TSTP Solution File: SET709+4 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SET709+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 : n032.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 15:26:05 EDT 2023
% Result : Theorem 14.76s 2.86s
% Output : Proof 22.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET709+4 : TPTP v8.1.2. Bugfixed v2.2.1.
% 0.00/0.10 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Sat Aug 26 10:12:58 EDT 2023
% 0.10/0.29 % CPUTime :
% 0.14/0.51 ________ _____
% 0.14/0.51 ___ __ \_________(_)________________________________
% 0.14/0.51 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.14/0.51 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.14/0.51 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.14/0.51
% 0.14/0.51 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.14/0.51 (2023-06-19)
% 0.14/0.51
% 0.14/0.51 (c) Philipp Rümmer, 2009-2023
% 0.14/0.51 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.14/0.51 Amanda Stjerna.
% 0.14/0.51 Free software under BSD-3-Clause.
% 0.14/0.51
% 0.14/0.51 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.14/0.51
% 0.14/0.52 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.14/0.53 Running up to 7 provers in parallel.
% 0.14/0.54 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.14/0.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.14/0.54 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.14/0.54 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.14/0.54 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.14/0.54 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.14/0.54 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.96/1.05 Prover 1: Preprocessing ...
% 2.96/1.06 Prover 4: Preprocessing ...
% 3.36/1.11 Prover 2: Preprocessing ...
% 3.36/1.11 Prover 0: Preprocessing ...
% 3.36/1.11 Prover 3: Preprocessing ...
% 3.36/1.11 Prover 6: Preprocessing ...
% 3.36/1.11 Prover 5: Preprocessing ...
% 8.82/1.84 Prover 5: Proving ...
% 8.82/1.87 Prover 2: Proving ...
% 9.58/1.91 Prover 6: Proving ...
% 9.58/1.92 Prover 1: Constructing countermodel ...
% 9.58/1.94 Prover 3: Constructing countermodel ...
% 10.25/2.07 Prover 3: gave up
% 10.91/2.10 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 10.91/2.16 Prover 7: Preprocessing ...
% 10.91/2.23 Prover 0: Proving ...
% 12.33/2.29 Prover 7: Warning: ignoring some quantifiers
% 12.48/2.31 Prover 4: Constructing countermodel ...
% 12.48/2.36 Prover 7: Constructing countermodel ...
% 14.76/2.69 Prover 1: gave up
% 14.76/2.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 14.76/2.75 Prover 8: Preprocessing ...
% 14.76/2.86 Prover 0: proved (2327ms)
% 14.76/2.86
% 14.76/2.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.76/2.86
% 14.76/2.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 14.76/2.87 Prover 5: stopped
% 15.62/2.87 Prover 6: stopped
% 15.62/2.88 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 15.62/2.88 Prover 2: stopped
% 15.62/2.89 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 15.62/2.89 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 15.62/2.94 Prover 8: Warning: ignoring some quantifiers
% 15.62/2.94 Prover 11: Preprocessing ...
% 15.62/2.95 Prover 10: Preprocessing ...
% 15.62/2.96 Prover 16: Preprocessing ...
% 17.33/2.96 Prover 8: Constructing countermodel ...
% 17.33/2.98 Prover 13: Preprocessing ...
% 17.33/3.04 Prover 10: Warning: ignoring some quantifiers
% 18.08/3.06 Prover 10: Constructing countermodel ...
% 18.08/3.07 Prover 16: Warning: ignoring some quantifiers
% 18.08/3.08 Prover 16: Constructing countermodel ...
% 18.75/3.15 Prover 13: Warning: ignoring some quantifiers
% 18.75/3.18 Prover 13: Constructing countermodel ...
% 19.25/3.23 Prover 10: gave up
% 19.25/3.24 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 19.66/3.30 Prover 19: Preprocessing ...
% 20.38/3.38 Prover 4: Found proof (size 280)
% 20.38/3.38 Prover 4: proved (2844ms)
% 20.38/3.38 Prover 8: stopped
% 20.38/3.38 Prover 16: stopped
% 20.38/3.38 Prover 7: stopped
% 20.38/3.38 Prover 13: stopped
% 20.88/3.53 Prover 19: Warning: ignoring some quantifiers
% 20.88/3.54 Prover 19: Constructing countermodel ...
% 20.88/3.56 Prover 19: stopped
% 21.03/3.59 Prover 11: Constructing countermodel ...
% 21.03/3.62 Prover 11: stopped
% 21.03/3.62
% 21.03/3.62 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.03/3.62
% 21.82/3.65 % SZS output start Proof for theBenchmark
% 21.82/3.65 Assumptions after simplification:
% 21.82/3.65 ---------------------------------
% 21.82/3.65
% 21.82/3.65 (compose_function)
% 22.09/3.70 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 22.09/3.70 $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~
% 22.09/3.70 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) |
% 22.09/3.70 ~ (apply(v1, v5, v9) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) |
% 22.09/3.70 ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any]
% 22.09/3.70 : ((apply(v0, v9, v6) = v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10
% 22.09/3.70 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 =
% 22.09/3.70 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 22.09/3.70 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8:
% 22.09/3.70 int] : ! [v9: $i] : (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) =
% 22.09/3.70 v7) | ~ (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9)
% 22.09/3.70 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 22.09/3.70 $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v11 &
% 22.09/3.70 member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) | (member(v6, v4)
% 22.09/3.70 = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))))) & !
% 22.09/3.70 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i]
% 22.09/3.70 : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] : (v8 = 0 | ~
% 22.09/3.70 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = v8) |
% 22.09/3.70 ~ (member(v9, v3) = 0) | ~ $i(v9) | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~
% 22.09/3.70 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v10: any] : ? [v11: any] :
% 22.09/3.70 ((apply(v1, v5, v9) = v10 & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~
% 22.09/3.70 (v10 = 0))) | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11
% 22.09/3.70 = 0) | ~ (v10 = 0))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 22.09/3.70 ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~
% 22.09/3.70 (compose_function(v0, v1, v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) |
% 22.09/3.70 ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 22.09/3.70 $i(v0) | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ?
% 22.09/3.70 [v12: int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 &
% 22.09/3.70 apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10, v3) = 0)
% 22.09/3.70 | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~ (v9 = 0) | ~ (v8 =
% 22.09/3.70 0))))))
% 22.09/3.70
% 22.09/3.70 (maps)
% 22.09/3.71 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 22.09/3.71 $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~
% 22.09/3.71 (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 22.09/3.71 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : ? [v8: any] :
% 22.09/3.71 (member(v5, v2) = v8 & member(v4, v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 =
% 22.09/3.71 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 22.09/3.71 [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0,
% 22.09/3.71 v1, v2) = 0) | ~ (apply(v0, v3, v5) = 0) | ~ (member(v4, v2) = 0) | ~
% 22.09/3.71 $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6:
% 22.09/3.71 any] : ? [v7: any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5,
% 22.09/3.71 v2) = v7 & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 =
% 22.09/3.71 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : !
% 22.09/3.71 [v4: $i] : ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0,
% 22.09/3.71 v3, v4) = 0) | ~ (member(v5, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 22.09/3.71 $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] :
% 22.09/3.71 ? [v8: any] : (apply(v0, v3, v5) = v8 & member(v4, v2) = v7 & member(v3, v1)
% 22.09/3.71 = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : ! [v1:
% 22.09/3.71 $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (v5 = v4 | ~
% 22.09/3.71 (maps(v0, v1, v2) = 0) | ~ (member(v5, v2) = 0) | ~ (member(v4, v2) = 0) |
% 22.09/3.71 ~ (member(v3, v1) = 0) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~
% 22.09/3.71 $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 &
% 22.09/3.71 apply(v0, v3, v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v0: $i] : !
% 22.09/3.71 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (maps(v0, v1, v2) = v3) |
% 22.09/3.71 ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : ? [v5: $i] : ? [v6: $i]
% 22.09/3.71 : ? [v7: int] : ? [v8: int] : ? [v9: int] : ? [v10: int] : ? [v11: int]
% 22.09/3.71 : ? [v12: $i] : ? [v13: int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13
% 22.09/3.71 = 0 & member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) =
% 22.09/3.71 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) & member(v14, v2)
% 22.09/3.71 = v15)) & ! [v14: $i] : ( ~ (member(v14, v2) = 0) | ~ $i(v14) |
% 22.09/3.71 ? [v15: int] : ( ~ (v15 = 0) & apply(v0, v12, v14) = v15))) | (v11 =
% 22.09/3.71 0 & v10 = 0 & v9 = 0 & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4,
% 22.09/3.71 v6) = 0 & apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5,
% 22.09/3.71 v2) = 0 & member(v4, v1) = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 22.09/3.71 [v2: $i] : ! [v3: $i] : ( ~ (maps(v0, v1, v2) = 0) | ~ (member(v3, v1) = 0)
% 22.09/3.71 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0,
% 22.09/3.71 v3, v4) = 0 & member(v4, v2) = 0 & $i(v4)))
% 22.09/3.71
% 22.09/3.71 (thII01)
% 22.09/3.71 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] : ? [v5:
% 22.09/3.71 $i] : ? [v6: int] : ( ~ (v6 = 0) & compose_function(v1, v0, v2, v3, v4) =
% 22.09/3.71 v5 & maps(v5, v2, v4) = v6 & maps(v1, v3, v4) = 0 & maps(v0, v2, v3) = 0 &
% 22.09/3.71 $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 22.09/3.71
% 22.09/3.71 (function-axioms)
% 22.09/3.73 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 22.09/3.73 [v3: $i] : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : (v1 = v0 |
% 22.09/3.73 ~ (compose_predicate(v7, v6, v5, v4, v3, v2) = v1) | ~
% 22.09/3.73 (compose_predicate(v7, v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 22.09/3.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 22.09/3.73 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (isomorphism(v6, v5,
% 22.09/3.73 v4, v3, v2) = v1) | ~ (isomorphism(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 22.09/3.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 22.09/3.73 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (decreasing(v6, v5,
% 22.09/3.73 v4, v3, v2) = v1) | ~ (decreasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 22.09/3.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 22.09/3.73 : ! [v4: $i] : ! [v5: $i] : ! [v6: $i] : (v1 = v0 | ~ (increasing(v6, v5,
% 22.09/3.73 v4, v3, v2) = v1) | ~ (increasing(v6, v5, v4, v3, v2) = v0)) & ! [v0:
% 22.09/3.73 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5: $i] :
% 22.09/3.73 ! [v6: $i] : (v1 = v0 | ~ (compose_function(v6, v5, v4, v3, v2) = v1) | ~
% 22.09/3.73 (compose_function(v6, v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] :
% 22.09/3.73 ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 22.09/3.73 $i] : (v1 = v0 | ~ (inverse_predicate(v5, v4, v3, v2) = v1) | ~
% 22.09/3.73 (inverse_predicate(v5, v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 22.09/3.73 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ! [v5:
% 22.09/3.73 $i] : (v1 = v0 | ~ (equal_maps(v5, v4, v3, v2) = v1) | ~ (equal_maps(v5,
% 22.09/3.73 v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 22.09/3.73 $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_image3(v4, v3, v2) = v1) | ~
% 22.09/3.73 (inverse_image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i]
% 22.09/3.73 : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (image3(v4, v3, v2) = v1) | ~
% 22.09/3.73 (image3(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 22.09/3.73 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (inverse_function(v4, v3, v2) = v1) |
% 22.09/3.73 ~ (inverse_function(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 22.09/3.73 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 |
% 22.09/3.73 ~ (one_to_one(v4, v3, v2) = v1) | ~ (one_to_one(v4, v3, v2) = v0)) & !
% 22.09/3.73 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 22.09/3.73 $i] : ! [v4: $i] : (v1 = v0 | ~ (surjective(v4, v3, v2) = v1) | ~
% 22.09/3.73 (surjective(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 22.09/3.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 22.09/3.73 (injective(v4, v3, v2) = v1) | ~ (injective(v4, v3, v2) = v0)) & ! [v0:
% 22.09/3.73 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 22.09/3.73 : ! [v4: $i] : (v1 = v0 | ~ (maps(v4, v3, v2) = v1) | ~ (maps(v4, v3, v2) =
% 22.09/3.73 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 22.09/3.73 $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 22.09/3.73 ~ (apply(v4, v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 22.09/3.73 [v3: $i] : (v1 = v0 | ~ (inverse_image2(v3, v2) = v1) | ~
% 22.09/3.73 (inverse_image2(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] :
% 22.09/3.73 ! [v3: $i] : (v1 = v0 | ~ (image2(v3, v2) = v1) | ~ (image2(v3, v2) = v0)) &
% 22.09/3.73 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 22.09/3.73 [v3: $i] : (v1 = v0 | ~ (identity(v3, v2) = v1) | ~ (identity(v3, v2) = v0))
% 22.09/3.73 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.09/3.73 (unordered_pair(v3, v2) = v1) | ~ (unordered_pair(v3, v2) = v0)) & ! [v0:
% 22.09/3.73 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.09/3.73 (difference(v3, v2) = v1) | ~ (difference(v3, v2) = v0)) & ! [v0: $i] : !
% 22.09/3.73 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (union(v3, v2) = v1) | ~
% 22.09/3.73 (union(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3:
% 22.09/3.73 $i] : (v1 = v0 | ~ (intersection(v3, v2) = v1) | ~ (intersection(v3, v2) =
% 22.09/3.73 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 22.09/3.73 $i] : ! [v3: $i] : (v1 = v0 | ~ (equal_set(v3, v2) = v1) | ~
% 22.09/3.73 (equal_set(v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 22.09/3.73 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (subset(v3,
% 22.09/3.73 v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0: MultipleValueBool] : !
% 22.09/3.73 [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 22.09/3.73 (member(v3, v2) = v1) | ~ (member(v3, v2) = v0)) & ! [v0: $i] : ! [v1:
% 22.09/3.73 $i] : ! [v2: $i] : (v1 = v0 | ~ (product(v2) = v1) | ~ (product(v2) =
% 22.09/3.73 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (sum(v2) =
% 22.09/3.73 v1) | ~ (sum(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 22.09/3.73 v0 | ~ (singleton(v2) = v1) | ~ (singleton(v2) = v0)) & ! [v0: $i] : !
% 22.09/3.73 [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (power_set(v2) = v1) | ~
% 22.09/3.73 (power_set(v2) = v0))
% 22.09/3.73
% 22.09/3.73 Further assumptions not needed in the proof:
% 22.09/3.73 --------------------------------------------
% 22.09/3.73 compose_predicate, decreasing_function, difference, empty_set, equal_maps,
% 22.09/3.73 equal_set, identity, image2, image3, increasing_function, injective,
% 22.09/3.73 intersection, inverse_function, inverse_image2, inverse_image3,
% 22.09/3.73 inverse_predicate, isomorphism, one_to_one, power_set, product, singleton,
% 22.09/3.73 subset, sum, surjective, union, unordered_pair
% 22.09/3.73
% 22.09/3.73 Those formulas are unsatisfiable:
% 22.09/3.73 ---------------------------------
% 22.09/3.73
% 22.09/3.73 Begin of proof
% 22.09/3.73 |
% 22.09/3.73 | ALPHA: (maps) implies:
% 22.09/3.73 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (maps(v0,
% 22.09/3.73 | v1, v2) = 0) | ~ (member(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) |
% 22.09/3.73 | ~ $i(v1) | ~ $i(v0) | ? [v4: $i] : (apply(v0, v3, v4) = 0 &
% 22.09/3.73 | member(v4, v2) = 0 & $i(v4)))
% 22.09/3.74 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 22.09/3.74 | (maps(v0, v1, v2) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4:
% 22.09/3.74 | $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: int] : ? [v8: int] : ?
% 22.09/3.74 | [v9: int] : ? [v10: int] : ? [v11: int] : ? [v12: $i] : ? [v13:
% 22.09/3.74 | int] : ($i(v12) & $i(v6) & $i(v5) & $i(v4) & ((v13 = 0 &
% 22.09/3.74 | member(v12, v1) = 0 & ! [v14: $i] : ( ~ (apply(v0, v12, v14) =
% 22.09/3.74 | 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) &
% 22.09/3.74 | member(v14, v2) = v15)) & ! [v14: $i] : ( ~ (member(v14,
% 22.09/3.74 | v2) = 0) | ~ $i(v14) | ? [v15: int] : ( ~ (v15 = 0) &
% 22.09/3.74 | apply(v0, v12, v14) = v15))) | (v11 = 0 & v10 = 0 & v9 = 0
% 22.09/3.74 | & v8 = 0 & v7 = 0 & ~ (v6 = v5) & apply(v0, v4, v6) = 0 &
% 22.09/3.74 | apply(v0, v4, v5) = 0 & member(v6, v2) = 0 & member(v5, v2) = 0
% 22.09/3.74 | & member(v4, v1) = 0))))
% 22.09/3.74 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 22.09/3.74 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (member(v5, v2)
% 22.09/3.74 | = 0) | ~ (member(v4, v2) = 0) | ~ (member(v3, v1) = 0) | ~
% 22.09/3.74 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 22.09/3.74 | ? [v6: any] : ? [v7: any] : (apply(v0, v3, v5) = v7 & apply(v0, v3,
% 22.09/3.74 | v4) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))
% 22.09/3.74 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 22.09/3.74 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3,
% 22.09/3.74 | v5) = 0) | ~ (member(v4, v2) = 0) | ~ $i(v5) | ~ $i(v4) | ~
% 22.09/3.74 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 22.09/3.74 | any] : ? [v8: any] : (apply(v0, v3, v4) = v8 & member(v5, v2) = v7
% 22.09/3.74 | & member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 22.09/3.74 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 22.09/3.74 | ! [v5: $i] : (v5 = v4 | ~ (maps(v0, v1, v2) = 0) | ~ (apply(v0, v3,
% 22.09/3.74 | v5) = 0) | ~ (apply(v0, v3, v4) = 0) | ~ $i(v5) | ~ $i(v4) |
% 22.09/3.74 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v6: any] : ? [v7:
% 22.09/3.74 | any] : ? [v8: any] : (member(v5, v2) = v8 & member(v4, v2) = v7 &
% 22.09/3.74 | member(v3, v1) = v6 & ( ~ (v8 = 0) | ~ (v7 = 0) | ~ (v6 = 0))))
% 22.09/3.74 |
% 22.09/3.74 | ALPHA: (compose_function) implies:
% 22.09/3.74 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 22.09/3.74 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (compose_function(v0, v1,
% 22.09/3.74 | v2, v3, v4) = v7) | ~ (apply(v7, v5, v6) = 0) | ~ $i(v6) | ~
% 22.09/3.74 | $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) |
% 22.09/3.74 | ? [v8: any] : ? [v9: any] : ? [v10: $i] : ? [v11: int] : ? [v12:
% 22.09/3.74 | int] : ? [v13: int] : ($i(v10) & ((v13 = 0 & v12 = 0 & v11 = 0 &
% 22.09/3.74 | apply(v1, v5, v10) = 0 & apply(v0, v10, v6) = 0 & member(v10,
% 22.09/3.74 | v3) = 0) | (member(v6, v4) = v9 & member(v5, v2) = v8 & ( ~
% 22.09/3.74 | (v9 = 0) | ~ (v8 = 0))))))
% 22.09/3.75 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 22.09/3.75 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] :
% 22.09/3.75 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~
% 22.09/3.75 | (apply(v7, v5, v6) = v8) | ~ (member(v9, v3) = 0) | ~ $i(v9) | ~
% 22.09/3.75 | $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) |
% 22.09/3.75 | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) = v10
% 22.09/3.75 | & apply(v0, v9, v6) = v11 & ( ~ (v11 = 0) | ~ (v10 = 0))) |
% 22.09/3.75 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~
% 22.09/3.75 | (v10 = 0)))))
% 22.09/3.75 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] :
% 22.09/3.75 | ! [v5: $i] : ! [v6: $i] : ! [v7: $i] : ! [v8: int] : ! [v9: $i] :
% 22.09/3.75 | (v8 = 0 | ~ (compose_function(v0, v1, v2, v3, v4) = v7) | ~
% 22.09/3.75 | (apply(v7, v5, v6) = v8) | ~ (apply(v0, v9, v6) = 0) | ~ $i(v9) |
% 22.09/3.75 | ~ $i(v6) | ~ $i(v5) | ~ $i(v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1)
% 22.09/3.75 | | ~ $i(v0) | ? [v10: any] : ? [v11: any] : ((apply(v1, v5, v9) =
% 22.09/3.75 | v11 & member(v9, v3) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0))) |
% 22.09/3.75 | (member(v6, v4) = v11 & member(v5, v2) = v10 & ( ~ (v11 = 0) | ~
% 22.09/3.75 | (v10 = 0)))))
% 22.09/3.75 |
% 22.09/3.75 | ALPHA: (function-axioms) implies:
% 22.09/3.75 | (9) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 22.09/3.75 | ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2)
% 22.09/3.75 | = v0))
% 22.09/3.75 | (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 22.09/3.75 | : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) |
% 22.09/3.75 | ~ (apply(v4, v3, v2) = v0))
% 22.09/3.75 |
% 22.09/3.75 | DELTA: instantiating (thII01) with fresh symbols all_32_0, all_32_1, all_32_2,
% 22.09/3.75 | all_32_3, all_32_4, all_32_5, all_32_6 gives:
% 22.09/3.75 | (11) ~ (all_32_0 = 0) & compose_function(all_32_5, all_32_6, all_32_4,
% 22.09/3.75 | all_32_3, all_32_2) = all_32_1 & maps(all_32_1, all_32_4, all_32_2)
% 22.09/3.75 | = all_32_0 & maps(all_32_5, all_32_3, all_32_2) = 0 & maps(all_32_6,
% 22.09/3.75 | all_32_4, all_32_3) = 0 & $i(all_32_1) & $i(all_32_2) & $i(all_32_3)
% 22.09/3.75 | & $i(all_32_4) & $i(all_32_5) & $i(all_32_6)
% 22.09/3.75 |
% 22.09/3.75 | ALPHA: (11) implies:
% 22.09/3.75 | (12) ~ (all_32_0 = 0)
% 22.09/3.75 | (13) $i(all_32_6)
% 22.09/3.75 | (14) $i(all_32_5)
% 22.09/3.75 | (15) $i(all_32_4)
% 22.09/3.75 | (16) $i(all_32_3)
% 22.09/3.75 | (17) $i(all_32_2)
% 22.09/3.75 | (18) $i(all_32_1)
% 22.09/3.75 | (19) maps(all_32_6, all_32_4, all_32_3) = 0
% 22.09/3.75 | (20) maps(all_32_5, all_32_3, all_32_2) = 0
% 22.09/3.75 | (21) maps(all_32_1, all_32_4, all_32_2) = all_32_0
% 22.09/3.75 | (22) compose_function(all_32_5, all_32_6, all_32_4, all_32_3, all_32_2) =
% 22.09/3.75 | all_32_1
% 22.09/3.75 |
% 22.09/3.75 | GROUND_INST: instantiating (2) with all_32_1, all_32_4, all_32_2, all_32_0,
% 22.09/3.75 | simplifying with (15), (17), (18), (21) gives:
% 22.09/3.75 | (23) all_32_0 = 0 | ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int]
% 22.09/3.75 | : ? [v4: int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8:
% 22.09/3.76 | $i] : ? [v9: int] : ($i(v8) & $i(v2) & $i(v1) & $i(v0) & ((v9 = 0 &
% 22.09/3.76 | member(v8, all_32_4) = 0 & ! [v10: $i] : ( ~ (apply(all_32_1,
% 22.09/3.76 | v8, v10) = 0) | ~ $i(v10) | ? [v11: int] : ( ~ (v11 = 0)
% 22.09/3.76 | & member(v10, all_32_2) = v11)) & ! [v10: $i] : ( ~
% 22.44/3.76 | (member(v10, all_32_2) = 0) | ~ $i(v10) | ? [v11: int] : ( ~
% 22.44/3.76 | (v11 = 0) & apply(all_32_1, v8, v10) = v11))) | (v7 = 0 & v6
% 22.44/3.76 | = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v2 = v1) & apply(all_32_1,
% 22.44/3.76 | v0, v2) = 0 & apply(all_32_1, v0, v1) = 0 & member(v2,
% 22.44/3.76 | all_32_2) = 0 & member(v1, all_32_2) = 0 & member(v0,
% 22.44/3.76 | all_32_4) = 0)))
% 22.44/3.76 |
% 22.44/3.76 | BETA: splitting (23) gives:
% 22.44/3.76 |
% 22.44/3.76 | Case 1:
% 22.44/3.76 | |
% 22.44/3.76 | | (24) all_32_0 = 0
% 22.44/3.76 | |
% 22.44/3.76 | | REDUCE: (12), (24) imply:
% 22.44/3.76 | | (25) $false
% 22.44/3.76 | |
% 22.44/3.76 | | CLOSE: (25) is inconsistent.
% 22.44/3.76 | |
% 22.44/3.76 | Case 2:
% 22.44/3.76 | |
% 22.44/3.76 | | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ? [v4:
% 22.44/3.76 | | int] : ? [v5: int] : ? [v6: int] : ? [v7: int] : ? [v8: $i] :
% 22.44/3.76 | | ? [v9: int] : ($i(v8) & $i(v2) & $i(v1) & $i(v0) & ((v9 = 0 &
% 22.44/3.76 | | member(v8, all_32_4) = 0 & ! [v10: $i] : ( ~ (apply(all_32_1,
% 22.44/3.76 | | v8, v10) = 0) | ~ $i(v10) | ? [v11: int] : ( ~ (v11 =
% 22.44/3.76 | | 0) & member(v10, all_32_2) = v11)) & ! [v10: $i] : ( ~
% 22.44/3.76 | | (member(v10, all_32_2) = 0) | ~ $i(v10) | ? [v11: int] : (
% 22.44/3.76 | | ~ (v11 = 0) & apply(all_32_1, v8, v10) = v11))) | (v7 = 0
% 22.44/3.76 | | & v6 = 0 & v5 = 0 & v4 = 0 & v3 = 0 & ~ (v2 = v1) &
% 22.44/3.76 | | apply(all_32_1, v0, v2) = 0 & apply(all_32_1, v0, v1) = 0 &
% 22.44/3.76 | | member(v2, all_32_2) = 0 & member(v1, all_32_2) = 0 &
% 22.44/3.76 | | member(v0, all_32_4) = 0)))
% 22.44/3.76 | |
% 22.44/3.76 | | DELTA: instantiating (26) with fresh symbols all_41_0, all_41_1, all_41_2,
% 22.44/3.76 | | all_41_3, all_41_4, all_41_5, all_41_6, all_41_7, all_41_8, all_41_9
% 22.44/3.76 | | gives:
% 22.44/3.76 | | (27) $i(all_41_1) & $i(all_41_7) & $i(all_41_8) & $i(all_41_9) &
% 22.44/3.76 | | ((all_41_0 = 0 & member(all_41_1, all_32_4) = 0 & ! [v0: $i] : ( ~
% 22.44/3.76 | | (apply(all_32_1, all_41_1, v0) = 0) | ~ $i(v0) | ? [v1: int]
% 22.44/3.76 | | : ( ~ (v1 = 0) & member(v0, all_32_2) = v1)) & ! [v0: $i] : (
% 22.44/3.76 | | ~ (member(v0, all_32_2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~
% 22.44/3.76 | | (v1 = 0) & apply(all_32_1, all_41_1, v0) = v1))) | (all_41_2
% 22.44/3.76 | | = 0 & all_41_3 = 0 & all_41_4 = 0 & all_41_5 = 0 & all_41_6 = 0
% 22.44/3.76 | | & ~ (all_41_7 = all_41_8) & apply(all_32_1, all_41_9, all_41_7)
% 22.44/3.76 | | = 0 & apply(all_32_1, all_41_9, all_41_8) = 0 & member(all_41_7,
% 22.44/3.76 | | all_32_2) = 0 & member(all_41_8, all_32_2) = 0 &
% 22.44/3.76 | | member(all_41_9, all_32_4) = 0))
% 22.44/3.76 | |
% 22.44/3.76 | | ALPHA: (27) implies:
% 22.44/3.76 | | (28) $i(all_41_9)
% 22.44/3.76 | | (29) $i(all_41_8)
% 22.44/3.76 | | (30) $i(all_41_7)
% 22.44/3.76 | | (31) $i(all_41_1)
% 22.44/3.76 | | (32) (all_41_0 = 0 & member(all_41_1, all_32_4) = 0 & ! [v0: $i] : ( ~
% 22.44/3.76 | | (apply(all_32_1, all_41_1, v0) = 0) | ~ $i(v0) | ? [v1: int] :
% 22.44/3.76 | | ( ~ (v1 = 0) & member(v0, all_32_2) = v1)) & ! [v0: $i] : ( ~
% 22.44/3.76 | | (member(v0, all_32_2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 22.44/3.76 | | = 0) & apply(all_32_1, all_41_1, v0) = v1))) | (all_41_2 = 0
% 22.44/3.76 | | & all_41_3 = 0 & all_41_4 = 0 & all_41_5 = 0 & all_41_6 = 0 & ~
% 22.44/3.76 | | (all_41_7 = all_41_8) & apply(all_32_1, all_41_9, all_41_7) = 0 &
% 22.44/3.76 | | apply(all_32_1, all_41_9, all_41_8) = 0 & member(all_41_7,
% 22.44/3.76 | | all_32_2) = 0 & member(all_41_8, all_32_2) = 0 &
% 22.44/3.76 | | member(all_41_9, all_32_4) = 0)
% 22.44/3.76 | |
% 22.44/3.76 | | BETA: splitting (32) gives:
% 22.44/3.76 | |
% 22.44/3.76 | | Case 1:
% 22.44/3.76 | | |
% 22.44/3.76 | | | (33) all_41_0 = 0 & member(all_41_1, all_32_4) = 0 & ! [v0: $i] : ( ~
% 22.44/3.76 | | | (apply(all_32_1, all_41_1, v0) = 0) | ~ $i(v0) | ? [v1: int] :
% 22.44/3.76 | | | ( ~ (v1 = 0) & member(v0, all_32_2) = v1)) & ! [v0: $i] : ( ~
% 22.44/3.76 | | | (member(v0, all_32_2) = 0) | ~ $i(v0) | ? [v1: int] : ( ~ (v1
% 22.44/3.76 | | | = 0) & apply(all_32_1, all_41_1, v0) = v1))
% 22.44/3.76 | | |
% 22.44/3.76 | | | ALPHA: (33) implies:
% 22.44/3.76 | | | (34) member(all_41_1, all_32_4) = 0
% 22.44/3.76 | | | (35) ! [v0: $i] : ( ~ (member(v0, all_32_2) = 0) | ~ $i(v0) | ? [v1:
% 22.44/3.76 | | | int] : ( ~ (v1 = 0) & apply(all_32_1, all_41_1, v0) = v1))
% 22.44/3.76 | | |
% 22.44/3.77 | | | GROUND_INST: instantiating (1) with all_32_6, all_32_4, all_32_3,
% 22.44/3.77 | | | all_41_1, simplifying with (13), (15), (16), (19), (31), (34)
% 22.44/3.77 | | | gives:
% 22.44/3.77 | | | (36) ? [v0: $i] : (apply(all_32_6, all_41_1, v0) = 0 & member(v0,
% 22.44/3.77 | | | all_32_3) = 0 & $i(v0))
% 22.44/3.77 | | |
% 22.44/3.77 | | | DELTA: instantiating (36) with fresh symbol all_56_0 gives:
% 22.44/3.77 | | | (37) apply(all_32_6, all_41_1, all_56_0) = 0 & member(all_56_0,
% 22.44/3.77 | | | all_32_3) = 0 & $i(all_56_0)
% 22.44/3.77 | | |
% 22.44/3.77 | | | ALPHA: (37) implies:
% 22.44/3.77 | | | (38) $i(all_56_0)
% 22.44/3.77 | | | (39) member(all_56_0, all_32_3) = 0
% 22.44/3.77 | | | (40) apply(all_32_6, all_41_1, all_56_0) = 0
% 22.44/3.77 | | |
% 22.44/3.77 | | | GROUND_INST: instantiating (1) with all_32_5, all_32_3, all_32_2,
% 22.44/3.77 | | | all_56_0, simplifying with (14), (16), (17), (20), (38), (39)
% 22.44/3.77 | | | gives:
% 22.44/3.77 | | | (41) ? [v0: $i] : (apply(all_32_5, all_56_0, v0) = 0 & member(v0,
% 22.44/3.77 | | | all_32_2) = 0 & $i(v0))
% 22.44/3.77 | | |
% 22.44/3.77 | | | DELTA: instantiating (41) with fresh symbol all_63_0 gives:
% 22.44/3.77 | | | (42) apply(all_32_5, all_56_0, all_63_0) = 0 & member(all_63_0,
% 22.44/3.77 | | | all_32_2) = 0 & $i(all_63_0)
% 22.44/3.77 | | |
% 22.44/3.77 | | | ALPHA: (42) implies:
% 22.44/3.77 | | | (43) $i(all_63_0)
% 22.44/3.77 | | | (44) member(all_63_0, all_32_2) = 0
% 22.44/3.77 | | | (45) apply(all_32_5, all_56_0, all_63_0) = 0
% 22.44/3.77 | | |
% 22.44/3.77 | | | GROUND_INST: instantiating (35) with all_63_0, simplifying with (43), (44)
% 22.44/3.77 | | | gives:
% 22.44/3.77 | | | (46) ? [v0: int] : ( ~ (v0 = 0) & apply(all_32_1, all_41_1, all_63_0)
% 22.44/3.77 | | | = v0)
% 22.44/3.77 | | |
% 22.44/3.77 | | | DELTA: instantiating (46) with fresh symbol all_70_0 gives:
% 22.44/3.77 | | | (47) ~ (all_70_0 = 0) & apply(all_32_1, all_41_1, all_63_0) = all_70_0
% 22.44/3.77 | | |
% 22.44/3.77 | | | ALPHA: (47) implies:
% 22.44/3.77 | | | (48) ~ (all_70_0 = 0)
% 22.51/3.77 | | | (49) apply(all_32_1, all_41_1, all_63_0) = all_70_0
% 22.51/3.77 | | |
% 22.51/3.77 | | | GROUND_INST: instantiating (8) with all_32_5, all_32_6, all_32_4,
% 22.51/3.77 | | | all_32_3, all_32_2, all_41_1, all_63_0, all_32_1, all_70_0,
% 22.51/3.77 | | | all_56_0, simplifying with (13), (14), (15), (16), (17),
% 22.51/3.77 | | | (22), (31), (38), (43), (45), (49) gives:
% 22.51/3.77 | | | (50) all_70_0 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_6,
% 22.51/3.77 | | | all_41_1, all_56_0) = v1 & member(all_56_0, all_32_3) = v0 &
% 22.51/3.77 | | | ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_63_0, all_32_2) =
% 22.51/3.77 | | | v1 & member(all_41_1, all_32_4) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 22.51/3.77 | | | 0))))
% 22.51/3.77 | | |
% 22.51/3.77 | | | GROUND_INST: instantiating (7) with all_32_5, all_32_6, all_32_4,
% 22.51/3.77 | | | all_32_3, all_32_2, all_41_1, all_63_0, all_32_1, all_70_0,
% 22.51/3.77 | | | all_56_0, simplifying with (13), (14), (15), (16), (17),
% 22.51/3.77 | | | (22), (31), (38), (39), (43), (49) gives:
% 22.51/3.77 | | | (51) all_70_0 = 0 | ? [v0: any] : ? [v1: any] : ((apply(all_32_5,
% 22.51/3.77 | | | all_56_0, all_63_0) = v1 & apply(all_32_6, all_41_1,
% 22.51/3.77 | | | all_56_0) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0))) |
% 22.51/3.77 | | | (member(all_63_0, all_32_2) = v1 & member(all_41_1, all_32_4) =
% 22.51/3.77 | | | v0 & ( ~ (v1 = 0) | ~ (v0 = 0))))
% 22.51/3.77 | | |
% 22.51/3.77 | | | BETA: splitting (51) gives:
% 22.51/3.77 | | |
% 22.51/3.77 | | | Case 1:
% 22.51/3.77 | | | |
% 22.51/3.77 | | | | (52) all_70_0 = 0
% 22.51/3.77 | | | |
% 22.51/3.77 | | | | REDUCE: (48), (52) imply:
% 22.51/3.77 | | | | (53) $false
% 22.51/3.77 | | | |
% 22.51/3.77 | | | | CLOSE: (53) is inconsistent.
% 22.51/3.77 | | | |
% 22.51/3.77 | | | Case 2:
% 22.51/3.77 | | | |
% 22.51/3.77 | | | | (54) ? [v0: any] : ? [v1: any] : ((apply(all_32_5, all_56_0,
% 22.51/3.77 | | | | all_63_0) = v1 & apply(all_32_6, all_41_1, all_56_0) = v0
% 22.51/3.77 | | | | & ( ~ (v1 = 0) | ~ (v0 = 0))) | (member(all_63_0, all_32_2)
% 22.51/3.77 | | | | = v1 & member(all_41_1, all_32_4) = v0 & ( ~ (v1 = 0) | ~
% 22.51/3.77 | | | | (v0 = 0))))
% 22.51/3.77 | | | |
% 22.51/3.77 | | | | DELTA: instantiating (54) with fresh symbols all_79_0, all_79_1 gives:
% 22.51/3.77 | | | | (55) (apply(all_32_5, all_56_0, all_63_0) = all_79_0 &
% 22.51/3.77 | | | | apply(all_32_6, all_41_1, all_56_0) = all_79_1 & ( ~ (all_79_0
% 22.51/3.77 | | | | = 0) | ~ (all_79_1 = 0))) | (member(all_63_0, all_32_2) =
% 22.51/3.77 | | | | all_79_0 & member(all_41_1, all_32_4) = all_79_1 & ( ~
% 22.51/3.77 | | | | (all_79_0 = 0) | ~ (all_79_1 = 0)))
% 22.51/3.77 | | | |
% 22.51/3.77 | | | | BETA: splitting (55) gives:
% 22.51/3.77 | | | |
% 22.51/3.77 | | | | Case 1:
% 22.51/3.77 | | | | |
% 22.51/3.77 | | | | | (56) apply(all_32_5, all_56_0, all_63_0) = all_79_0 &
% 22.51/3.77 | | | | | apply(all_32_6, all_41_1, all_56_0) = all_79_1 & ( ~ (all_79_0
% 22.51/3.77 | | | | | = 0) | ~ (all_79_1 = 0))
% 22.51/3.77 | | | | |
% 22.51/3.77 | | | | | ALPHA: (56) implies:
% 22.51/3.77 | | | | | (57) apply(all_32_6, all_41_1, all_56_0) = all_79_1
% 22.51/3.77 | | | | | (58) apply(all_32_5, all_56_0, all_63_0) = all_79_0
% 22.51/3.77 | | | | | (59) ~ (all_79_0 = 0) | ~ (all_79_1 = 0)
% 22.51/3.77 | | | | |
% 22.51/3.77 | | | | | BETA: splitting (50) gives:
% 22.51/3.77 | | | | |
% 22.51/3.77 | | | | | Case 1:
% 22.51/3.77 | | | | | |
% 22.51/3.77 | | | | | | (60) all_70_0 = 0
% 22.51/3.77 | | | | | |
% 22.51/3.77 | | | | | | REDUCE: (48), (60) imply:
% 22.51/3.78 | | | | | | (61) $false
% 22.51/3.78 | | | | | |
% 22.51/3.78 | | | | | | CLOSE: (61) is inconsistent.
% 22.51/3.78 | | | | | |
% 22.51/3.78 | | | | | Case 2:
% 22.51/3.78 | | | | | |
% 22.51/3.78 | | | | | |
% 22.51/3.78 | | | | | | GROUND_INST: instantiating (10) with 0, all_79_1, all_56_0,
% 22.51/3.78 | | | | | | all_41_1, all_32_6, simplifying with (40), (57) gives:
% 22.51/3.78 | | | | | | (62) all_79_1 = 0
% 22.51/3.78 | | | | | |
% 22.51/3.78 | | | | | | GROUND_INST: instantiating (10) with 0, all_79_0, all_63_0,
% 22.51/3.78 | | | | | | all_56_0, all_32_5, simplifying with (45), (58) gives:
% 22.51/3.78 | | | | | | (63) all_79_0 = 0
% 22.51/3.78 | | | | | |
% 22.51/3.78 | | | | | | REF_CLOSE: (59), (62), (63) are inconsistent by sub-proof #3.
% 22.51/3.78 | | | | | |
% 22.51/3.78 | | | | | End of split
% 22.51/3.78 | | | | |
% 22.51/3.78 | | | | Case 2:
% 22.51/3.78 | | | | |
% 22.51/3.78 | | | | | (64) member(all_63_0, all_32_2) = all_79_0 & member(all_41_1,
% 22.51/3.78 | | | | | all_32_4) = all_79_1 & ( ~ (all_79_0 = 0) | ~ (all_79_1 =
% 22.51/3.78 | | | | | 0))
% 22.51/3.78 | | | | |
% 22.51/3.78 | | | | | ALPHA: (64) implies:
% 22.51/3.78 | | | | | (65) member(all_41_1, all_32_4) = all_79_1
% 22.51/3.78 | | | | | (66) member(all_63_0, all_32_2) = all_79_0
% 22.51/3.78 | | | | | (67) ~ (all_79_0 = 0) | ~ (all_79_1 = 0)
% 22.51/3.78 | | | | |
% 22.51/3.78 | | | | | GROUND_INST: instantiating (9) with 0, all_79_1, all_32_4, all_41_1,
% 22.51/3.78 | | | | | simplifying with (34), (65) gives:
% 22.51/3.78 | | | | | (68) all_79_1 = 0
% 22.51/3.78 | | | | |
% 22.51/3.78 | | | | | GROUND_INST: instantiating (9) with 0, all_79_0, all_32_2, all_63_0,
% 22.51/3.78 | | | | | simplifying with (44), (66) gives:
% 22.51/3.78 | | | | | (69) all_79_0 = 0
% 22.51/3.78 | | | | |
% 22.51/3.78 | | | | | REF_CLOSE: (67), (68), (69) are inconsistent by sub-proof #3.
% 22.51/3.78 | | | | |
% 22.51/3.78 | | | | End of split
% 22.51/3.78 | | | |
% 22.51/3.78 | | | End of split
% 22.51/3.78 | | |
% 22.51/3.78 | | Case 2:
% 22.51/3.78 | | |
% 22.51/3.78 | | | (70) all_41_2 = 0 & all_41_3 = 0 & all_41_4 = 0 & all_41_5 = 0 &
% 22.51/3.78 | | | all_41_6 = 0 & ~ (all_41_7 = all_41_8) & apply(all_32_1,
% 22.51/3.78 | | | all_41_9, all_41_7) = 0 & apply(all_32_1, all_41_9, all_41_8) =
% 22.51/3.78 | | | 0 & member(all_41_7, all_32_2) = 0 & member(all_41_8, all_32_2) =
% 22.51/3.78 | | | 0 & member(all_41_9, all_32_4) = 0
% 22.51/3.78 | | |
% 22.51/3.78 | | | ALPHA: (70) implies:
% 22.51/3.78 | | | (71) ~ (all_41_7 = all_41_8)
% 22.51/3.78 | | | (72) member(all_41_9, all_32_4) = 0
% 22.51/3.78 | | | (73) member(all_41_8, all_32_2) = 0
% 22.51/3.78 | | | (74) member(all_41_7, all_32_2) = 0
% 22.51/3.78 | | | (75) apply(all_32_1, all_41_9, all_41_8) = 0
% 22.51/3.78 | | | (76) apply(all_32_1, all_41_9, all_41_7) = 0
% 22.51/3.78 | | |
% 22.51/3.78 | | | GROUND_INST: instantiating (1) with all_32_6, all_32_4, all_32_3,
% 22.51/3.78 | | | all_41_9, simplifying with (13), (15), (16), (19), (28), (72)
% 22.51/3.78 | | | gives:
% 22.51/3.78 | | | (77) ? [v0: $i] : (apply(all_32_6, all_41_9, v0) = 0 & member(v0,
% 22.51/3.78 | | | all_32_3) = 0 & $i(v0))
% 22.51/3.78 | | |
% 22.51/3.78 | | | GROUND_INST: instantiating (6) with all_32_5, all_32_6, all_32_4,
% 22.51/3.78 | | | all_32_3, all_32_2, all_41_9, all_41_8, all_32_1, simplifying
% 22.51/3.78 | | | with (13), (14), (15), (16), (17), (22), (28), (29), (75)
% 22.51/3.78 | | | gives:
% 22.51/3.78 | | | (78) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: int] : ? [v4:
% 22.51/3.78 | | | int] : ? [v5: int] : ($i(v2) & ((v5 = 0 & v4 = 0 & v3 = 0 &
% 22.51/3.78 | | | apply(all_32_5, v2, all_41_8) = 0 & apply(all_32_6,
% 22.51/3.78 | | | all_41_9, v2) = 0 & member(v2, all_32_3) = 0) |
% 22.51/3.78 | | | (member(all_41_8, all_32_2) = v1 & member(all_41_9, all_32_4)
% 22.51/3.78 | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))))
% 22.51/3.78 | | |
% 22.51/3.78 | | | GROUND_INST: instantiating (6) with all_32_5, all_32_6, all_32_4,
% 22.51/3.78 | | | all_32_3, all_32_2, all_41_9, all_41_7, all_32_1, simplifying
% 22.51/3.78 | | | with (13), (14), (15), (16), (17), (22), (28), (30), (76)
% 22.51/3.78 | | | gives:
% 22.51/3.78 | | | (79) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: int] : ? [v4:
% 22.51/3.78 | | | int] : ? [v5: int] : ($i(v2) & ((v5 = 0 & v4 = 0 & v3 = 0 &
% 22.51/3.78 | | | apply(all_32_5, v2, all_41_7) = 0 & apply(all_32_6,
% 22.51/3.78 | | | all_41_9, v2) = 0 & member(v2, all_32_3) = 0) |
% 22.51/3.78 | | | (member(all_41_7, all_32_2) = v1 & member(all_41_9, all_32_4)
% 22.51/3.78 | | | = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))))
% 22.51/3.78 | | |
% 22.51/3.78 | | | DELTA: instantiating (77) with fresh symbol all_55_0 gives:
% 22.51/3.78 | | | (80) apply(all_32_6, all_41_9, all_55_0) = 0 & member(all_55_0,
% 22.51/3.78 | | | all_32_3) = 0 & $i(all_55_0)
% 22.51/3.78 | | |
% 22.51/3.78 | | | ALPHA: (80) implies:
% 22.51/3.78 | | | (81) $i(all_55_0)
% 22.51/3.78 | | | (82) member(all_55_0, all_32_3) = 0
% 22.51/3.78 | | | (83) apply(all_32_6, all_41_9, all_55_0) = 0
% 22.51/3.78 | | |
% 22.51/3.78 | | | DELTA: instantiating (79) with fresh symbols all_57_0, all_57_1, all_57_2,
% 22.51/3.78 | | | all_57_3, all_57_4, all_57_5 gives:
% 22.51/3.78 | | | (84) $i(all_57_3) & ((all_57_0 = 0 & all_57_1 = 0 & all_57_2 = 0 &
% 22.51/3.78 | | | apply(all_32_5, all_57_3, all_41_7) = 0 & apply(all_32_6,
% 22.51/3.78 | | | all_41_9, all_57_3) = 0 & member(all_57_3, all_32_3) = 0) |
% 22.51/3.78 | | | (member(all_41_7, all_32_2) = all_57_4 & member(all_41_9,
% 22.51/3.78 | | | all_32_4) = all_57_5 & ( ~ (all_57_4 = 0) | ~ (all_57_5 =
% 22.51/3.78 | | | 0))))
% 22.51/3.78 | | |
% 22.51/3.78 | | | ALPHA: (84) implies:
% 22.51/3.78 | | | (85) $i(all_57_3)
% 22.51/3.78 | | | (86) (all_57_0 = 0 & all_57_1 = 0 & all_57_2 = 0 & apply(all_32_5,
% 22.51/3.78 | | | all_57_3, all_41_7) = 0 & apply(all_32_6, all_41_9, all_57_3)
% 22.51/3.78 | | | = 0 & member(all_57_3, all_32_3) = 0) | (member(all_41_7,
% 22.51/3.78 | | | all_32_2) = all_57_4 & member(all_41_9, all_32_4) = all_57_5 &
% 22.51/3.78 | | | ( ~ (all_57_4 = 0) | ~ (all_57_5 = 0)))
% 22.51/3.78 | | |
% 22.51/3.78 | | | DELTA: instantiating (78) with fresh symbols all_59_0, all_59_1, all_59_2,
% 22.51/3.78 | | | all_59_3, all_59_4, all_59_5 gives:
% 22.51/3.78 | | | (87) $i(all_59_3) & ((all_59_0 = 0 & all_59_1 = 0 & all_59_2 = 0 &
% 22.51/3.79 | | | apply(all_32_5, all_59_3, all_41_8) = 0 & apply(all_32_6,
% 22.51/3.79 | | | all_41_9, all_59_3) = 0 & member(all_59_3, all_32_3) = 0) |
% 22.51/3.79 | | | (member(all_41_8, all_32_2) = all_59_4 & member(all_41_9,
% 22.51/3.79 | | | all_32_4) = all_59_5 & ( ~ (all_59_4 = 0) | ~ (all_59_5 =
% 22.51/3.79 | | | 0))))
% 22.51/3.79 | | |
% 22.51/3.79 | | | ALPHA: (87) implies:
% 22.51/3.79 | | | (88) $i(all_59_3)
% 22.51/3.79 | | | (89) (all_59_0 = 0 & all_59_1 = 0 & all_59_2 = 0 & apply(all_32_5,
% 22.51/3.79 | | | all_59_3, all_41_8) = 0 & apply(all_32_6, all_41_9, all_59_3)
% 22.51/3.79 | | | = 0 & member(all_59_3, all_32_3) = 0) | (member(all_41_8,
% 22.51/3.79 | | | all_32_2) = all_59_4 & member(all_41_9, all_32_4) = all_59_5 &
% 22.51/3.79 | | | ( ~ (all_59_4 = 0) | ~ (all_59_5 = 0)))
% 22.51/3.79 | | |
% 22.51/3.79 | | | BETA: splitting (89) gives:
% 22.51/3.79 | | |
% 22.51/3.79 | | | Case 1:
% 22.51/3.79 | | | |
% 22.51/3.79 | | | | (90) all_59_0 = 0 & all_59_1 = 0 & all_59_2 = 0 & apply(all_32_5,
% 22.51/3.79 | | | | all_59_3, all_41_8) = 0 & apply(all_32_6, all_41_9, all_59_3)
% 22.51/3.79 | | | | = 0 & member(all_59_3, all_32_3) = 0
% 22.51/3.79 | | | |
% 22.51/3.79 | | | | ALPHA: (90) implies:
% 22.51/3.79 | | | | (91) member(all_59_3, all_32_3) = 0
% 22.51/3.79 | | | | (92) apply(all_32_6, all_41_9, all_59_3) = 0
% 22.51/3.79 | | | | (93) apply(all_32_5, all_59_3, all_41_8) = 0
% 22.51/3.79 | | | |
% 22.51/3.79 | | | | BETA: splitting (86) gives:
% 22.51/3.79 | | | |
% 22.51/3.79 | | | | Case 1:
% 22.51/3.79 | | | | |
% 22.51/3.79 | | | | | (94) all_57_0 = 0 & all_57_1 = 0 & all_57_2 = 0 & apply(all_32_5,
% 22.51/3.79 | | | | | all_57_3, all_41_7) = 0 & apply(all_32_6, all_41_9,
% 22.51/3.79 | | | | | all_57_3) = 0 & member(all_57_3, all_32_3) = 0
% 22.51/3.79 | | | | |
% 22.51/3.79 | | | | | ALPHA: (94) implies:
% 22.51/3.79 | | | | | (95) member(all_57_3, all_32_3) = 0
% 22.51/3.79 | | | | | (96) apply(all_32_6, all_41_9, all_57_3) = 0
% 22.51/3.79 | | | | | (97) apply(all_32_5, all_57_3, all_41_7) = 0
% 22.51/3.79 | | | | |
% 22.51/3.79 | | | | | GROUND_INST: instantiating (3) with all_32_5, all_32_3, all_32_2,
% 22.51/3.79 | | | | | all_55_0, all_41_8, all_41_7, simplifying with (14),
% 22.51/3.79 | | | | | (16), (17), (20), (29), (30), (73), (74), (81), (82)
% 22.51/3.79 | | | | | gives:
% 22.51/3.79 | | | | | (98) all_41_7 = all_41_8 | ? [v0: any] : ? [v1: any] :
% 22.51/3.79 | | | | | (apply(all_32_5, all_55_0, all_41_7) = v1 & apply(all_32_5,
% 22.51/3.79 | | | | | all_55_0, all_41_8) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.51/3.79 | | | | |
% 22.51/3.79 | | | | | GROUND_INST: instantiating (3) with all_32_6, all_32_4, all_32_3,
% 22.51/3.79 | | | | | all_41_9, all_59_3, all_57_3, simplifying with (13),
% 22.51/3.79 | | | | | (15), (16), (19), (28), (72), (85), (88), (91), (95)
% 22.51/3.79 | | | | | gives:
% 22.51/3.79 | | | | | (99) all_59_3 = all_57_3 | ? [v0: any] : ? [v1: any] :
% 22.51/3.79 | | | | | (apply(all_32_6, all_41_9, all_59_3) = v0 & apply(all_32_6,
% 22.51/3.79 | | | | | all_41_9, all_57_3) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.51/3.79 | | | | |
% 22.51/3.79 | | | | | GROUND_INST: instantiating (3) with all_32_6, all_32_4, all_32_3,
% 22.51/3.79 | | | | | all_41_9, all_59_3, all_55_0, simplifying with (13),
% 22.51/3.79 | | | | | (15), (16), (19), (28), (72), (81), (82), (88), (91)
% 22.51/3.79 | | | | | gives:
% 22.51/3.79 | | | | | (100) all_59_3 = all_55_0 | ? [v0: any] : ? [v1: any] :
% 22.51/3.79 | | | | | (apply(all_32_6, all_41_9, all_59_3) = v0 & apply(all_32_6,
% 22.51/3.79 | | | | | all_41_9, all_55_0) = v1 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.51/3.79 | | | | |
% 22.51/3.79 | | | | | GROUND_INST: instantiating (4) with all_32_6, all_32_4, all_32_3,
% 22.51/3.79 | | | | | all_41_9, all_59_3, all_55_0, simplifying with (13),
% 22.51/3.79 | | | | | (15), (16), (19), (28), (81), (83), (88), (91) gives:
% 22.51/3.79 | | | | | (101) all_59_3 = all_55_0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 22.51/3.79 | | | | | any] : (apply(all_32_6, all_41_9, all_59_3) = v2 &
% 22.51/3.79 | | | | | member(all_55_0, all_32_3) = v1 & member(all_41_9,
% 22.51/3.79 | | | | | all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 22.51/3.79 | | | | | 0)))
% 22.51/3.79 | | | | |
% 22.51/3.79 | | | | | GROUND_INST: instantiating (5) with all_32_6, all_32_4, all_32_3,
% 22.51/3.79 | | | | | all_41_9, all_59_3, all_55_0, simplifying with (13),
% 22.51/3.79 | | | | | (15), (16), (19), (28), (81), (83), (88), (92) gives:
% 22.51/3.79 | | | | | (102) all_59_3 = all_55_0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 22.51/3.79 | | | | | any] : (member(all_59_3, all_32_3) = v1 & member(all_55_0,
% 22.51/3.79 | | | | | all_32_3) = v2 & member(all_41_9, all_32_4) = v0 & ( ~
% 22.51/3.79 | | | | | (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 22.51/3.79 | | | | |
% 22.51/3.79 | | | | | GROUND_INST: instantiating (4) with all_32_6, all_32_4, all_32_3,
% 22.51/3.79 | | | | | all_41_9, all_57_3, all_59_3, simplifying with (13),
% 22.51/3.79 | | | | | (15), (16), (19), (28), (85), (88), (92), (95) gives:
% 22.51/3.79 | | | | | (103) all_59_3 = all_57_3 | ? [v0: any] : ? [v1: any] : ? [v2:
% 22.51/3.79 | | | | | any] : (apply(all_32_6, all_41_9, all_57_3) = v2 &
% 22.51/3.79 | | | | | member(all_59_3, all_32_3) = v1 & member(all_41_9,
% 22.51/3.79 | | | | | all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 22.51/3.79 | | | | | 0)))
% 22.51/3.79 | | | | |
% 22.51/3.79 | | | | | GROUND_INST: instantiating (4) with all_32_6, all_32_4, all_32_3,
% 22.51/3.79 | | | | | all_41_9, all_55_0, all_59_3, simplifying with (13),
% 22.51/3.79 | | | | | (15), (16), (19), (28), (81), (82), (88), (92) gives:
% 22.51/3.79 | | | | | (104) all_59_3 = all_55_0 | ? [v0: any] : ? [v1: any] : ? [v2:
% 22.51/3.79 | | | | | any] : (apply(all_32_6, all_41_9, all_55_0) = v2 &
% 22.51/3.79 | | | | | member(all_59_3, all_32_3) = v1 & member(all_41_9,
% 22.51/3.79 | | | | | all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 22.51/3.79 | | | | | 0)))
% 22.51/3.79 | | | | |
% 22.51/3.79 | | | | | GROUND_INST: instantiating (4) with all_32_5, all_32_3, all_32_2,
% 22.51/3.79 | | | | | all_57_3, all_41_8, all_41_7, simplifying with (14),
% 22.51/3.79 | | | | | (16), (17), (20), (29), (30), (73), (85), (97) gives:
% 22.51/3.79 | | | | | (105) all_41_7 = all_41_8 | ? [v0: any] : ? [v1: any] : ? [v2:
% 22.51/3.79 | | | | | any] : (apply(all_32_5, all_57_3, all_41_8) = v2 &
% 22.51/3.79 | | | | | member(all_57_3, all_32_3) = v0 & member(all_41_7,
% 22.51/3.79 | | | | | all_32_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 22.51/3.79 | | | | | 0)))
% 22.51/3.79 | | | | |
% 22.51/3.79 | | | | | GROUND_INST: instantiating (4) with all_32_5, all_32_3, all_32_2,
% 22.51/3.79 | | | | | all_59_3, all_41_7, all_41_8, simplifying with (14),
% 22.51/3.79 | | | | | (16), (17), (20), (29), (30), (74), (88), (93) gives:
% 22.51/3.80 | | | | | (106) all_41_7 = all_41_8 | ? [v0: any] : ? [v1: any] : ? [v2:
% 22.51/3.80 | | | | | any] : (apply(all_32_5, all_59_3, all_41_7) = v2 &
% 22.51/3.80 | | | | | member(all_59_3, all_32_3) = v0 & member(all_41_8,
% 22.51/3.80 | | | | | all_32_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 22.51/3.80 | | | | | 0)))
% 22.51/3.80 | | | | |
% 22.51/3.80 | | | | | BETA: splitting (103) gives:
% 22.51/3.80 | | | | |
% 22.51/3.80 | | | | | Case 1:
% 22.51/3.80 | | | | | |
% 22.51/3.80 | | | | | | (107) all_59_3 = all_57_3
% 22.51/3.80 | | | | | |
% 22.51/3.80 | | | | | | BETA: splitting (106) gives:
% 22.51/3.80 | | | | | |
% 22.51/3.80 | | | | | | Case 1:
% 22.51/3.80 | | | | | | |
% 22.51/3.80 | | | | | | | (108) all_41_7 = all_41_8
% 22.51/3.80 | | | | | | |
% 22.51/3.80 | | | | | | | REDUCE: (71), (108) imply:
% 22.51/3.80 | | | | | | | (109) $false
% 22.51/3.80 | | | | | | |
% 22.51/3.80 | | | | | | | CLOSE: (109) is inconsistent.
% 22.51/3.80 | | | | | | |
% 22.51/3.80 | | | | | | Case 2:
% 22.51/3.80 | | | | | | |
% 22.51/3.80 | | | | | | | (110) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 22.51/3.80 | | | | | | | (apply(all_32_5, all_59_3, all_41_7) = v2 &
% 22.51/3.80 | | | | | | | member(all_59_3, all_32_3) = v0 & member(all_41_8,
% 22.51/3.80 | | | | | | | all_32_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0
% 22.51/3.80 | | | | | | | = 0)))
% 22.51/3.80 | | | | | | |
% 22.51/3.80 | | | | | | | DELTA: instantiating (110) with fresh symbols all_87_0, all_87_1,
% 22.51/3.80 | | | | | | | all_87_2 gives:
% 22.51/3.80 | | | | | | | (111) apply(all_32_5, all_59_3, all_41_7) = all_87_0 &
% 22.51/3.80 | | | | | | | member(all_59_3, all_32_3) = all_87_2 & member(all_41_8,
% 22.51/3.80 | | | | | | | all_32_2) = all_87_1 & ( ~ (all_87_0 = 0) | ~
% 22.51/3.80 | | | | | | | (all_87_1 = 0) | ~ (all_87_2 = 0))
% 22.51/3.80 | | | | | | |
% 22.51/3.80 | | | | | | | REF_CLOSE: (9), (10), (71), (73), (95), (97), (98), (101), (102),
% 22.51/3.80 | | | | | | | (104), (105), (107), (111) are inconsistent by
% 22.51/3.80 | | | | | | | sub-proof #1.
% 22.51/3.80 | | | | | | |
% 22.51/3.80 | | | | | | End of split
% 22.51/3.80 | | | | | |
% 22.51/3.80 | | | | | Case 2:
% 22.51/3.80 | | | | | |
% 22.51/3.80 | | | | | | (112) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 22.51/3.80 | | | | | | (apply(all_32_6, all_41_9, all_57_3) = v2 &
% 22.51/3.80 | | | | | | member(all_59_3, all_32_3) = v1 & member(all_41_9,
% 22.51/3.80 | | | | | | all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 22.51/3.80 | | | | | | 0)))
% 22.51/3.80 | | | | | |
% 22.51/3.80 | | | | | | DELTA: instantiating (112) with fresh symbols all_84_0, all_84_1,
% 22.51/3.80 | | | | | | all_84_2 gives:
% 22.51/3.80 | | | | | | (113) apply(all_32_6, all_41_9, all_57_3) = all_84_0 &
% 22.51/3.80 | | | | | | member(all_59_3, all_32_3) = all_84_1 & member(all_41_9,
% 22.51/3.80 | | | | | | all_32_4) = all_84_2 & ( ~ (all_84_0 = 0) | ~ (all_84_1
% 22.51/3.80 | | | | | | = 0) | ~ (all_84_2 = 0))
% 22.51/3.80 | | | | | |
% 22.51/3.80 | | | | | | ALPHA: (113) implies:
% 22.51/3.80 | | | | | | (114) apply(all_32_6, all_41_9, all_57_3) = all_84_0
% 22.51/3.80 | | | | | |
% 22.51/3.80 | | | | | | BETA: splitting (106) gives:
% 22.51/3.80 | | | | | |
% 22.51/3.80 | | | | | | Case 1:
% 22.51/3.80 | | | | | | |
% 22.51/3.80 | | | | | | | (115) all_41_7 = all_41_8
% 22.51/3.80 | | | | | | |
% 22.51/3.80 | | | | | | | REDUCE: (71), (115) imply:
% 22.51/3.80 | | | | | | | (116) $false
% 22.51/3.80 | | | | | | |
% 22.51/3.80 | | | | | | | CLOSE: (116) is inconsistent.
% 22.51/3.80 | | | | | | |
% 22.51/3.80 | | | | | | Case 2:
% 22.51/3.80 | | | | | | |
% 22.51/3.80 | | | | | | | (117) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 22.51/3.80 | | | | | | | (apply(all_32_5, all_59_3, all_41_7) = v2 &
% 22.51/3.80 | | | | | | | member(all_59_3, all_32_3) = v0 & member(all_41_8,
% 22.51/3.80 | | | | | | | all_32_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0
% 22.51/3.80 | | | | | | | = 0)))
% 22.51/3.80 | | | | | | |
% 22.51/3.80 | | | | | | | BETA: splitting (100) gives:
% 22.51/3.80 | | | | | | |
% 22.51/3.80 | | | | | | | Case 1:
% 22.51/3.80 | | | | | | | |
% 22.51/3.80 | | | | | | | | (118) all_59_3 = all_55_0
% 22.51/3.80 | | | | | | | |
% 22.51/3.80 | | | | | | | | BETA: splitting (99) gives:
% 22.51/3.80 | | | | | | | |
% 22.51/3.80 | | | | | | | | Case 1:
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | (119) all_59_3 = all_57_3
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | DELTA: instantiating (117) with fresh symbols all_87_0,
% 22.51/3.80 | | | | | | | | | all_87_1, all_87_2 gives:
% 22.51/3.80 | | | | | | | | | (120) apply(all_32_5, all_59_3, all_41_7) = all_87_0 &
% 22.51/3.80 | | | | | | | | | member(all_59_3, all_32_3) = all_87_2 &
% 22.51/3.80 | | | | | | | | | member(all_41_8, all_32_2) = all_87_1 & ( ~ (all_87_0
% 22.51/3.80 | | | | | | | | | = 0) | ~ (all_87_1 = 0) | ~ (all_87_2 = 0))
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | REF_CLOSE: (9), (10), (71), (73), (95), (97), (98), (101),
% 22.51/3.80 | | | | | | | | | (102), (104), (105), (119), (120) are inconsistent
% 22.51/3.80 | | | | | | | | | by sub-proof #1.
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | Case 2:
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | (121) ? [v0: any] : ? [v1: any] : (apply(all_32_6,
% 22.51/3.80 | | | | | | | | | all_41_9, all_59_3) = v0 & apply(all_32_6,
% 22.51/3.80 | | | | | | | | | all_41_9, all_57_3) = v1 & ( ~ (v1 = 0) | ~ (v0
% 22.51/3.80 | | | | | | | | | = 0)))
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | DELTA: instantiating (121) with fresh symbols all_110_0,
% 22.51/3.80 | | | | | | | | | all_110_1 gives:
% 22.51/3.80 | | | | | | | | | (122) apply(all_32_6, all_41_9, all_59_3) = all_110_1 &
% 22.51/3.80 | | | | | | | | | apply(all_32_6, all_41_9, all_57_3) = all_110_0 & ( ~
% 22.51/3.80 | | | | | | | | | (all_110_0 = 0) | ~ (all_110_1 = 0))
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | ALPHA: (122) implies:
% 22.51/3.80 | | | | | | | | | (123) apply(all_32_6, all_41_9, all_57_3) = all_110_0
% 22.51/3.80 | | | | | | | | | (124) apply(all_32_6, all_41_9, all_59_3) = all_110_1
% 22.51/3.80 | | | | | | | | | (125) ~ (all_110_0 = 0) | ~ (all_110_1 = 0)
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | REDUCE: (118), (124) imply:
% 22.51/3.80 | | | | | | | | | (126) apply(all_32_6, all_41_9, all_55_0) = all_110_1
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_110_1, all_55_0,
% 22.51/3.80 | | | | | | | | | all_41_9, all_32_6, simplifying with (83), (126)
% 22.51/3.80 | | | | | | | | | gives:
% 22.51/3.80 | | | | | | | | | (127) all_110_1 = 0
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_110_0, all_57_3,
% 22.51/3.80 | | | | | | | | | all_41_9, all_32_6, simplifying with (96), (123)
% 22.51/3.80 | | | | | | | | | gives:
% 22.51/3.80 | | | | | | | | | (128) all_110_0 = 0
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | GROUND_INST: instantiating (10) with all_84_0, all_110_0,
% 22.51/3.80 | | | | | | | | | all_57_3, all_41_9, all_32_6, simplifying with
% 22.51/3.80 | | | | | | | | | (114), (123) gives:
% 22.51/3.80 | | | | | | | | | (129) all_110_0 = all_84_0
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | COMBINE_EQS: (128), (129) imply:
% 22.51/3.80 | | | | | | | | | (130) all_84_0 = 0
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | BETA: splitting (125) gives:
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | Case 1:
% 22.51/3.80 | | | | | | | | | |
% 22.51/3.80 | | | | | | | | | | (131) ~ (all_110_0 = 0)
% 22.51/3.80 | | | | | | | | | |
% 22.51/3.80 | | | | | | | | | | REDUCE: (128), (131) imply:
% 22.51/3.80 | | | | | | | | | | (132) $false
% 22.51/3.80 | | | | | | | | | |
% 22.51/3.80 | | | | | | | | | | CLOSE: (132) is inconsistent.
% 22.51/3.80 | | | | | | | | | |
% 22.51/3.80 | | | | | | | | | Case 2:
% 22.51/3.80 | | | | | | | | | |
% 22.51/3.80 | | | | | | | | | | (133) ~ (all_110_1 = 0)
% 22.51/3.80 | | | | | | | | | |
% 22.51/3.80 | | | | | | | | | | REDUCE: (127), (133) imply:
% 22.51/3.80 | | | | | | | | | | (134) $false
% 22.51/3.80 | | | | | | | | | |
% 22.51/3.80 | | | | | | | | | | CLOSE: (134) is inconsistent.
% 22.51/3.80 | | | | | | | | | |
% 22.51/3.80 | | | | | | | | | End of split
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | End of split
% 22.51/3.80 | | | | | | | |
% 22.51/3.80 | | | | | | | Case 2:
% 22.51/3.80 | | | | | | | |
% 22.51/3.80 | | | | | | | | (135) ~ (all_59_3 = all_55_0)
% 22.51/3.80 | | | | | | | | (136) ? [v0: any] : ? [v1: any] : (apply(all_32_6,
% 22.51/3.80 | | | | | | | | all_41_9, all_59_3) = v0 & apply(all_32_6,
% 22.51/3.80 | | | | | | | | all_41_9, all_55_0) = v1 & ( ~ (v1 = 0) | ~ (v0 =
% 22.51/3.80 | | | | | | | | 0)))
% 22.51/3.80 | | | | | | | |
% 22.51/3.80 | | | | | | | | DELTA: instantiating (136) with fresh symbols all_100_0,
% 22.51/3.80 | | | | | | | | all_100_1 gives:
% 22.51/3.80 | | | | | | | | (137) apply(all_32_6, all_41_9, all_59_3) = all_100_1 &
% 22.51/3.80 | | | | | | | | apply(all_32_6, all_41_9, all_55_0) = all_100_0 & ( ~
% 22.51/3.80 | | | | | | | | (all_100_0 = 0) | ~ (all_100_1 = 0))
% 22.51/3.80 | | | | | | | |
% 22.51/3.80 | | | | | | | | ALPHA: (137) implies:
% 22.51/3.80 | | | | | | | | (138) apply(all_32_6, all_41_9, all_55_0) = all_100_0
% 22.51/3.80 | | | | | | | | (139) apply(all_32_6, all_41_9, all_59_3) = all_100_1
% 22.51/3.80 | | | | | | | | (140) ~ (all_100_0 = 0) | ~ (all_100_1 = 0)
% 22.51/3.80 | | | | | | | |
% 22.51/3.80 | | | | | | | | BETA: splitting (101) gives:
% 22.51/3.80 | | | | | | | |
% 22.51/3.80 | | | | | | | | Case 1:
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | (141) all_59_3 = all_55_0
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | REDUCE: (135), (141) imply:
% 22.51/3.80 | | | | | | | | | (142) $false
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | CLOSE: (142) is inconsistent.
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | Case 2:
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | (143) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 22.51/3.80 | | | | | | | | | (apply(all_32_6, all_41_9, all_59_3) = v2 &
% 22.51/3.80 | | | | | | | | | member(all_55_0, all_32_3) = v1 & member(all_41_9,
% 22.51/3.80 | | | | | | | | | all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 22.51/3.80 | | | | | | | | | (v0 = 0)))
% 22.51/3.80 | | | | | | | | |
% 22.51/3.80 | | | | | | | | | DELTA: instantiating (143) with fresh symbols all_106_0,
% 22.51/3.80 | | | | | | | | | all_106_1, all_106_2 gives:
% 22.51/3.81 | | | | | | | | | (144) apply(all_32_6, all_41_9, all_59_3) = all_106_0 &
% 22.51/3.81 | | | | | | | | | member(all_55_0, all_32_3) = all_106_1 &
% 22.51/3.81 | | | | | | | | | member(all_41_9, all_32_4) = all_106_2 & ( ~
% 22.51/3.81 | | | | | | | | | (all_106_0 = 0) | ~ (all_106_1 = 0) | ~
% 22.51/3.81 | | | | | | | | | (all_106_2 = 0))
% 22.51/3.81 | | | | | | | | |
% 22.51/3.81 | | | | | | | | | ALPHA: (144) implies:
% 22.51/3.81 | | | | | | | | | (145) apply(all_32_6, all_41_9, all_59_3) = all_106_0
% 22.51/3.81 | | | | | | | | |
% 22.51/3.81 | | | | | | | | | BETA: splitting (98) gives:
% 22.51/3.81 | | | | | | | | |
% 22.51/3.81 | | | | | | | | | Case 1:
% 22.51/3.81 | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | (146) all_41_7 = all_41_8
% 22.51/3.81 | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | REDUCE: (71), (146) imply:
% 22.51/3.81 | | | | | | | | | | (147) $false
% 22.51/3.81 | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | CLOSE: (147) is inconsistent.
% 22.51/3.81 | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | Case 2:
% 22.51/3.81 | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_100_0, all_55_0,
% 22.51/3.81 | | | | | | | | | | all_41_9, all_32_6, simplifying with (83), (138)
% 22.51/3.81 | | | | | | | | | | gives:
% 22.51/3.81 | | | | | | | | | | (148) all_100_0 = 0
% 22.51/3.81 | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | GROUND_INST: instantiating (10) with 0, all_106_0, all_59_3,
% 22.51/3.81 | | | | | | | | | | all_41_9, all_32_6, simplifying with (92), (145)
% 22.51/3.81 | | | | | | | | | | gives:
% 22.51/3.81 | | | | | | | | | | (149) all_106_0 = 0
% 22.51/3.81 | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | GROUND_INST: instantiating (10) with all_100_1, all_106_0,
% 22.51/3.81 | | | | | | | | | | all_59_3, all_41_9, all_32_6, simplifying with
% 22.51/3.81 | | | | | | | | | | (139), (145) gives:
% 22.51/3.81 | | | | | | | | | | (150) all_106_0 = all_100_1
% 22.51/3.81 | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | COMBINE_EQS: (149), (150) imply:
% 22.51/3.81 | | | | | | | | | | (151) all_100_1 = 0
% 22.51/3.81 | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | BETA: splitting (140) gives:
% 22.51/3.81 | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | Case 1:
% 22.51/3.81 | | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | | (152) ~ (all_100_0 = 0)
% 22.51/3.81 | | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | | REDUCE: (148), (152) imply:
% 22.51/3.81 | | | | | | | | | | | (153) $false
% 22.51/3.81 | | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | | CLOSE: (153) is inconsistent.
% 22.51/3.81 | | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | Case 2:
% 22.51/3.81 | | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | | (154) ~ (all_100_1 = 0)
% 22.51/3.81 | | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | | REDUCE: (151), (154) imply:
% 22.51/3.81 | | | | | | | | | | | (155) $false
% 22.51/3.81 | | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | | CLOSE: (155) is inconsistent.
% 22.51/3.81 | | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | | End of split
% 22.51/3.81 | | | | | | | | | |
% 22.51/3.81 | | | | | | | | | End of split
% 22.51/3.81 | | | | | | | | |
% 22.51/3.81 | | | | | | | | End of split
% 22.51/3.81 | | | | | | | |
% 22.51/3.81 | | | | | | | End of split
% 22.51/3.81 | | | | | | |
% 22.51/3.81 | | | | | | End of split
% 22.51/3.81 | | | | | |
% 22.51/3.81 | | | | | End of split
% 22.51/3.81 | | | | |
% 22.51/3.81 | | | | Case 2:
% 22.51/3.81 | | | | |
% 22.51/3.81 | | | | | (156) member(all_41_7, all_32_2) = all_57_4 & member(all_41_9,
% 22.51/3.81 | | | | | all_32_4) = all_57_5 & ( ~ (all_57_4 = 0) | ~ (all_57_5 =
% 22.51/3.81 | | | | | 0))
% 22.51/3.81 | | | | |
% 22.51/3.81 | | | | | ALPHA: (156) implies:
% 22.51/3.81 | | | | | (157) member(all_41_9, all_32_4) = all_57_5
% 22.51/3.81 | | | | | (158) member(all_41_7, all_32_2) = all_57_4
% 22.51/3.81 | | | | | (159) ~ (all_57_4 = 0) | ~ (all_57_5 = 0)
% 22.51/3.81 | | | | |
% 22.51/3.81 | | | | | GROUND_INST: instantiating (9) with 0, all_57_5, all_32_4, all_41_9,
% 22.51/3.81 | | | | | simplifying with (72), (157) gives:
% 22.51/3.81 | | | | | (160) all_57_5 = 0
% 22.51/3.81 | | | | |
% 22.51/3.81 | | | | | GROUND_INST: instantiating (9) with 0, all_57_4, all_32_2, all_41_7,
% 22.51/3.81 | | | | | simplifying with (74), (158) gives:
% 22.51/3.81 | | | | | (161) all_57_4 = 0
% 22.51/3.81 | | | | |
% 22.51/3.81 | | | | | BETA: splitting (159) gives:
% 22.51/3.81 | | | | |
% 22.51/3.81 | | | | | Case 1:
% 22.51/3.81 | | | | | |
% 22.51/3.81 | | | | | | (162) ~ (all_57_4 = 0)
% 22.51/3.81 | | | | | |
% 22.51/3.81 | | | | | | REDUCE: (161), (162) imply:
% 22.51/3.81 | | | | | | (163) $false
% 22.51/3.81 | | | | | |
% 22.51/3.81 | | | | | | CLOSE: (163) is inconsistent.
% 22.51/3.81 | | | | | |
% 22.51/3.81 | | | | | Case 2:
% 22.51/3.81 | | | | | |
% 22.51/3.81 | | | | | | (164) ~ (all_57_5 = 0)
% 22.51/3.81 | | | | | |
% 22.70/3.81 | | | | | | REDUCE: (160), (164) imply:
% 22.70/3.81 | | | | | | (165) $false
% 22.70/3.81 | | | | | |
% 22.70/3.81 | | | | | | CLOSE: (165) is inconsistent.
% 22.70/3.81 | | | | | |
% 22.70/3.81 | | | | | End of split
% 22.70/3.81 | | | | |
% 22.70/3.81 | | | | End of split
% 22.70/3.81 | | | |
% 22.70/3.81 | | | Case 2:
% 22.70/3.81 | | | |
% 22.70/3.81 | | | | (166) member(all_41_8, all_32_2) = all_59_4 & member(all_41_9,
% 22.70/3.81 | | | | all_32_4) = all_59_5 & ( ~ (all_59_4 = 0) | ~ (all_59_5 =
% 22.70/3.81 | | | | 0))
% 22.70/3.81 | | | |
% 22.70/3.81 | | | | ALPHA: (166) implies:
% 22.70/3.81 | | | | (167) member(all_41_9, all_32_4) = all_59_5
% 22.70/3.81 | | | | (168) member(all_41_8, all_32_2) = all_59_4
% 22.70/3.81 | | | | (169) ~ (all_59_4 = 0) | ~ (all_59_5 = 0)
% 22.70/3.81 | | | |
% 22.70/3.81 | | | | GROUND_INST: instantiating (9) with 0, all_59_5, all_32_4, all_41_9,
% 22.70/3.81 | | | | simplifying with (72), (167) gives:
% 22.70/3.81 | | | | (170) all_59_5 = 0
% 22.70/3.81 | | | |
% 22.70/3.81 | | | | GROUND_INST: instantiating (9) with 0, all_59_4, all_32_2, all_41_8,
% 22.70/3.81 | | | | simplifying with (73), (168) gives:
% 22.70/3.81 | | | | (171) all_59_4 = 0
% 22.70/3.81 | | | |
% 22.70/3.81 | | | | BETA: splitting (169) gives:
% 22.70/3.81 | | | |
% 22.70/3.81 | | | | Case 1:
% 22.70/3.81 | | | | |
% 22.70/3.81 | | | | | (172) ~ (all_59_4 = 0)
% 22.70/3.81 | | | | |
% 22.70/3.81 | | | | | REDUCE: (171), (172) imply:
% 22.70/3.81 | | | | | (173) $false
% 22.70/3.81 | | | | |
% 22.70/3.81 | | | | | CLOSE: (173) is inconsistent.
% 22.70/3.81 | | | | |
% 22.70/3.81 | | | | Case 2:
% 22.70/3.81 | | | | |
% 22.70/3.81 | | | | | (174) ~ (all_59_5 = 0)
% 22.70/3.81 | | | | |
% 22.70/3.81 | | | | | REDUCE: (170), (174) imply:
% 22.70/3.81 | | | | | (175) $false
% 22.70/3.81 | | | | |
% 22.70/3.81 | | | | | CLOSE: (175) is inconsistent.
% 22.70/3.81 | | | | |
% 22.70/3.81 | | | | End of split
% 22.70/3.81 | | | |
% 22.70/3.81 | | | End of split
% 22.70/3.81 | | |
% 22.70/3.81 | | End of split
% 22.70/3.81 | |
% 22.70/3.81 | End of split
% 22.70/3.81 |
% 22.70/3.81 End of proof
% 22.70/3.81
% 22.70/3.81 Sub-proof #1 shows that the following formulas are inconsistent:
% 22.70/3.81 ----------------------------------------------------------------
% 22.70/3.81 (1) all_59_3 = all_55_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 22.70/3.81 (member(all_59_3, all_32_3) = v1 & member(all_55_0, all_32_3) = v2 &
% 22.70/3.81 member(all_41_9, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 =
% 22.70/3.81 0)))
% 22.70/3.81 (2) all_41_7 = all_41_8 | ? [v0: any] : ? [v1: any] : (apply(all_32_5,
% 22.70/3.81 all_55_0, all_41_7) = v1 & apply(all_32_5, all_55_0, all_41_8) = v0 &
% 22.70/3.81 ( ~ (v1 = 0) | ~ (v0 = 0)))
% 22.70/3.81 (3) all_59_3 = all_55_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 22.70/3.81 (apply(all_32_6, all_41_9, all_59_3) = v2 & member(all_55_0, all_32_3) =
% 22.70/3.81 v1 & member(all_41_9, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 22.70/3.81 (v0 = 0)))
% 22.70/3.81 (4) apply(all_32_5, all_57_3, all_41_7) = 0
% 22.70/3.81 (5) member(all_41_8, all_32_2) = 0
% 22.70/3.81 (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 22.70/3.81 ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (apply(v4, v3, v2) = v1) | ~
% 22.70/3.81 (apply(v4, v3, v2) = v0))
% 22.70/3.81 (7) apply(all_32_5, all_59_3, all_41_7) = all_87_0 & member(all_59_3,
% 22.70/3.81 all_32_3) = all_87_2 & member(all_41_8, all_32_2) = all_87_1 & ( ~
% 22.70/3.81 (all_87_0 = 0) | ~ (all_87_1 = 0) | ~ (all_87_2 = 0))
% 22.70/3.81 (8) all_41_7 = all_41_8 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 22.70/3.81 (apply(all_32_5, all_57_3, all_41_8) = v2 & member(all_57_3, all_32_3) =
% 22.70/3.81 v0 & member(all_41_7, all_32_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 22.70/3.81 (v0 = 0)))
% 22.70/3.82 (9) ~ (all_41_7 = all_41_8)
% 22.70/3.82 (10) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 22.70/3.82 ! [v3: $i] : (v1 = v0 | ~ (member(v3, v2) = v1) | ~ (member(v3, v2) =
% 22.70/3.82 v0))
% 22.70/3.82 (11) all_59_3 = all_55_0 | ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 22.70/3.82 (apply(all_32_6, all_41_9, all_55_0) = v2 & member(all_59_3, all_32_3) =
% 22.70/3.82 v1 & member(all_41_9, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 22.70/3.82 (v0 = 0)))
% 22.70/3.82 (12) member(all_57_3, all_32_3) = 0
% 22.70/3.82 (13) all_59_3 = all_57_3
% 22.70/3.82
% 22.70/3.82 Begin of proof
% 22.70/3.82 |
% 22.70/3.82 | ALPHA: (7) implies:
% 22.70/3.82 | (14) member(all_41_8, all_32_2) = all_87_1
% 22.70/3.82 | (15) member(all_59_3, all_32_3) = all_87_2
% 22.70/3.82 | (16) apply(all_32_5, all_59_3, all_41_7) = all_87_0
% 22.70/3.82 | (17) ~ (all_87_0 = 0) | ~ (all_87_1 = 0) | ~ (all_87_2 = 0)
% 22.70/3.82 |
% 22.70/3.82 | REDUCE: (13), (16) imply:
% 22.70/3.82 | (18) apply(all_32_5, all_57_3, all_41_7) = all_87_0
% 22.70/3.82 |
% 22.70/3.82 | REDUCE: (13), (15) imply:
% 22.70/3.82 | (19) member(all_57_3, all_32_3) = all_87_2
% 22.70/3.82 |
% 22.70/3.82 | BETA: splitting (8) gives:
% 22.70/3.82 |
% 22.70/3.82 | Case 1:
% 22.70/3.82 | |
% 22.70/3.82 | | (20) all_41_7 = all_41_8
% 22.70/3.82 | |
% 22.70/3.82 | | REDUCE: (9), (20) imply:
% 22.70/3.82 | | (21) $false
% 22.70/3.82 | |
% 22.70/3.82 | | CLOSE: (21) is inconsistent.
% 22.70/3.82 | |
% 22.70/3.82 | Case 2:
% 22.70/3.82 | |
% 22.70/3.82 | | (22) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_5,
% 22.70/3.82 | | all_57_3, all_41_8) = v2 & member(all_57_3, all_32_3) = v0 &
% 22.70/3.82 | | member(all_41_7, all_32_2) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~
% 22.70/3.82 | | (v0 = 0)))
% 22.70/3.82 | |
% 22.70/3.82 | | DELTA: instantiating (22) with fresh symbols all_92_0, all_92_1, all_92_2
% 22.70/3.82 | | gives:
% 22.70/3.82 | | (23) apply(all_32_5, all_57_3, all_41_8) = all_92_0 & member(all_57_3,
% 22.70/3.82 | | all_32_3) = all_92_2 & member(all_41_7, all_32_2) = all_92_1 & ( ~
% 22.70/3.82 | | (all_92_0 = 0) | ~ (all_92_1 = 0) | ~ (all_92_2 = 0))
% 22.70/3.82 | |
% 22.70/3.82 | | ALPHA: (23) implies:
% 22.70/3.82 | | (24) member(all_57_3, all_32_3) = all_92_2
% 22.70/3.82 | |
% 22.70/3.82 | | BETA: splitting (3) gives:
% 22.70/3.82 | |
% 22.70/3.82 | | Case 1:
% 22.70/3.82 | | |
% 22.70/3.82 | | | (25) all_59_3 = all_55_0
% 22.70/3.82 | | |
% 22.70/3.82 | | | COMBINE_EQS: (13), (25) imply:
% 22.70/3.82 | | | (26) all_57_3 = all_55_0
% 22.70/3.82 | | |
% 22.70/3.82 | | | REDUCE: (18), (26) imply:
% 22.70/3.82 | | | (27) apply(all_32_5, all_55_0, all_41_7) = all_87_0
% 22.70/3.82 | | |
% 22.70/3.82 | | | REDUCE: (4), (26) imply:
% 22.70/3.82 | | | (28) apply(all_32_5, all_55_0, all_41_7) = 0
% 22.70/3.82 | | |
% 22.70/3.82 | | | REDUCE: (19), (26) imply:
% 22.70/3.82 | | | (29) member(all_55_0, all_32_3) = all_87_2
% 22.70/3.82 | | |
% 22.70/3.82 | | | REDUCE: (12), (26) imply:
% 22.70/3.82 | | | (30) member(all_55_0, all_32_3) = 0
% 22.70/3.82 | | |
% 22.70/3.82 | | | GROUND_INST: instantiating (10) with 0, all_87_1, all_32_2, all_41_8,
% 22.70/3.82 | | | simplifying with (5), (14) gives:
% 22.70/3.82 | | | (31) all_87_1 = 0
% 22.70/3.82 | | |
% 22.70/3.82 | | | GROUND_INST: instantiating (10) with 0, all_87_2, all_32_3, all_55_0,
% 22.70/3.82 | | | simplifying with (29), (30) gives:
% 22.70/3.82 | | | (32) all_87_2 = 0
% 22.70/3.82 | | |
% 22.70/3.82 | | | GROUND_INST: instantiating (6) with 0, all_87_0, all_41_7, all_55_0,
% 22.70/3.82 | | | all_32_5, simplifying with (27), (28) gives:
% 22.70/3.82 | | | (33) all_87_0 = 0
% 22.70/3.82 | | |
% 22.70/3.82 | | | REF_CLOSE: (17), (31), (32), (33) are inconsistent by sub-proof #2.
% 22.70/3.82 | | |
% 22.70/3.82 | | Case 2:
% 22.70/3.82 | | |
% 22.70/3.82 | | | (34) ~ (all_59_3 = all_55_0)
% 22.70/3.82 | | |
% 22.70/3.82 | | | REDUCE: (13), (34) imply:
% 22.70/3.82 | | | (35) ~ (all_57_3 = all_55_0)
% 22.70/3.82 | | |
% 22.70/3.82 | | | BETA: splitting (11) gives:
% 22.70/3.82 | | |
% 22.70/3.82 | | | Case 1:
% 22.70/3.82 | | | |
% 22.70/3.82 | | | | (36) all_59_3 = all_55_0
% 22.70/3.82 | | | |
% 22.70/3.82 | | | | COMBINE_EQS: (13), (36) imply:
% 22.70/3.82 | | | | (37) all_57_3 = all_55_0
% 22.70/3.82 | | | |
% 22.70/3.82 | | | | REDUCE: (35), (37) imply:
% 22.70/3.82 | | | | (38) $false
% 22.70/3.82 | | | |
% 22.70/3.82 | | | | CLOSE: (38) is inconsistent.
% 22.70/3.82 | | | |
% 22.70/3.82 | | | Case 2:
% 22.70/3.82 | | | |
% 22.70/3.82 | | | | (39) ? [v0: any] : ? [v1: any] : ? [v2: any] : (apply(all_32_6,
% 22.70/3.82 | | | | all_41_9, all_55_0) = v2 & member(all_59_3, all_32_3) = v1 &
% 22.70/3.82 | | | | member(all_41_9, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) |
% 22.70/3.82 | | | | ~ (v0 = 0)))
% 22.70/3.82 | | | |
% 22.70/3.82 | | | | DELTA: instantiating (39) with fresh symbols all_104_0, all_104_1,
% 22.70/3.82 | | | | all_104_2 gives:
% 22.70/3.82 | | | | (40) apply(all_32_6, all_41_9, all_55_0) = all_104_0 &
% 22.70/3.82 | | | | member(all_59_3, all_32_3) = all_104_1 & member(all_41_9,
% 22.70/3.82 | | | | all_32_4) = all_104_2 & ( ~ (all_104_0 = 0) | ~ (all_104_1 =
% 22.70/3.82 | | | | 0) | ~ (all_104_2 = 0))
% 22.70/3.82 | | | |
% 22.70/3.82 | | | | ALPHA: (40) implies:
% 22.70/3.82 | | | | (41) member(all_59_3, all_32_3) = all_104_1
% 22.70/3.82 | | | |
% 22.70/3.82 | | | | REDUCE: (13), (41) imply:
% 22.70/3.82 | | | | (42) member(all_57_3, all_32_3) = all_104_1
% 22.70/3.82 | | | |
% 22.70/3.82 | | | | BETA: splitting (1) gives:
% 22.70/3.82 | | | |
% 22.70/3.82 | | | | Case 1:
% 22.70/3.82 | | | | |
% 22.70/3.82 | | | | | (43) all_59_3 = all_55_0
% 22.70/3.82 | | | | |
% 22.70/3.82 | | | | | COMBINE_EQS: (13), (43) imply:
% 22.70/3.82 | | | | | (44) all_57_3 = all_55_0
% 22.70/3.82 | | | | |
% 22.70/3.82 | | | | | REDUCE: (35), (44) imply:
% 22.70/3.82 | | | | | (45) $false
% 22.70/3.82 | | | | |
% 22.70/3.82 | | | | | CLOSE: (45) is inconsistent.
% 22.70/3.82 | | | | |
% 22.70/3.82 | | | | Case 2:
% 22.70/3.82 | | | | |
% 22.70/3.82 | | | | | (46) ? [v0: any] : ? [v1: any] : ? [v2: any] : (member(all_59_3,
% 22.70/3.82 | | | | | all_32_3) = v1 & member(all_55_0, all_32_3) = v2 &
% 22.70/3.82 | | | | | member(all_41_9, all_32_4) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0)
% 22.70/3.82 | | | | | | ~ (v0 = 0)))
% 22.70/3.82 | | | | |
% 22.70/3.82 | | | | | DELTA: instantiating (46) with fresh symbols all_110_0, all_110_1,
% 22.70/3.82 | | | | | all_110_2 gives:
% 22.70/3.82 | | | | | (47) member(all_59_3, all_32_3) = all_110_1 & member(all_55_0,
% 22.70/3.82 | | | | | all_32_3) = all_110_0 & member(all_41_9, all_32_4) =
% 22.70/3.82 | | | | | all_110_2 & ( ~ (all_110_0 = 0) | ~ (all_110_1 = 0) | ~
% 22.70/3.82 | | | | | (all_110_2 = 0))
% 22.70/3.82 | | | | |
% 22.70/3.82 | | | | | ALPHA: (47) implies:
% 22.70/3.82 | | | | | (48) member(all_59_3, all_32_3) = all_110_1
% 22.70/3.82 | | | | |
% 22.70/3.82 | | | | | REDUCE: (13), (48) imply:
% 22.70/3.82 | | | | | (49) member(all_57_3, all_32_3) = all_110_1
% 22.70/3.82 | | | | |
% 22.70/3.82 | | | | | BETA: splitting (2) gives:
% 22.70/3.82 | | | | |
% 22.70/3.82 | | | | | Case 1:
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | | (50) all_41_7 = all_41_8
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | | REDUCE: (9), (50) imply:
% 22.70/3.82 | | | | | | (51) $false
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | | CLOSE: (51) is inconsistent.
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | Case 2:
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | | GROUND_INST: instantiating (10) with 0, all_87_1, all_32_2,
% 22.70/3.82 | | | | | | all_41_8, simplifying with (5), (14) gives:
% 22.70/3.82 | | | | | | (52) all_87_1 = 0
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | | GROUND_INST: instantiating (10) with 0, all_104_1, all_32_3,
% 22.70/3.82 | | | | | | all_57_3, simplifying with (12), (42) gives:
% 22.70/3.82 | | | | | | (53) all_104_1 = 0
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | | GROUND_INST: instantiating (10) with all_87_2, all_104_1, all_32_3,
% 22.70/3.82 | | | | | | all_57_3, simplifying with (19), (42) gives:
% 22.70/3.82 | | | | | | (54) all_104_1 = all_87_2
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | | GROUND_INST: instantiating (10) with all_104_1, all_110_1, all_32_3,
% 22.70/3.82 | | | | | | all_57_3, simplifying with (42), (49) gives:
% 22.70/3.82 | | | | | | (55) all_110_1 = all_104_1
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | | GROUND_INST: instantiating (10) with all_92_2, all_110_1, all_32_3,
% 22.70/3.82 | | | | | | all_57_3, simplifying with (24), (49) gives:
% 22.70/3.82 | | | | | | (56) all_110_1 = all_92_2
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | | GROUND_INST: instantiating (6) with 0, all_87_0, all_41_7, all_57_3,
% 22.70/3.82 | | | | | | all_32_5, simplifying with (4), (18) gives:
% 22.70/3.82 | | | | | | (57) all_87_0 = 0
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | | COMBINE_EQS: (55), (56) imply:
% 22.70/3.82 | | | | | | (58) all_104_1 = all_92_2
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | | SIMP: (58) implies:
% 22.70/3.82 | | | | | | (59) all_104_1 = all_92_2
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | | COMBINE_EQS: (53), (59) imply:
% 22.70/3.82 | | | | | | (60) all_92_2 = 0
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | | COMBINE_EQS: (54), (59) imply:
% 22.70/3.82 | | | | | | (61) all_92_2 = all_87_2
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | | COMBINE_EQS: (60), (61) imply:
% 22.70/3.82 | | | | | | (62) all_87_2 = 0
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | | REF_CLOSE: (17), (52), (57), (62) are inconsistent by sub-proof #2.
% 22.70/3.82 | | | | | |
% 22.70/3.82 | | | | | End of split
% 22.70/3.82 | | | | |
% 22.70/3.82 | | | | End of split
% 22.70/3.82 | | | |
% 22.70/3.82 | | | End of split
% 22.70/3.82 | | |
% 22.70/3.82 | | End of split
% 22.70/3.82 | |
% 22.70/3.82 | End of split
% 22.70/3.82 |
% 22.70/3.82 End of proof
% 22.70/3.82
% 22.70/3.82 Sub-proof #2 shows that the following formulas are inconsistent:
% 22.70/3.82 ----------------------------------------------------------------
% 22.70/3.82 (1) ~ (all_87_0 = 0) | ~ (all_87_1 = 0) | ~ (all_87_2 = 0)
% 22.70/3.83 (2) all_87_0 = 0
% 22.70/3.83 (3) all_87_1 = 0
% 22.70/3.83 (4) all_87_2 = 0
% 22.70/3.83
% 22.70/3.83 Begin of proof
% 22.70/3.83 |
% 22.70/3.83 | BETA: splitting (1) gives:
% 22.70/3.83 |
% 22.70/3.83 | Case 1:
% 22.70/3.83 | |
% 22.70/3.83 | | (5) ~ (all_87_0 = 0)
% 22.70/3.83 | |
% 22.70/3.83 | | REDUCE: (2), (5) imply:
% 22.70/3.83 | | (6) $false
% 22.70/3.83 | |
% 22.70/3.83 | | CLOSE: (6) is inconsistent.
% 22.70/3.83 | |
% 22.70/3.83 | Case 2:
% 22.70/3.83 | |
% 22.70/3.83 | | (7) ~ (all_87_1 = 0) | ~ (all_87_2 = 0)
% 22.70/3.83 | |
% 22.70/3.83 | | BETA: splitting (7) gives:
% 22.70/3.83 | |
% 22.70/3.83 | | Case 1:
% 22.70/3.83 | | |
% 22.70/3.83 | | | (8) ~ (all_87_1 = 0)
% 22.70/3.83 | | |
% 22.70/3.83 | | | REDUCE: (3), (8) imply:
% 22.70/3.83 | | | (9) $false
% 22.70/3.83 | | |
% 22.70/3.83 | | | CLOSE: (9) is inconsistent.
% 22.70/3.83 | | |
% 22.70/3.83 | | Case 2:
% 22.70/3.83 | | |
% 22.70/3.83 | | | (10) ~ (all_87_2 = 0)
% 22.70/3.83 | | |
% 22.70/3.83 | | | REDUCE: (4), (10) imply:
% 22.70/3.83 | | | (11) $false
% 22.70/3.83 | | |
% 22.70/3.83 | | | CLOSE: (11) is inconsistent.
% 22.70/3.83 | | |
% 22.70/3.83 | | End of split
% 22.70/3.83 | |
% 22.70/3.83 | End of split
% 22.70/3.83 |
% 22.70/3.83 End of proof
% 22.70/3.83
% 22.70/3.83 Sub-proof #3 shows that the following formulas are inconsistent:
% 22.70/3.83 ----------------------------------------------------------------
% 22.70/3.83 (1) ~ (all_79_0 = 0) | ~ (all_79_1 = 0)
% 22.70/3.83 (2) all_79_0 = 0
% 22.70/3.83 (3) all_79_1 = 0
% 22.70/3.83
% 22.70/3.83 Begin of proof
% 22.70/3.83 |
% 22.70/3.83 | BETA: splitting (1) gives:
% 22.70/3.83 |
% 22.70/3.83 | Case 1:
% 22.70/3.83 | |
% 22.70/3.83 | | (4) ~ (all_79_0 = 0)
% 22.70/3.83 | |
% 22.70/3.83 | | REDUCE: (2), (4) imply:
% 22.70/3.83 | | (5) $false
% 22.70/3.83 | |
% 22.70/3.83 | | CLOSE: (5) is inconsistent.
% 22.70/3.83 | |
% 22.70/3.83 | Case 2:
% 22.70/3.83 | |
% 22.70/3.83 | | (6) ~ (all_79_1 = 0)
% 22.70/3.83 | |
% 22.70/3.83 | | REDUCE: (3), (6) imply:
% 22.70/3.83 | | (7) $false
% 22.70/3.83 | |
% 22.70/3.83 | | CLOSE: (7) is inconsistent.
% 22.70/3.83 | |
% 22.70/3.83 | End of split
% 22.70/3.83 |
% 22.70/3.83 End of proof
% 22.70/3.83 % SZS output end Proof for theBenchmark
% 22.70/3.83
% 22.70/3.83 3310ms
%------------------------------------------------------------------------------