
% 106.86/14.84 | | | | | | |
% 106.86/14.84 | | | | | | | REDUCE: (89), (179) imply:
% 106.86/14.84 | | | | | | | (180) $false
% 106.86/14.84 | | | | | | |
% 106.86/14.84 | | | | | | | CLOSE: (180) is inconsistent.
% 106.86/14.84 | | | | | | |
% 106.86/14.84 | | | | | | End of split
% 106.86/14.84 | | | | | |
% 106.86/14.84 | | | | | End of split
% 106.86/14.84 | | | | |
% 106.86/14.84 | | | | End of split
% 106.86/14.84 | | | |
% 106.86/14.84 | | | End of split
% 106.86/14.84 | | |
% 106.86/14.84 | | End of split
% 106.86/14.84 | |
% 106.86/14.84 | End of split
% 106.86/14.84 |
% 106.86/14.84 End of proof
% 106.86/14.84
% 106.86/14.84 Sub-proof #1 shows that the following formulas are inconsistent:
% 106.86/14.84 ----------------------------------------------------------------
% 106.86/14.84 (1) maps(all_32_8, all_32_5, all_32_4) = 0
% 106.86/14.84 (2) (all_121_0 = 0 & all_121_1 = 0 & all_121_2 = 0 & apply(all_32_7,
% 106.86/14.84 all_121_3, all_41_1) = 0 & apply(all_32_8, all_41_1, all_121_3) = 0 &
% 106.86/14.84 member(all_121_3, all_32_4) = 0) | (member(all_41_1, all_32_5) =
% 106.86/14.84 all_121_4 & member(all_41_1, all_32_5) = all_121_5 & ( ~ (all_121_4 =
% 106.86/14.84 0) | ~ (all_121_5 = 0)))
% 106.86/14.84 (3) $i(all_32_8)
% 106.86/14.84 (4) member(all_41_0, all_32_5) = 0
% 106.86/14.84 (5) all_53_0 = all_41_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_7,
% 106.86/14.84 all_49_0, all_53_0) = v1 & apply(all_32_7, all_49_0, all_41_1) = v0 &
% 106.86/14.84 ( ~ (v1 = 0) | ~ (v0 = 0)))
% 106.86/14.84 (6) $i(all_55_0)
% 106.86/14.84 (7) ~ (all_41_0 = all_41_1)
% 106.86/14.84 (8) $i(all_41_2)
% 106.86/14.84 (9) $i(all_41_1)
% 106.86/14.84 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 106.86/14.84 [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5)
% 106.86/14.84 = 0) | ~ (member(v4, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) |
% 106.86/14.84 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ?
% 106.86/14.84 [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, v2) = v7 & member(v3,
% 106.86/14.84 v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 106.86/14.84 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 106.86/14.84 [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5)
% 106.86/14.84 = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 106.86/14.84 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 106.86/14.84 any] : ? [v8: any] : (member(v5, v2) = v8 & member(v4, v2) = v7 &
% 106.86/14.84 member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 106.86/14.84 (12) apply(all_32_7, all_41_2, all_41_1) = all_63_1
% 106.86/14.84 (13) all_49_0 = all_41_2
% 106.86/14.84 (14) $i(all_32_6)
% 106.86/14.84 (15) $i(all_121_3)
% 106.86/14.84 (16) apply(all_32_6, all_41_2, all_55_0) = 0
% 106.86/14.84 (17) all_53_0 = all_41_0
% 106.86/14.84 (18) apply(all_32_8, all_41_1, all_41_2) = 0
% 106.86/14.84 (19) member(all_113_0, all_32_4) = 0
% 106.86/14.84 (20) all_53_0 = all_41_1 | ? [v0: any] : ? [v1: any] : (apply(all_32_7,
% 106.86/14.84 all_49_0, all_53_0) = v0 & apply(all_32_7, all_49_0, all_41_1) = v1
% 106.86/14.84 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 106.86/14.84 (21) $i(all_41_0)
% 106.86/14.84 (22) apply(all_32_8, all_55_0, all_113_0) = 0
% 106.86/14.84 (23) $i(all_32_5)
% 106.86/14.84 (24) (all_119_0 = 0 & all_119_1 = 0 & all_119_2 = 0 & apply(all_32_6,
% 106.86/14.84 all_41_2, all_119_3) = 0 & apply(all_32_8, all_119_3, all_41_2) = 0
% 106.86/14.84 & member(all_119_3, all_32_5) = 0) | (member(all_41_2, all_32_4) =
% 106.86/14.84 all_119_4 & member(all_41_2, all_32_4) = all_119_5 & ( ~ (all_119_4 =
% 106.86/14.84 0) | ~ (all_119_5 = 0)))
% 106.86/14.84 (25) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 106.86/14.84 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~
% 106.86/14.84 (apply(v4, v3, v2) = v0))
% 106.86/14.84 (26) member(all_55_0, all_32_5) = 0
% 106.86/14.84 (27) $i(all_113_0)
% 106.86/14.84 (28) $i(all_32_4)
% 106.86/14.84 (29) ~ (all_63_1 = 0)
% 106.86/14.84 (30) member(all_41_2, all_32_4) = 0
% 106.86/14.84 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : !
% 106.86/14.84 [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) =
% 106.86/14.84 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v5) |
% 106.86/14.84 ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 106.86/14.84 any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & apply(v0, v3, v4) =
% 106.86/14.84 v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 106.86/14.84 (32) member(all_41_1, all_32_5) = 0
% 106.86/14.84 (33) $i(all_119_3)
% 106.86/14.84 (34) maps(all_32_6, all_32_4, all_32_5) = 0
% 106.86/14.84 (35) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 106.86/14.84 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) =
% 106.86/14.84 v0))
% 106.86/14.84
% 106.86/14.84 Begin of proof
% 106.86/14.84 |
% 106.86/14.84 | BETA: splitting (5) gives:
% 106.86/14.84 |
% 106.86/14.84 | Case 1:
% 106.86/14.84 | |
% 106.86/14.85 | | (36) all_53_0 = all_41_1
% 106.86/14.85 | |
% 106.86/14.85 | | COMBINE_EQS: (17), (36) imply:
% 106.86/14.85 | | (37) all_41_0 = all_41_1
% 106.86/14.85 | |
% 106.86/14.85 | | SIMP: (37) implies:
% 106.86/14.85 | | (38) all_41_0 = all_41_1
% 106.86/14.85 | |
% 106.86/14.85 | | REDUCE: (7), (38) imply:
% 106.86/14.85 | | (39) $false
% 106.86/14.85 | |
% 106.86/14.85 | | CLOSE: (39) is inconsistent.
% 106.86/14.85 | |
% 106.86/14.85 | Case 2:
% 106.86/14.85 | |
% 106.86/14.85 | | (40) ~ (all_53_0 = all_41_1)
% 106.86/14.85 | | (41) ? [v0: any] : ? [v1: any] : (apply(all_32_7, all_49_0, all_53_0) =
% 106.86/14.85 | | v1 & apply(all_32_7, all_49_0, all_41_1) = v0 & ( ~ (v1 = 0) | ~
% 106.86/14.85 | | (v0 = 0)))
% 106.86/14.85 | |
% 106.86/14.85 | | DELTA: instantiating (41) with fresh symbols all_140_0, all_140_1 gives:
% 106.86/14.85 | | (42) apply(all_32_7, all_49_0, all_53_0) = all_140_0 & apply(all_32_7,
% 106.86/14.85 | | all_49_0, all_41_1) = all_140_1 & ( ~ (all_140_0 = 0) | ~
% 106.86/14.85 | | (all_140_1 = 0))
% 106.86/14.85 | |
% 106.86/14.85 | | ALPHA: (42) implies:
% 106.86/14.85 | | (43) apply(all_32_7, all_49_0, all_41_1) = all_140_1
% 106.86/14.85 | |
% 106.86/14.85 | | REDUCE: (13), (43) imply:
% 106.86/14.85 | | (44) apply(all_32_7, all_41_2, all_41_1) = all_140_1
% 106.86/14.85 | |
% 106.86/14.85 | | BETA: splitting (20) gives:
% 106.86/14.85 | |
% 106.86/14.85 | | Case 1:
% 106.86/14.85 | | |
% 106.86/14.85 | | | (45) all_53_0 = all_41_1
% 106.86/14.85 | | |
% 106.86/14.85 | | | COMBINE_EQS: (17), (45) imply:
% 106.86/14.85 | | | (46) all_41_0 = all_41_1
% 106.86/14.85 | | |
% 106.86/14.85 | | | SIMP: (46) implies:
% 106.86/14.85 | | | (47) all_41_0 = all_41_1
% 106.86/14.85 | | |
% 106.86/14.85 | | | REDUCE: (7), (47) imply:
% 106.86/14.85 | | | (48) $false
% 106.86/14.85 | | |
% 106.86/14.85 | | | CLOSE: (48) is inconsistent.
% 106.86/14.85 | | |
% 106.86/14.85 | | Case 2:
% 106.86/14.85 | | |
% 106.86/14.85 | | | (49) ? [v0: any] : ? [v1: any] : (apply(all_32_7, all_49_0, all_53_0)
% 106.86/14.85 | | | = v0 & apply(all_32_7, all_49_0, all_41_1) = v1 & ( ~ (v1 = 0) |
% 106.86/14.85 | | | ~ (v0 = 0)))
% 106.86/14.85 | | |
% 106.86/14.85 | | | DELTA: instantiating (49) with fresh symbols all_150_0, all_150_1 gives:
% 106.86/14.85 | | | (50) apply(all_32_7, all_49_0, all_53_0) = all_150_1 & apply(all_32_7,
% 106.86/14.85 | | | all_49_0, all_41_1) = all_150_0 & ( ~ (all_150_0 = 0) | ~
% 106.86/14.85 | | | (all_150_1 = 0))
% 106.86/14.85 | | |
% 106.86/14.85 | | | ALPHA: (50) implies:
% 106.86/14.85 | | | (51) apply(all_32_7, all_49_0, all_41_1) = all_150_0
% 106.86/14.85 | | |
% 106.86/14.85 | | | REDUCE: (13), (51) imply:
% 106.86/14.85 | | | (52) apply(all_32_7, all_41_2, all_41_1) = all_150_0
% 106.86/14.85 | | |
% 106.86/14.85 | | | BETA: splitting (2) gives:
% 106.86/14.85 | | |
% 106.86/14.85 | | | Case 1:
% 106.86/14.85 | | | |
% 106.86/14.85 | | | | (53) all_121_0 = 0 & all_121_1 = 0 & all_121_2 = 0 & apply(all_32_7,
% 106.86/14.85 | | | | all_121_3, all_41_1) = 0 & apply(all_32_8, all_41_1,
% 106.86/14.85 | | | | all_121_3) = 0 & member(all_121_3, all_32_4) = 0
% 106.86/14.85 | | | |
% 106.86/14.85 | | | | ALPHA: (53) implies:
% 106.86/14.85 | | | | (54) member(all_121_3, all_32_4) = 0
% 106.86/14.85 | | | | (55) apply(all_32_8, all_41_1, all_121_3) = 0
% 106.86/14.85 | | | | (56) apply(all_32_7, all_121_3, all_41_1) = 0
% 106.86/14.85 | | | |
% 106.86/14.85 | | | | BETA: splitting (24) gives:
% 106.86/14.85 | | | |
% 106.86/14.85 | | | | Case 1:
% 106.86/14.85 | | | | |
% 106.86/14.85 | | | | | (57) all_119_0 = 0 & all_119_1 = 0 & all_119_2 = 0 &
% 106.86/14.85 | | | | | apply(all_32_6, all_41_2, all_119_3) = 0 & apply(all_32_8,
% 106.86/14.85 | | | | | all_119_3, all_41_2) = 0 & member(all_119_3, all_32_5) = 0
% 106.86/14.85 | | | | |
% 106.86/14.85 | | | | | ALPHA: (57) implies:
% 106.86/14.85 | | | | | (58) member(all_119_3, all_32_5) = 0
% 106.86/14.85 | | | | | (59) apply(all_32_8, all_119_3, all_41_2) = 0
% 106.86/14.85 | | | | | (60) apply(all_32_6, all_41_2, all_119_3) = 0
% 106.86/14.85 | | | | |
% 106.86/14.85 | | | | | GROUND_INST: instantiating (25) with all_63_1, all_150_0, all_41_1,
% 106.86/14.85 | | | | | all_41_2, all_32_7, simplifying with (12), (52) gives:
% 106.86/14.85 | | | | | (61) all_150_0 = all_63_1
% 106.86/14.85 | | | | |
% 106.86/14.85 | | | | | GROUND_INST: instantiating (25) with all_140_1, all_150_0, all_41_1,
% 106.86/14.85 | | | | | all_41_2, all_32_7, simplifying with (44), (52) gives:
% 106.86/14.85 | | | | | (62) all_150_0 = all_140_1
% 106.86/14.85 | | | | |
% 106.86/14.85 | | | | | COMBINE_EQS: (61), (62) imply:
% 106.86/14.85 | | | | | (63) all_140_1 = all_63_1
% 106.86/14.85 | | | | |
% 106.86/14.85 | | | | | GROUND_INST: instantiating (31) with all_32_6, all_32_4, all_32_5,
% 106.86/14.85 | | | | | all_113_0, all_41_0, all_41_1, simplifying with (4), (9),
% 106.86/14.85 | | | | | (14), (19), (21), (23), (27), (28), (32), (34) gives:
% 106.86/14.85 | | | | | (64) all_41_0 = all_41_1 | ? [v0: any] : ? [v1: any] :
% 106.86/14.85 | | | | | (apply(all_32_6, all_113_0, all_41_0) = v0 & apply(all_32_6,
% 106.86/14.85 | | | | | all_113_0, all_41_1) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 106.86/14.85 | | | | |
% 106.86/14.85 | | | | | GROUND_INST: instantiating (31) with all_32_8, all_32_5, all_32_4,
% 106.86/14.85 | | | | | all_55_0, all_113_0, all_41_2, simplifying with (1), (3),
% 106.86/14.85 | | | | | (6), (8), (19), (23), (26), (27), (28), (30) gives:
% 106.86/14.85 | | | | | (65) all_113_0 = all_41_2 | ? [v0: any] : ? [v1: any] :
% 106.86/14.85 | | | | | (apply(all_32_8, all_55_0, all_113_0) = v0 & apply(all_32_8,
% 106.86/14.85 | | | | | all_55_0, all_41_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 106.86/14.85 | | | | |
% 106.86/14.85 | | | | | GROUND_INST: instantiating (31) with all_32_6, all_32_4, all_32_5,
% 106.86/14.85 | | | | | all_41_2, all_55_0, all_119_3, simplifying with (6), (8),
% 106.86/14.85 | | | | | (14), (23), (26), (28), (30), (33), (34), (58) gives:
% 106.86/14.85 | | | | | (66) all_119_3 = all_55_0 | ? [v0: any] : ? [v1: any] :
% 106.86/14.85 | | | | | (apply(all_32_6, all_41_2, all_119_3) = v1 & apply(all_32_6,
% 106.86/14.85 | | | | | all_41_2, all_55_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 106.86/14.85 | | | | |
% 106.86/14.85 | | | | | GROUND_INST: instantiating (31) with all_32_6, all_32_4, all_32_5,
% 106.86/14.85 | | | | | all_121_3, all_119_3, all_55_0, simplifying with (6),
% 106.86/14.85 | | | | | (14), (15), (23), (26), (28), (33), (34), (54), (58)
% 106.86/14.85 | | | | | gives:
% 106.86/14.85 | | | | | (67) all_119_3 = all_55_0 | ? [v0: any] : ? [v1: any] :
% 106.86/14.85 | | | | | (apply(all_32_6, all_121_3, all_119_3) = v0 & apply(all_32_6,
% 106.86/14.85 | | | | | all_121_3, all_55_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 106.86/14.85 | | | | |
% 106.86/14.85 | | | | | GROUND_INST: instantiating (10) with all_32_8, all_32_5, all_32_4,
% 106.86/14.85 | | | | | all_41_1, all_121_3, all_41_2, simplifying with (1), (3),
% 106.86/14.85 | | | | | (8), (9), (15), (18), (23), (28), (54) gives:
% 106.86/14.85 | | | | | (68) all_121_3 = all_41_2 | ? [v0: any] : ? [v1: any] : ? [v2:
% 106.86/14.85 | | | | | any] : (apply(all_32_8, all_41_1, all_121_3) = v2 &
% 106.86/14.85 | | | | | member(all_41_1, all_32_5) = v0 & member(all_41_2, all_32_4)
% 106.86/14.85 | | | | | = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 106.86/14.85 | | | | |
% 106.86/14.85 | | | | | GROUND_INST: instantiating (31) with all_32_8, all_32_5, all_32_4,
% 106.86/14.85 | | | | | all_55_0, all_41_2, all_121_3, simplifying with (1), (3),
% 106.86/14.85 | | | | | (6), (8), (15), (23), (26), (28), (30), (54) gives:
% 106.86/14.85 | | | | | (69) all_121_3 = all_41_2 | ? [v0: any] : ? [v1: any] :
% 106.86/14.85 | | | | | (apply(all_32_8, all_55_0, all_121_3) = v1 & apply(all_32_8,
% 106.86/14.85 | | | | | all_55_0, all_41_2) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 106.86/14.85 | | | | |
% 106.86/14.85 | | | | | GROUND_INST: instantiating (31) with all_32_8, all_32_5, all_32_4,
% 106.86/14.85 | | | | | all_55_0, all_121_3, all_41_2, simplifying with (1), (3),
% 106.86/14.85 | | | | | (6), (8), (15), (23), (26), (28), (30), (54) gives:
% 106.86/14.85 | | | | | (70) all_121_3 = all_41_2 | ? [v0: any] : ? [v1: any] :
% 106.86/14.85 | | | | | (apply(all_32_8, all_55_0, all_121_3) = v0 & apply(all_32_8,
% 106.86/14.85 | | | | | all_55_0, all_41_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 106.86/14.85 | | | | |
% 106.86/14.85 | | | | | GROUND_INST: instantiating (31) with all_32_8, all_32_5, all_32_4,
% 106.86/14.85 | | | | | all_41_0, all_121_3, all_41_2, simplifying with (1), (3),
% 106.86/14.85 | | | | | (4), (8), (15), (21), (23), (28), (30), (54) gives:
% 106.86/14.86 | | | | | (71) all_121_3 = all_41_2 | ? [v0: any] : ? [v1: any] :
% 106.86/14.86 | | | | | (apply(all_32_8, all_41_0, all_121_3) = v0 & apply(all_32_8,
% 106.86/14.86 | | | | | all_41_0, all_41_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 106.86/14.86 | | | | |
% 106.86/14.86 | | | | | GROUND_INST: instantiating (31) with all_32_8, all_32_5, all_32_4,
% 106.86/14.86 | | | | | all_41_1, all_113_0, all_121_3, simplifying with (1),
% 106.86/14.86 | | | | | (3), (9), (15), (19), (23), (27), (28), (32), (54) gives:
% 106.86/14.86 | | | | | (72) all_121_3 = all_113_0 | ? [v0: any] : ? [v1: any] :
% 106.86/14.86 | | | | | (apply(all_32_8, all_41_1, all_121_3) = v1 & apply(all_32_8,
% 106.86/14.86 | | | | | all_41_1, all_113_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 106.86/14.86 | | | | |
% 106.86/14.86 | | | | | GROUND_INST: instantiating (31) with all_32_8, all_32_5, all_32_4,
% 106.86/14.86 | | | | | all_41_1, all_121_3, all_113_0, simplifying with (1),
% 106.86/14.86 | | | | | (3), (9), (15), (19), (23), (27), (28), (32), (54) gives:
% 106.86/14.86 | | | | | (73) all_121_3 = all_113_0 | ? [v0: any] : ? [v1: any] :
% 106.86/14.86 | | | | | (apply(all_32_8, all_41_1, all_121_3) = v0 & apply(all_32_8,
% 106.86/14.86 | | | | | all_41_1, all_113_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 106.86/14.86 | | | | |
% 106.86/14.86 | | | | | GROUND_INST: instantiating (10) with all_32_8, all_32_5, all_32_4,
% 106.86/14.86 | | | | | all_41_1, all_113_0, all_121_3, simplifying with (1),
% 106.86/14.86 | | | | | (3), (9), (15), (19), (23), (27), (28), (55) gives:
% 106.86/14.86 | | | | | (74) all_121_3 = all_113_0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 106.86/14.86 | | | | | any] : (apply(all_32_8, all_41_1, all_113_0) = v2 &
% 106.86/14.86 | | | | | member(all_121_3, all_32_4) = v1 & member(all_41_1,
% 106.86/14.86 | | | | | all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 106.86/14.86 | | | | | 0)))
% 106.86/14.86 | | | | |
% 106.86/14.86 | | | | | GROUND_INST: instantiating (10) with all_32_8, all_32_5, all_32_4,
% 106.86/14.86 | | | | | all_55_0, all_41_2, all_113_0, simplifying with (1), (3),
% 106.86/14.86 | | | | | (6), (8), (22), (23), (27), (28), (30) gives:
% 106.86/14.86 | | | | | (75) all_113_0 = all_41_2 | ? [v0: any] : ? [v1: any] : ? [v2:
% 106.86/14.86 | | | | | any] : (apply(all_32_8, all_55_0, all_41_2) = v2 &
% 106.86/14.86 | | | | | member(all_113_0, all_32_4) = v1 & member(all_55_0,
% 106.86/14.86 | | | | | all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 106.86/14.86 | | | | | 0)))
% 106.86/14.86 | | | | |
% 106.86/14.86 | | | | | GROUND_INST: instantiating (11) with all_32_6, all_32_4, all_32_5,
% 106.86/14.86 | | | | | all_41_2, all_119_3, all_55_0, simplifying with (6), (8),
% 106.86/14.86 | | | | | (14), (16), (23), (28), (33), (34), (60) gives:
% 106.86/14.86 | | | | | (76) all_119_3 = all_55_0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 106.86/14.86 | | | | | any] : (member(all_119_3, all_32_5) = v1 & member(all_55_0,
% 106.86/14.86 | | | | | all_32_5) = v2 & member(all_41_2, all_32_4) = v0 & ( ~ (v2
% 106.86/14.86 | | | | | = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 106.86/14.86 | | | | |
% 106.86/14.86 | | | | | BETA: splitting (66) gives:
% 106.86/14.86 | | | | |
% 106.86/14.86 | | | | | Case 1:
% 106.86/14.86 | | | | | |
% 106.86/14.86 | | | | | | (77) all_119_3 = all_55_0
% 106.86/14.86 | | | | | |
% 106.86/14.86 | | | | | | REDUCE: (59), (77) imply:
% 106.86/14.86 | | | | | | (78) apply(all_32_8, all_55_0, all_41_2) = 0
% 106.86/14.86 | | | | | |
% 106.86/14.86 | | | | | | BETA: splitting (68) gives:
% 106.86/14.86 | | | | | |
% 106.86/14.86 | | | | | | Case 1:
% 106.86/14.86 | | | | | | |
% 106.86/14.86 | | | | | | | (79) all_121_3 = all_41_2
% 106.86/14.86 | | | | | | |
% 106.86/14.86 | | | | | | | REDUCE: (56), (79) imply:
% 106.86/14.86 | | | | | | | (80) apply(all_32_7, all_41_2, all_41_1) = 0
% 106.86/14.86 | | | | | | |
% 106.86/14.86 | | | | | | | GROUND_INST: instantiating (25) with all_63_1, 0, all_41_1,
% 106.86/14.86 | | | | | | | all_41_2, all_32_7, simplifying with (12), (80)
% 106.86/14.86 | | | | | | | gives:
% 106.86/14.86 | | | | | | | (81) all_63_1 = 0
% 106.86/14.86 | | | | | | |
% 106.86/14.86 | | | | | | | REDUCE: (29), (81) imply:
% 106.86/14.86 | | | | | | | (82) $false
% 106.86/14.86 | | | | | | |
% 106.86/14.86 | | | | | | | CLOSE: (82) is inconsistent.
% 106.86/14.86 | | | | | | |
% 106.86/14.86 | | | | | | Case 2:
% 106.86/14.86 | | | | | | |
% 106.86/14.86 | | | | | | | (83) ~ (all_121_3 = all_41_2)
% 106.86/14.86 | | | | | | | (84) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 106.86/14.86 | | | | | | | (apply(all_32_8, all_41_1, all_121_3) = v2 &
% 106.86/14.86 | | | | | | | member(all_41_1, all_32_5) = v0 & member(all_41_2,
% 106.86/14.86 | | | | | | | all_32_4) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 106.86/14.86 | | | | | | | 0)))
% 106.86/14.86 | | | | | | |
% 106.86/14.86 | | | | | | | DELTA: instantiating (84) with fresh symbols all_223_0, all_223_1,
% 106.86/14.86 | | | | | | | all_223_2 gives:
% 106.86/14.86 | | | | | | | (85) apply(all_32_8, all_41_1, all_121_3) = all_223_0 &
% 106.86/14.86 | | | | | | | member(all_41_1, all_32_5) = all_223_2 & member(all_41_2,
% 106.86/14.86 | | | | | | | all_32_4) = all_223_1 & ( ~ (all_223_0 = 0) | ~
% 106.86/14.86 | | | | | | | (all_223_1 = 0) | ~ (all_223_2 = 0))
% 106.86/14.86 | | | | | | |
% 106.86/14.86 | | | | | | | ALPHA: (85) implies:
% 106.86/14.86 | | | | | | | (86) apply(all_32_8, all_41_1, all_121_3) = all_223_0
% 106.86/14.86 | | | | | | |
% 106.86/14.86 | | | | | | | BETA: splitting (65) gives:
% 106.86/14.86 | | | | | | |
% 106.86/14.86 | | | | | | | Case 1:
% 106.86/14.86 | | | | | | | |
% 106.86/14.86 | | | | | | | | (87) all_113_0 = all_41_2
% 106.86/14.86 | | | | | | | |
% 106.86/14.86 | | | | | | | | REF_CLOSE: (18), (25), (55), (71), (72), (73), (74), (83), (86),
% 106.86/14.86 | | | | | | | | (87) are inconsistent by sub-proof #2.
% 106.86/14.86 | | | | | | | |
% 106.86/14.86 | | | | | | | Case 2:
% 106.86/14.86 | | | | | | | |
% 106.86/14.86 | | | | | | | | (88) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_55_0,
% 106.86/14.86 | | | | | | | | all_113_0) = v0 & apply(all_32_8, all_55_0,
% 106.86/14.86 | | | | | | | | all_41_2) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 106.86/14.86 | | | | | | | |
% 106.86/14.86 | | | | | | | | DELTA: instantiating (88) with fresh symbols all_229_0,
% 106.86/14.86 | | | | | | | | all_229_1 gives:
% 106.86/14.86 | | | | | | | | (89) apply(all_32_8, all_55_0, all_113_0) = all_229_1 &
% 106.86/14.86 | | | | | | | | apply(all_32_8, all_55_0, all_41_2) = all_229_0 & ( ~
% 106.86/14.86 | | | | | | | | (all_229_0 = 0) | ~ (all_229_1 = 0))
% 106.86/14.86 | | | | | | | |
% 106.86/14.86 | | | | | | | | ALPHA: (89) implies:
% 106.86/14.86 | | | | | | | | (90) apply(all_32_8, all_55_0, all_41_2) = all_229_0
% 106.86/14.86 | | | | | | | |
% 106.86/14.86 | | | | | | | | BETA: splitting (70) gives:
% 106.86/14.86 | | | | | | | |
% 106.86/14.86 | | | | | | | | Case 1:
% 106.86/14.86 | | | | | | | | |
% 106.86/14.86 | | | | | | | | | (91) all_121_3 = all_41_2
% 106.86/14.86 | | | | | | | | |
% 106.86/14.86 | | | | | | | | | REDUCE: (83), (91) imply:
% 106.86/14.86 | | | | | | | | | (92) $false
% 106.86/14.86 | | | | | | | | |
% 106.86/14.86 | | | | | | | | | CLOSE: (92) is inconsistent.
% 106.86/14.86 | | | | | | | | |
% 106.86/14.86 | | | | | | | | Case 2:
% 106.86/14.86 | | | | | | | | |
% 106.86/14.86 | | | | | | | | | (93) ? [v0: any] : ? [v1: any] : (apply(all_32_8,
% 106.86/14.86 | | | | | | | | | all_55_0, all_121_3) = v0 & apply(all_32_8,
% 106.86/14.86 | | | | | | | | | all_55_0, all_41_2) = v1 & ( ~ (v1 = 0) | ~ (v0 =
% 106.86/14.86 | | | | | | | | | 0)))
% 106.86/14.86 | | | | | | | | |
% 106.86/14.86 | | | | | | | | | DELTA: instantiating (93) with fresh symbols all_449_0,
% 106.86/14.86 | | | | | | | | | all_449_1 gives:
% 107.09/14.86 | | | | | | | | | (94) apply(all_32_8, all_55_0, all_121_3) = all_449_1 &
% 107.09/14.86 | | | | | | | | | apply(all_32_8, all_55_0, all_41_2) = all_449_0 & ( ~
% 107.09/14.86 | | | | | | | | | (all_449_0 = 0) | ~ (all_449_1 = 0))
% 107.09/14.86 | | | | | | | | |
% 107.09/14.86 | | | | | | | | | ALPHA: (94) implies:
% 107.09/14.86 | | | | | | | | | (95) apply(all_32_8, all_55_0, all_41_2) = all_449_0
% 107.09/14.86 | | | | | | | | |
% 107.09/14.86 | | | | | | | | | BETA: splitting (69) gives:
% 107.09/14.86 | | | | | | | | |
% 107.09/14.86 | | | | | | | | | Case 1:
% 107.09/14.86 | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | (96) all_121_3 = all_41_2
% 107.09/14.86 | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | REDUCE: (83), (96) imply:
% 107.09/14.86 | | | | | | | | | | (97) $false
% 107.09/14.86 | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | CLOSE: (97) is inconsistent.
% 107.09/14.86 | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | Case 2:
% 107.09/14.86 | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | (98) ? [v0: any] : ? [v1: any] : (apply(all_32_8,
% 107.09/14.86 | | | | | | | | | | all_55_0, all_121_3) = v1 & apply(all_32_8,
% 107.09/14.86 | | | | | | | | | | all_55_0, all_41_2) = v0 & ( ~ (v1 = 0) | ~ (v0
% 107.09/14.86 | | | | | | | | | | = 0)))
% 107.09/14.86 | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | DELTA: instantiating (98) with fresh symbols all_454_0,
% 107.09/14.86 | | | | | | | | | | all_454_1 gives:
% 107.09/14.86 | | | | | | | | | | (99) apply(all_32_8, all_55_0, all_121_3) = all_454_0 &
% 107.09/14.86 | | | | | | | | | | apply(all_32_8, all_55_0, all_41_2) = all_454_1 & (
% 107.09/14.86 | | | | | | | | | | ~ (all_454_0 = 0) | ~ (all_454_1 = 0))
% 107.09/14.86 | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | ALPHA: (99) implies:
% 107.09/14.86 | | | | | | | | | | (100) apply(all_32_8, all_55_0, all_41_2) = all_454_1
% 107.09/14.86 | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | BETA: splitting (75) gives:
% 107.09/14.86 | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | Case 1:
% 107.09/14.86 | | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | | (101) all_113_0 = all_41_2
% 107.09/14.86 | | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | | REF_CLOSE: (18), (25), (55), (71), (72), (73), (74), (83),
% 107.09/14.86 | | | | | | | | | | | (86), (101) are inconsistent by sub-proof #2.
% 107.09/14.86 | | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | Case 2:
% 107.09/14.86 | | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | | (102) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 107.09/14.86 | | | | | | | | | | | (apply(all_32_8, all_55_0, all_41_2) = v2 &
% 107.09/14.86 | | | | | | | | | | | member(all_113_0, all_32_4) = v1 &
% 107.09/14.86 | | | | | | | | | | | member(all_55_0, all_32_5) = v0 & ( ~ (v2 = 0) |
% 107.09/14.86 | | | | | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 107.09/14.86 | | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | | DELTA: instantiating (102) with fresh symbols all_470_0,
% 107.09/14.86 | | | | | | | | | | | all_470_1, all_470_2 gives:
% 107.09/14.86 | | | | | | | | | | | (103) apply(all_32_8, all_55_0, all_41_2) = all_470_0 &
% 107.09/14.86 | | | | | | | | | | | member(all_113_0, all_32_4) = all_470_1 &
% 107.09/14.86 | | | | | | | | | | | member(all_55_0, all_32_5) = all_470_2 & ( ~
% 107.09/14.86 | | | | | | | | | | | (all_470_0 = 0) | ~ (all_470_1 = 0) | ~
% 107.09/14.86 | | | | | | | | | | | (all_470_2 = 0))
% 107.09/14.86 | | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | | ALPHA: (103) implies:
% 107.09/14.86 | | | | | | | | | | | (104) member(all_55_0, all_32_5) = all_470_2
% 107.09/14.86 | | | | | | | | | | | (105) member(all_113_0, all_32_4) = all_470_1
% 107.09/14.86 | | | | | | | | | | | (106) apply(all_32_8, all_55_0, all_41_2) = all_470_0
% 107.09/14.86 | | | | | | | | | | | (107) ~ (all_470_0 = 0) | ~ (all_470_1 = 0) | ~
% 107.09/14.86 | | | | | | | | | | | (all_470_2 = 0)
% 107.09/14.86 | | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | | BETA: splitting (64) gives:
% 107.09/14.86 | | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | | Case 1:
% 107.09/14.86 | | | | | | | | | | | |
% 107.09/14.86 | | | | | | | | | | | | (108) all_41_0 = all_41_1
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | REDUCE: (7), (108) imply:
% 107.09/14.87 | | | | | | | | | | | | (109) $false
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | CLOSE: (109) is inconsistent.
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | Case 2:
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | GROUND_INST: instantiating (35) with 0, all_470_2, all_32_5,
% 107.09/14.87 | | | | | | | | | | | | all_55_0, simplifying with (26), (104) gives:
% 107.09/14.87 | | | | | | | | | | | | (110) all_470_2 = 0
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | GROUND_INST: instantiating (35) with 0, all_470_1, all_32_4,
% 107.09/14.87 | | | | | | | | | | | | all_113_0, simplifying with (19), (105) gives:
% 107.09/14.87 | | | | | | | | | | | | (111) all_470_1 = 0
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | GROUND_INST: instantiating (25) with 0, all_449_0, all_41_2,
% 107.09/14.87 | | | | | | | | | | | | all_55_0, all_32_8, simplifying with (78), (95)
% 107.09/14.87 | | | | | | | | | | | | gives:
% 107.09/14.87 | | | | | | | | | | | | (112) all_449_0 = 0
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_449_0, all_454_1,
% 107.09/14.87 | | | | | | | | | | | | all_41_2, all_55_0, all_32_8, simplifying with
% 107.09/14.87 | | | | | | | | | | | | (95), (100) gives:
% 107.09/14.87 | | | | | | | | | | | | (113) all_454_1 = all_449_0
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_454_1, all_470_0,
% 107.09/14.87 | | | | | | | | | | | | all_41_2, all_55_0, all_32_8, simplifying with
% 107.09/14.87 | | | | | | | | | | | | (100), (106) gives:
% 107.09/14.87 | | | | | | | | | | | | (114) all_470_0 = all_454_1
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | GROUND_INST: instantiating (25) with all_229_0, all_470_0,
% 107.09/14.87 | | | | | | | | | | | | all_41_2, all_55_0, all_32_8, simplifying with
% 107.09/14.87 | | | | | | | | | | | | (90), (106) gives:
% 107.09/14.87 | | | | | | | | | | | | (115) all_470_0 = all_229_0
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | COMBINE_EQS: (114), (115) imply:
% 107.09/14.87 | | | | | | | | | | | | (116) all_454_1 = all_229_0
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | SIMP: (116) implies:
% 107.09/14.87 | | | | | | | | | | | | (117) all_454_1 = all_229_0
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | COMBINE_EQS: (113), (117) imply:
% 107.09/14.87 | | | | | | | | | | | | (118) all_449_0 = all_229_0
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | SIMP: (118) implies:
% 107.09/14.87 | | | | | | | | | | | | (119) all_449_0 = all_229_0
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | COMBINE_EQS: (112), (119) imply:
% 107.09/14.87 | | | | | | | | | | | | (120) all_229_0 = 0
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | SIMP: (120) implies:
% 107.09/14.87 | | | | | | | | | | | | (121) all_229_0 = 0
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | COMBINE_EQS: (115), (121) imply:
% 107.09/14.87 | | | | | | | | | | | | (122) all_470_0 = 0
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | BETA: splitting (107) gives:
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | Case 1:
% 107.09/14.87 | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | | (123) ~ (all_470_0 = 0)
% 107.09/14.87 | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | | REDUCE: (122), (123) imply:
% 107.09/14.87 | | | | | | | | | | | | | (124) $false
% 107.09/14.87 | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | | CLOSE: (124) is inconsistent.
% 107.09/14.87 | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | Case 2:
% 107.09/14.87 | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | | (125) ~ (all_470_1 = 0) | ~ (all_470_2 = 0)
% 107.09/14.87 | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | | BETA: splitting (125) gives:
% 107.09/14.87 | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | | Case 1:
% 107.09/14.87 | | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | | | (126) ~ (all_470_1 = 0)
% 107.09/14.87 | | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | | | REDUCE: (111), (126) imply:
% 107.09/14.87 | | | | | | | | | | | | | | (127) $false
% 107.09/14.87 | | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | | | CLOSE: (127) is inconsistent.
% 107.09/14.87 | | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | | Case 2:
% 107.09/14.87 | | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | | | (128) ~ (all_470_2 = 0)
% 107.09/14.87 | | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | | | REDUCE: (110), (128) imply:
% 107.09/14.87 | | | | | | | | | | | | | | (129) $false
% 107.09/14.87 | | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | | | CLOSE: (129) is inconsistent.
% 107.09/14.87 | | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | | End of split
% 107.09/14.87 | | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | | End of split
% 107.09/14.87 | | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | | End of split
% 107.09/14.87 | | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | End of split
% 107.09/14.87 | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | End of split
% 107.09/14.87 | | | | | | | | |
% 107.09/14.87 | | | | | | | | End of split
% 107.09/14.87 | | | | | | | |
% 107.09/14.87 | | | | | | | End of split
% 107.09/14.87 | | | | | | |
% 107.09/14.87 | | | | | | End of split
% 107.09/14.87 | | | | | |
% 107.09/14.87 | | | | | Case 2:
% 107.09/14.87 | | | | | |
% 107.09/14.87 | | | | | | (130) ~ (all_119_3 = all_55_0)
% 107.09/14.87 | | | | | |
% 107.09/14.87 | | | | | | BETA: splitting (76) gives:
% 107.09/14.87 | | | | | |
% 107.09/14.87 | | | | | | Case 1:
% 107.09/14.87 | | | | | | |
% 107.09/14.87 | | | | | | | (131) all_119_3 = all_55_0
% 107.09/14.87 | | | | | | |
% 107.09/14.87 | | | | | | | REDUCE: (130), (131) imply:
% 107.09/14.87 | | | | | | | (132) $false
% 107.09/14.87 | | | | | | |
% 107.09/14.87 | | | | | | | CLOSE: (132) is inconsistent.
% 107.09/14.87 | | | | | | |
% 107.09/14.87 | | | | | | Case 2:
% 107.09/14.87 | | | | | | |
% 107.09/14.87 | | | | | | | (133) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 107.09/14.87 | | | | | | | (member(all_119_3, all_32_5) = v1 & member(all_55_0,
% 107.09/14.87 | | | | | | | all_32_5) = v2 & member(all_41_2, all_32_4) = v0 & (
% 107.09/14.87 | | | | | | | ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 107.09/14.87 | | | | | | |
% 107.09/14.87 | | | | | | | DELTA: instantiating (133) with fresh symbols all_369_0,
% 107.09/14.87 | | | | | | | all_369_1, all_369_2 gives:
% 107.09/14.87 | | | | | | | (134) member(all_119_3, all_32_5) = all_369_1 &
% 107.09/14.87 | | | | | | | member(all_55_0, all_32_5) = all_369_0 & member(all_41_2,
% 107.09/14.87 | | | | | | | all_32_4) = all_369_2 & ( ~ (all_369_0 = 0) | ~
% 107.09/14.87 | | | | | | | (all_369_1 = 0) | ~ (all_369_2 = 0))
% 107.09/14.87 | | | | | | |
% 107.09/14.87 | | | | | | | ALPHA: (134) implies:
% 107.09/14.87 | | | | | | | (135) member(all_41_2, all_32_4) = all_369_2
% 107.09/14.87 | | | | | | | (136) member(all_55_0, all_32_5) = all_369_0
% 107.09/14.87 | | | | | | | (137) member(all_119_3, all_32_5) = all_369_1
% 107.09/14.87 | | | | | | | (138) ~ (all_369_0 = 0) | ~ (all_369_1 = 0) | ~ (all_369_2 =
% 107.09/14.87 | | | | | | | 0)
% 107.09/14.87 | | | | | | |
% 107.09/14.87 | | | | | | | BETA: splitting (67) gives:
% 107.09/14.87 | | | | | | |
% 107.09/14.87 | | | | | | | Case 1:
% 107.09/14.87 | | | | | | | |
% 107.09/14.87 | | | | | | | | (139) all_119_3 = all_55_0
% 107.09/14.87 | | | | | | | |
% 107.09/14.87 | | | | | | | | REDUCE: (130), (139) imply:
% 107.09/14.87 | | | | | | | | (140) $false
% 107.09/14.87 | | | | | | | |
% 107.09/14.87 | | | | | | | | CLOSE: (140) is inconsistent.
% 107.09/14.87 | | | | | | | |
% 107.09/14.87 | | | | | | | Case 2:
% 107.09/14.87 | | | | | | | |
% 107.09/14.87 | | | | | | | |
% 107.09/14.87 | | | | | | | | GROUND_INST: instantiating (35) with 0, all_369_2, all_32_4,
% 107.09/14.87 | | | | | | | | all_41_2, simplifying with (30), (135) gives:
% 107.09/14.87 | | | | | | | | (141) all_369_2 = 0
% 107.09/14.87 | | | | | | | |
% 107.09/14.87 | | | | | | | | GROUND_INST: instantiating (35) with 0, all_369_0, all_32_5,
% 107.09/14.87 | | | | | | | | all_55_0, simplifying with (26), (136) gives:
% 107.09/14.87 | | | | | | | | (142) all_369_0 = 0
% 107.09/14.87 | | | | | | | |
% 107.09/14.87 | | | | | | | | GROUND_INST: instantiating (35) with 0, all_369_1, all_32_5,
% 107.09/14.87 | | | | | | | | all_119_3, simplifying with (58), (137) gives:
% 107.09/14.87 | | | | | | | | (143) all_369_1 = 0
% 107.09/14.87 | | | | | | | |
% 107.09/14.87 | | | | | | | | BETA: splitting (138) gives:
% 107.09/14.87 | | | | | | | |
% 107.09/14.87 | | | | | | | | Case 1:
% 107.09/14.87 | | | | | | | | |
% 107.09/14.87 | | | | | | | | | (144) ~ (all_369_0 = 0)
% 107.09/14.87 | | | | | | | | |
% 107.09/14.87 | | | | | | | | | REDUCE: (142), (144) imply:
% 107.09/14.87 | | | | | | | | | (145) $false
% 107.09/14.87 | | | | | | | | |
% 107.09/14.87 | | | | | | | | | CLOSE: (145) is inconsistent.
% 107.09/14.87 | | | | | | | | |
% 107.09/14.87 | | | | | | | | Case 2:
% 107.09/14.87 | | | | | | | | |
% 107.09/14.87 | | | | | | | | | (146) ~ (all_369_1 = 0) | ~ (all_369_2 = 0)
% 107.09/14.87 | | | | | | | | |
% 107.09/14.87 | | | | | | | | | BETA: splitting (146) gives:
% 107.09/14.87 | | | | | | | | |
% 107.09/14.87 | | | | | | | | | Case 1:
% 107.09/14.87 | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | (147) ~ (all_369_1 = 0)
% 107.09/14.87 | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | REDUCE: (143), (147) imply:
% 107.09/14.87 | | | | | | | | | | (148) $false
% 107.09/14.87 | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | CLOSE: (148) is inconsistent.
% 107.09/14.87 | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | Case 2:
% 107.09/14.87 | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | (149) ~ (all_369_2 = 0)
% 107.09/14.87 | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | REDUCE: (141), (149) imply:
% 107.09/14.87 | | | | | | | | | | (150) $false
% 107.09/14.87 | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | | CLOSE: (150) is inconsistent.
% 107.09/14.87 | | | | | | | | | |
% 107.09/14.87 | | | | | | | | | End of split
% 107.09/14.87 | | | | | | | | |
% 107.09/14.87 | | | | | | | | End of split
% 107.09/14.87 | | | | | | | |
% 107.09/14.87 | | | | | | | End of split
% 107.09/14.87 | | | | | | |
% 107.09/14.87 | | | | | | End of split
% 107.09/14.87 | | | | | |
% 107.09/14.87 | | | | | End of split
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | Case 2:
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | | (151) member(all_41_2, all_32_4) = all_119_4 & member(all_41_2,
% 107.09/14.87 | | | | | all_32_4) = all_119_5 & ( ~ (all_119_4 = 0) | ~ (all_119_5
% 107.09/14.87 | | | | | = 0))
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | | ALPHA: (151) implies:
% 107.09/14.87 | | | | | (152) member(all_41_2, all_32_4) = all_119_5
% 107.09/14.87 | | | | | (153) member(all_41_2, all_32_4) = all_119_4
% 107.09/14.87 | | | | | (154) ~ (all_119_4 = 0) | ~ (all_119_5 = 0)
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | | GROUND_INST: instantiating (35) with 0, all_119_4, all_32_4, all_41_2,
% 107.09/14.87 | | | | | simplifying with (30), (153) gives:
% 107.09/14.87 | | | | | (155) all_119_4 = 0
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | | GROUND_INST: instantiating (35) with all_119_5, all_119_4, all_32_4,
% 107.09/14.87 | | | | | all_41_2, simplifying with (152), (153) gives:
% 107.09/14.87 | | | | | (156) all_119_4 = all_119_5
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | | COMBINE_EQS: (155), (156) imply:
% 107.09/14.87 | | | | | (157) all_119_5 = 0
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | | SIMP: (157) implies:
% 107.09/14.87 | | | | | (158) all_119_5 = 0
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | | BETA: splitting (154) gives:
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | | Case 1:
% 107.09/14.87 | | | | | |
% 107.09/14.87 | | | | | | (159) ~ (all_119_4 = 0)
% 107.09/14.87 | | | | | |
% 107.09/14.87 | | | | | | REDUCE: (155), (159) imply:
% 107.09/14.87 | | | | | | (160) $false
% 107.09/14.87 | | | | | |
% 107.09/14.87 | | | | | | CLOSE: (160) is inconsistent.
% 107.09/14.87 | | | | | |
% 107.09/14.87 | | | | | Case 2:
% 107.09/14.87 | | | | | |
% 107.09/14.87 | | | | | | (161) ~ (all_119_5 = 0)
% 107.09/14.87 | | | | | |
% 107.09/14.87 | | | | | | REDUCE: (158), (161) imply:
% 107.09/14.87 | | | | | | (162) $false
% 107.09/14.87 | | | | | |
% 107.09/14.87 | | | | | | CLOSE: (162) is inconsistent.
% 107.09/14.87 | | | | | |
% 107.09/14.87 | | | | | End of split
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | End of split
% 107.09/14.87 | | | |
% 107.09/14.87 | | | Case 2:
% 107.09/14.87 | | | |
% 107.09/14.87 | | | | (163) member(all_41_1, all_32_5) = all_121_4 & member(all_41_1,
% 107.09/14.87 | | | | all_32_5) = all_121_5 & ( ~ (all_121_4 = 0) | ~ (all_121_5 =
% 107.09/14.87 | | | | 0))
% 107.09/14.87 | | | |
% 107.09/14.87 | | | | ALPHA: (163) implies:
% 107.09/14.87 | | | | (164) member(all_41_1, all_32_5) = all_121_5
% 107.09/14.87 | | | | (165) member(all_41_1, all_32_5) = all_121_4
% 107.09/14.87 | | | | (166) ~ (all_121_4 = 0) | ~ (all_121_5 = 0)
% 107.09/14.87 | | | |
% 107.09/14.87 | | | | GROUND_INST: instantiating (35) with 0, all_121_4, all_32_5, all_41_1,
% 107.09/14.87 | | | | simplifying with (32), (165) gives:
% 107.09/14.87 | | | | (167) all_121_4 = 0
% 107.09/14.87 | | | |
% 107.09/14.87 | | | | GROUND_INST: instantiating (35) with all_121_5, all_121_4, all_32_5,
% 107.09/14.87 | | | | all_41_1, simplifying with (164), (165) gives:
% 107.09/14.87 | | | | (168) all_121_4 = all_121_5
% 107.09/14.87 | | | |
% 107.09/14.87 | | | | COMBINE_EQS: (167), (168) imply:
% 107.09/14.87 | | | | (169) all_121_5 = 0
% 107.09/14.87 | | | |
% 107.09/14.87 | | | | BETA: splitting (166) gives:
% 107.09/14.87 | | | |
% 107.09/14.87 | | | | Case 1:
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | | (170) ~ (all_121_4 = 0)
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | | REDUCE: (167), (170) imply:
% 107.09/14.87 | | | | | (171) $false
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | | CLOSE: (171) is inconsistent.
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | Case 2:
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | | (172) ~ (all_121_5 = 0)
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | | REDUCE: (169), (172) imply:
% 107.09/14.87 | | | | | (173) $false
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | | CLOSE: (173) is inconsistent.
% 107.09/14.87 | | | | |
% 107.09/14.87 | | | | End of split
% 107.09/14.87 | | | |
% 107.09/14.87 | | | End of split
% 107.09/14.87 | | |
% 107.09/14.87 | | End of split
% 107.09/14.87 | |
% 107.09/14.87 | End of split
% 107.09/14.87 |
% 107.09/14.87 End of proof
% 107.09/14.87
% 107.09/14.87 Sub-proof #2 shows that the following formulas are inconsistent:
% 107.09/14.87 ----------------------------------------------------------------
% 107.09/14.87 (1) apply(all_32_8, all_41_1, all_121_3) = all_223_0
% 107.09/14.88 (2) ~ (all_121_3 = all_41_2)
% 107.09/14.88 (3) all_121_3 = all_113_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8,
% 107.09/14.88 all_41_1, all_121_3) = v0 & apply(all_32_8, all_41_1, all_113_0) = v1
% 107.09/14.88 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 107.09/14.88 (4) all_121_3 = all_113_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 107.09/14.88 (apply(all_32_8, all_41_1, all_113_0) = v2 & member(all_121_3, all_32_4)
% 107.09/14.88 = v1 & member(all_41_1, all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) |
% 107.09/14.88 ~ (v0 = 0)))
% 107.09/14.88 (5) all_121_3 = all_113_0 | ? [v0: any] : ? [v1: any] : (apply(all_32_8,
% 107.09/14.88 all_41_1, all_121_3) = v1 & apply(all_32_8, all_41_1, all_113_0) = v0
% 107.09/14.88 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 107.09/14.88 (6) apply(all_32_8, all_41_1, all_41_2) = 0
% 107.09/14.88 (7) all_113_0 = all_41_2
% 107.09/14.88 (8) apply(all_32_8, all_41_1, all_121_3) = 0
% 107.09/14.88 (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 107.09/14.88 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~
% 107.09/14.88 (apply(v4, v3, v2) = v0))
% 107.09/14.88 (10) all_121_3 = all_41_2 | ? [v0: any] : ? [v1: any] : (apply(all_32_8,
% 107.09/14.88 all_41_0, all_121_3) = v0 & apply(all_32_8, all_41_0, all_41_2) = v1
% 107.09/14.88 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 107.09/14.88
% 107.09/14.88 Begin of proof
% 107.09/14.88 |
% 107.09/14.88 | BETA: splitting (4) gives:
% 107.09/14.88 |
% 107.09/14.88 | Case 1:
% 107.09/14.88 | |
% 107.09/14.88 | | (11) all_121_3 = all_113_0
% 107.09/14.88 | |
% 107.09/14.88 | | COMBINE_EQS: (7), (11) imply:
% 107.09/14.88 | | (12) all_121_3 = all_41_2
% 107.09/14.88 | |
% 107.09/14.88 | | REDUCE: (2), (12) imply:
% 107.09/14.88 | | (13) $false
% 107.09/14.88 | |
% 107.09/14.88 | | CLOSE: (13) is inconsistent.
% 107.09/14.88 | |
% 107.09/14.88 | Case 2:
% 107.09/14.88 | |
% 107.09/14.88 | | (14) ~ (all_121_3 = all_113_0)
% 107.09/14.88 | | (15) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_8,
% 107.09/14.88 | | all_41_1, all_113_0) = v2 & member(all_121_3, all_32_4) = v1 &
% 107.09/14.88 | | member(all_41_1, all_32_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 107.09/14.88 | | (v0 = 0)))
% 107.09/14.88 | |
% 107.09/14.88 | | DELTA: instantiating (15) with fresh symbols all_265_0, all_265_1, all_265_2
% 107.09/14.88 | | gives:
% 107.09/14.88 | | (16) apply(all_32_8, all_41_1, all_113_0) = all_265_0 & member(all_121_3,
% 107.09/14.88 | | all_32_4) = all_265_1 & member(all_41_1, all_32_5) = all_265_2 & (
% 107.09/14.88 | | ~ (all_265_0 = 0) | ~ (all_265_1 = 0) | ~ (all_265_2 = 0))
% 107.09/14.88 | |
% 107.09/14.88 | | ALPHA: (16) implies:
% 107.09/14.88 | | (17) apply(all_32_8, all_41_1, all_113_0) = all_265_0
% 107.09/14.88 | |
% 107.09/14.88 | | REDUCE: (7), (17) imply:
% 107.09/14.88 | | (18) apply(all_32_8, all_41_1, all_41_2) = all_265_0
% 107.09/14.88 | |
% 107.09/14.88 | | BETA: splitting (3) gives:
% 107.09/14.88 | |
% 107.09/14.88 | | Case 1:
% 107.09/14.88 | | |
% 107.09/14.88 | | | (19) all_121_3 = all_113_0
% 107.09/14.88 | | |
% 107.09/14.88 | | | COMBINE_EQS: (7), (19) imply:
% 107.09/14.88 | | | (20) all_121_3 = all_41_2
% 107.09/14.88 | | |
% 107.09/14.88 | | | REDUCE: (2), (20) imply:
% 107.09/14.88 | | | (21) $false
% 107.09/14.88 | | |
% 107.09/14.88 | | | CLOSE: (21) is inconsistent.
% 107.09/14.88 | | |
% 107.09/14.88 | | Case 2:
% 107.09/14.88 | | |
% 107.09/14.88 | | | (22) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_41_1,
% 107.09/14.88 | | | all_121_3) = v0 & apply(all_32_8, all_41_1, all_113_0) = v1 &
% 107.09/14.88 | | | ( ~ (v1 = 0) | ~ (v0 = 0)))
% 107.09/14.88 | | |
% 107.09/14.88 | | | DELTA: instantiating (22) with fresh symbols all_271_0, all_271_1 gives:
% 107.09/14.88 | | | (23) apply(all_32_8, all_41_1, all_121_3) = all_271_1 & apply(all_32_8,
% 107.09/14.88 | | | all_41_1, all_113_0) = all_271_0 & ( ~ (all_271_0 = 0) | ~
% 107.09/14.88 | | | (all_271_1 = 0))
% 107.09/14.88 | | |
% 107.09/14.88 | | | ALPHA: (23) implies:
% 107.09/14.88 | | | (24) apply(all_32_8, all_41_1, all_113_0) = all_271_0
% 107.09/14.88 | | | (25) apply(all_32_8, all_41_1, all_121_3) = all_271_1
% 107.09/14.88 | | | (26) ~ (all_271_0 = 0) | ~ (all_271_1 = 0)
% 107.09/14.88 | | |
% 107.09/14.88 | | | REDUCE: (7), (24) imply:
% 107.09/14.88 | | | (27) apply(all_32_8, all_41_1, all_41_2) = all_271_0
% 107.09/14.88 | | |
% 107.09/14.88 | | | BETA: splitting (5) gives:
% 107.09/14.88 | | |
% 107.09/14.88 | | | Case 1:
% 107.09/14.88 | | | |
% 107.09/14.88 | | | | (28) all_121_3 = all_113_0
% 107.09/14.88 | | | |
% 107.09/14.88 | | | | COMBINE_EQS: (7), (28) imply:
% 107.09/14.88 | | | | (29) all_121_3 = all_41_2
% 107.09/14.88 | | | |
% 107.09/14.88 | | | | REDUCE: (2), (29) imply:
% 107.09/14.88 | | | | (30) $false
% 107.09/14.88 | | | |
% 107.09/14.88 | | | | CLOSE: (30) is inconsistent.
% 107.09/14.88 | | | |
% 107.09/14.88 | | | Case 2:
% 107.09/14.88 | | | |
% 107.09/14.88 | | | | (31) ? [v0: any] : ? [v1: any] : (apply(all_32_8, all_41_1,
% 107.09/14.88 | | | | all_121_3) = v1 & apply(all_32_8, all_41_1, all_113_0) = v0
% 107.09/14.88 | | | | & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 107.09/14.88 | | | |
% 107.09/14.88 | | | | DELTA: instantiating (31) with fresh symbols all_421_0, all_421_1 gives:
% 107.09/14.88 | | | | (32) apply(all_32_8, all_41_1, all_121_3) = all_421_0 &
% 107.09/14.88 | | | | apply(all_32_8, all_41_1, all_113_0) = all_421_1 & ( ~
% 107.09/14.88 | | | | (all_421_0 = 0) | ~ (all_421_1 = 0))
% 107.09/14.88 | | | |
% 107.09/14.88 | | | | ALPHA: (32) implies:
% 107.09/14.88 | | | | (33) apply(all_32_8, all_41_1, all_113_0) = all_421_1
% 107.09/14.88 | | | | (34) apply(all_32_8, all_41_1, all_121_3) = all_421_0
% 107.09/14.88 | | | |
% 107.09/14.88 | | | | REDUCE: (7), (33) imply:
% 107.09/14.88 | | | | (35) apply(all_32_8, all_41_1, all_41_2) = all_421_1
% 107.09/14.88 | | | |
% 107.09/14.88 | | | | BETA: splitting (10) gives:
% 107.09/14.88 | | | |
% 107.09/14.88 | | | | Case 1:
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | (36) all_121_3 = all_41_2
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | REDUCE: (2), (36) imply:
% 107.09/14.88 | | | | | (37) $false
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | CLOSE: (37) is inconsistent.
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | Case 2:
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | GROUND_INST: instantiating (9) with all_265_0, all_271_0, all_41_2,
% 107.09/14.88 | | | | | all_41_1, all_32_8, simplifying with (18), (27) gives:
% 107.09/14.88 | | | | | (38) all_271_0 = all_265_0
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | GROUND_INST: instantiating (9) with 0, all_421_1, all_41_2, all_41_1,
% 107.09/14.88 | | | | | all_32_8, simplifying with (6), (35) gives:
% 107.09/14.88 | | | | | (39) all_421_1 = 0
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | GROUND_INST: instantiating (9) with all_271_0, all_421_1, all_41_2,
% 107.09/14.88 | | | | | all_41_1, all_32_8, simplifying with (27), (35) gives:
% 107.09/14.88 | | | | | (40) all_421_1 = all_271_0
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | GROUND_INST: instantiating (9) with all_223_0, all_271_1, all_121_3,
% 107.09/14.88 | | | | | all_41_1, all_32_8, simplifying with (1), (25) gives:
% 107.09/14.88 | | | | | (41) all_271_1 = all_223_0
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | GROUND_INST: instantiating (9) with 0, all_421_0, all_121_3, all_41_1,
% 107.09/14.88 | | | | | all_32_8, simplifying with (8), (34) gives:
% 107.09/14.88 | | | | | (42) all_421_0 = 0
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | GROUND_INST: instantiating (9) with all_271_1, all_421_0, all_121_3,
% 107.09/14.88 | | | | | all_41_1, all_32_8, simplifying with (25), (34) gives:
% 107.09/14.88 | | | | | (43) all_421_0 = all_271_1
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | COMBINE_EQS: (42), (43) imply:
% 107.09/14.88 | | | | | (44) all_271_1 = 0
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | SIMP: (44) implies:
% 107.09/14.88 | | | | | (45) all_271_1 = 0
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | COMBINE_EQS: (39), (40) imply:
% 107.09/14.88 | | | | | (46) all_271_0 = 0
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | SIMP: (46) implies:
% 107.09/14.88 | | | | | (47) all_271_0 = 0
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | COMBINE_EQS: (38), (47) imply:
% 107.09/14.88 | | | | | (48) all_265_0 = 0
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | COMBINE_EQS: (41), (45) imply:
% 107.09/14.88 | | | | | (49) all_223_0 = 0
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | BETA: splitting (26) gives:
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | | Case 1:
% 107.09/14.88 | | | | | |
% 107.09/14.88 | | | | | | (50) ~ (all_271_0 = 0)
% 107.09/14.88 | | | | | |
% 107.09/14.88 | | | | | | REDUCE: (47), (50) imply:
% 107.09/14.88 | | | | | | (51) $false
% 107.09/14.88 | | | | | |
% 107.09/14.88 | | | | | | CLOSE: (51) is inconsistent.
% 107.09/14.88 | | | | | |
% 107.09/14.88 | | | | | Case 2:
% 107.09/14.88 | | | | | |
% 107.09/14.88 | | | | | | (52) ~ (all_271_1 = 0)
% 107.09/14.88 | | | | | |
% 107.09/14.88 | | | | | | REDUCE: (45), (52) imply:
% 107.09/14.88 | | | | | | (53) $false
% 107.09/14.88 | | | | | |
% 107.09/14.88 | | | | | | CLOSE: (53) is inconsistent.
% 107.09/14.88 | | | | | |
% 107.09/14.88 | | | | | End of split
% 107.09/14.88 | | | | |
% 107.09/14.88 | | | | End of split
% 107.09/14.88 | | | |
% 107.09/14.88 | | | End of split
% 107.09/14.88 | | |
% 107.09/14.88 | | End of split
% 107.09/14.88 | |
% 107.09/14.88 | End of split
% 107.09/14.88 |
% 107.09/14.88 End of proof
% 107.09/14.88 % SZS output end Proof for theBenchmark
% 107.09/14.88
% 107.09/14.88 14269ms
%------------------------------------------------------------------------------