TSTP Solution File: KLE029+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : KLE029+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 05:34:18 EDT 2023
% Result : Theorem 10.35s 2.18s
% Output : Proof 12.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : KLE029+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 11:43:22 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.55/1.05 Prover 1: Preprocessing ...
% 2.55/1.05 Prover 4: Preprocessing ...
% 2.73/1.09 Prover 2: Preprocessing ...
% 2.73/1.09 Prover 0: Preprocessing ...
% 2.73/1.09 Prover 6: Preprocessing ...
% 2.73/1.09 Prover 5: Preprocessing ...
% 2.73/1.09 Prover 3: Preprocessing ...
% 5.11/1.42 Prover 6: Proving ...
% 5.31/1.44 Prover 5: Proving ...
% 5.31/1.44 Prover 1: Constructing countermodel ...
% 5.31/1.45 Prover 3: Constructing countermodel ...
% 5.31/1.52 Prover 2: Proving ...
% 5.95/1.53 Prover 4: Constructing countermodel ...
% 5.95/1.54 Prover 0: Proving ...
% 6.97/1.70 Prover 3: gave up
% 6.97/1.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 6.97/1.70 Prover 1: gave up
% 7.25/1.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 7.42/1.73 Prover 7: Preprocessing ...
% 7.42/1.74 Prover 8: Preprocessing ...
% 8.08/1.82 Prover 8: Warning: ignoring some quantifiers
% 8.08/1.82 Prover 7: Warning: ignoring some quantifiers
% 8.08/1.83 Prover 7: Constructing countermodel ...
% 8.08/1.84 Prover 8: Constructing countermodel ...
% 8.08/1.88 Prover 7: gave up
% 8.55/1.89 Prover 9: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allMinimal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1423531889
% 8.55/1.92 Prover 9: Preprocessing ...
% 8.55/1.95 Prover 8: gave up
% 8.55/1.95 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 8.55/1.98 Prover 10: Preprocessing ...
% 8.55/2.04 Prover 10: Warning: ignoring some quantifiers
% 9.97/2.09 Prover 10: Constructing countermodel ...
% 9.97/2.12 Prover 10: gave up
% 10.24/2.13 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 10.24/2.13 Prover 9: Constructing countermodel ...
% 10.35/2.15 Prover 11: Preprocessing ...
% 10.35/2.18 Prover 0: proved (1557ms)
% 10.35/2.18
% 10.35/2.18 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.35/2.18
% 10.35/2.18 Prover 9: stopped
% 10.35/2.18 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.35/2.18 Prover 2: stopped
% 10.35/2.18 Prover 6: stopped
% 10.35/2.18 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 10.35/2.18 Prover 5: stopped
% 10.35/2.18 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 10.35/2.19 Prover 4: Found proof (size 183)
% 10.35/2.19 Prover 4: proved (1570ms)
% 10.35/2.19 Prover 11: stopped
% 10.35/2.20 Prover 13: Preprocessing ...
% 10.35/2.20 Prover 16: Preprocessing ...
% 10.35/2.20 Prover 19: Preprocessing ...
% 10.89/2.22 Prover 13: stopped
% 10.89/2.22 Prover 16: stopped
% 10.89/2.26 Prover 19: Warning: ignoring some quantifiers
% 10.89/2.27 Prover 19: Constructing countermodel ...
% 11.21/2.27 Prover 19: stopped
% 11.21/2.27
% 11.21/2.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.21/2.27
% 11.21/2.30 % SZS output start Proof for theBenchmark
% 11.21/2.30 Assumptions after simplification:
% 11.21/2.30 ---------------------------------
% 11.21/2.30
% 11.21/2.30 (additive_associativity)
% 11.21/2.34 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : ( ~
% 11.21/2.34 (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) | ~ $i(v1)
% 11.21/2.34 | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 & addition(v1, v0) = v5 &
% 11.21/2.34 $i(v5) & $i(v4))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i]
% 11.21/2.34 : ! [v4: $i] : ( ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~
% 11.21/2.34 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 &
% 11.21/2.34 addition(v2, v1) = v5 & $i(v5) & $i(v4)))
% 11.21/2.34
% 11.21/2.34 (additive_idempotence)
% 11.21/2.34 ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~ $i(v0))
% 11.21/2.34
% 11.21/2.34 (goals)
% 11.21/2.35 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: any] : ? [v4: any] :
% 11.21/2.35 (ismeetu(v0, v1, v2) = v4 & ismeet(v0, v1, v2) = v3 & $i(v2) & $i(v1) & $i(v0)
% 11.21/2.35 & ((v4 = 0 & ~ (v3 = 0)) | (v3 = 0 & ~ (v4 = 0))))
% 11.21/2.35
% 11.21/2.35 (ismeet)
% 11.21/2.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 11.21/2.35 | ~ (ismeet(v2, v0, v1) = 0) | ~ (leq(v3, v2) = v4) | ~ $i(v3) | ~
% 11.21/2.36 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (leq(v3, v1)
% 11.21/2.36 = v6 & leq(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 11.21/2.36 [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~ (ismeet(v2, v0, v1) = v3)
% 11.21/2.36 | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : ? [v6:
% 11.21/2.36 $i] : ? [v7: int] : ? [v8: int] : ? [v9: int] : ($i(v6) & ((v8 = 0 & v7
% 11.21/2.36 = 0 & ~ (v9 = 0) & leq(v6, v2) = v9 & leq(v6, v1) = 0 & leq(v6, v0) =
% 11.21/2.36 0) | (leq(v2, v1) = v5 & leq(v2, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 =
% 11.21/2.36 0)))))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] :
% 11.21/2.36 ( ~ (ismeet(v2, v0, v1) = 0) | ~ (leq(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) |
% 11.21/2.36 ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (leq(v3, v2) = v5 &
% 11.21/2.36 leq(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0))) & ! [v0: $i] : ! [v1: $i] :
% 11.21/2.36 ! [v2: $i] : ! [v3: $i] : ( ~ (ismeet(v2, v0, v1) = 0) | ~ (leq(v3, v0) = 0)
% 11.21/2.36 | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5:
% 11.21/2.36 any] : (leq(v3, v2) = v5 & leq(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0))) &
% 11.21/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ismeet(v2, v0, v1) = 0) | ~
% 11.21/2.36 $i(v2) | ~ $i(v1) | ~ $i(v0) | (leq(v2, v1) = 0 & leq(v2, v0) = 0))
% 11.21/2.36
% 11.21/2.36 (ismeetu)
% 11.63/2.36 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] : (v4 = 0
% 11.63/2.36 | ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v2) = v4) | ~ $i(v3) | ~
% 11.63/2.36 $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] : (leq(v3, v1)
% 11.63/2.36 = v6 & leq(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0)))) & ! [v0: $i] : !
% 11.63/2.36 [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (ismeetu(v2, v0, v1)
% 11.63/2.36 = 0) | ~ (leq(v3, v1) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 11.63/2.36 $i(v0) | ? [v5: any] : ? [v6: any] : (leq(v3, v2) = v5 & leq(v3, v0) = v6
% 11.63/2.36 & ( ~ (v5 = 0) | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : !
% 11.63/2.36 [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~ (ismeetu(v2, v0, v1) = 0) | ~
% 11.63/2.36 (leq(v3, v0) = v4) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5:
% 11.63/2.36 any] : ? [v6: any] : (leq(v3, v2) = v5 & leq(v3, v1) = v6 & ( ~ (v5 = 0)
% 11.63/2.36 | (v6 = 0 & v4 = 0)))) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : !
% 11.63/2.36 [v3: int] : (v3 = 0 | ~ (ismeetu(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) |
% 11.63/2.36 ~ $i(v0) | ? [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] :
% 11.63/2.36 (leq(v4, v2) = v7 & leq(v4, v1) = v6 & leq(v4, v0) = v5 & $i(v4) & ( ~ (v7 =
% 11.63/2.36 0) | ~ (v6 = 0) | ~ (v5 = 0)) & (v7 = 0 | (v6 = 0 & v5 = 0)))) & !
% 11.63/2.36 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (ismeetu(v2, v0, v1)
% 11.63/2.36 = 0) | ~ (leq(v3, v2) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 11.63/2.36 $i(v0) | (leq(v3, v1) = 0 & leq(v3, v0) = 0)) & ! [v0: $i] : ! [v1: $i] :
% 11.63/2.36 ! [v2: $i] : ! [v3: $i] : ( ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v1) =
% 11.63/2.36 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ?
% 11.63/2.36 [v5: any] : (leq(v3, v2) = v5 & leq(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 11.63/2.36 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (ismeetu(v2, v0,
% 11.63/2.36 v1) = 0) | ~ (leq(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~ $i(v1) | ~
% 11.63/2.36 $i(v0) | ? [v4: any] : ? [v5: any] : (leq(v3, v2) = v5 & leq(v3, v1) = v4
% 11.63/2.36 & ( ~ (v4 = 0) | v5 = 0)))
% 11.63/2.36
% 11.63/2.36 (order)
% 11.63/2.37 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v2 = v1 | ~ (addition(v0, v1) =
% 11.63/2.37 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) & leq(v0, v1) =
% 11.63/2.37 v3)) & ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0,
% 11.63/2.37 v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 11.63/2.37 addition(v0, v1) = v3 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 11.63/2.37 (leq(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | addition(v0, v1) = v1) & ! [v0:
% 11.63/2.37 $i] : ! [v1: $i] : ( ~ (addition(v0, v1) = v1) | ~ $i(v1) | ~ $i(v0) |
% 11.63/2.37 leq(v0, v1) = 0)
% 11.63/2.37
% 11.63/2.37 (function-axioms)
% 11.63/2.37 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 11.63/2.37 [v3: $i] : ! [v4: $i] : (v1 = v0 | ~ (ismeetu(v4, v3, v2) = v1) | ~
% 11.63/2.37 (ismeetu(v4, v3, v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 11.63/2.37 MultipleValueBool] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (v1 = v0 | ~
% 11.63/2.37 (ismeet(v4, v3, v2) = v1) | ~ (ismeet(v4, v3, v2) = v0)) & ! [v0:
% 11.63/2.37 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 11.63/2.37 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0: $i] : !
% 11.63/2.37 [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (multiplication(v3, v2) =
% 11.63/2.37 v1) | ~ (multiplication(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] : !
% 11.63/2.37 [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (addition(v3, v2) = v1) | ~
% 11.63/2.37 (addition(v3, v2) = v0))
% 11.63/2.37
% 11.63/2.37 Further assumptions not needed in the proof:
% 11.63/2.37 --------------------------------------------
% 11.63/2.37 additive_commutativity, additive_identity, left_annihilation,
% 11.63/2.37 left_distributivity, multiplicative_associativity, multiplicative_left_identity,
% 11.63/2.37 multiplicative_right_identity, right_annihilation, right_distributivity
% 11.63/2.37
% 11.63/2.37 Those formulas are unsatisfiable:
% 11.63/2.37 ---------------------------------
% 11.63/2.37
% 11.63/2.37 Begin of proof
% 11.63/2.37 |
% 11.63/2.37 | ALPHA: (additive_associativity) implies:
% 11.63/2.37 | (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 11.63/2.37 | ~ (addition(v2, v3) = v4) | ~ (addition(v1, v0) = v3) | ~ $i(v2) |
% 11.63/2.37 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v5, v0) = v4 &
% 11.63/2.37 | addition(v2, v1) = v5 & $i(v5) & $i(v4)))
% 11.63/2.37 | (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: $i] : (
% 11.63/2.37 | ~ (addition(v3, v0) = v4) | ~ (addition(v2, v1) = v3) | ~ $i(v2) |
% 11.63/2.37 | ~ $i(v1) | ~ $i(v0) | ? [v5: $i] : (addition(v2, v5) = v4 &
% 11.63/2.37 | addition(v1, v0) = v5 & $i(v5) & $i(v4)))
% 11.63/2.37 |
% 11.63/2.37 | ALPHA: (order) implies:
% 11.63/2.37 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (leq(v0, v1) = 0) | ~ $i(v1) | ~
% 11.63/2.37 | $i(v0) | addition(v0, v1) = v1)
% 11.63/2.38 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (leq(v0, v1) =
% 11.63/2.38 | v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ( ~ (v3 = v1) &
% 11.63/2.38 | addition(v0, v1) = v3 & $i(v3)))
% 11.63/2.38 |
% 11.63/2.38 | ALPHA: (ismeet) implies:
% 11.63/2.38 | (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (ismeet(v2, v0, v1) = 0)
% 11.63/2.38 | | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | (leq(v2, v1) = 0 & leq(v2, v0)
% 11.63/2.38 | = 0))
% 11.63/2.38 | (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (ismeet(v2,
% 11.63/2.38 | v0, v1) = 0) | ~ (leq(v3, v0) = 0) | ~ $i(v3) | ~ $i(v2) | ~
% 11.63/2.38 | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (leq(v3, v2) = v5
% 11.63/2.38 | & leq(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 11.63/2.38 | (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (ismeet(v2,
% 11.63/2.38 | v0, v1) = 0) | ~ (leq(v3, v1) = 0) | ~ $i(v3) | ~ $i(v2) | ~
% 11.63/2.38 | $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] : (leq(v3, v2) = v5
% 11.63/2.38 | & leq(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 11.63/2.38 | (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 11.63/2.38 | (ismeet(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 11.63/2.38 | [v4: any] : ? [v5: any] : ? [v6: $i] : ? [v7: int] : ? [v8: int]
% 11.63/2.38 | : ? [v9: int] : ($i(v6) & ((v8 = 0 & v7 = 0 & ~ (v9 = 0) & leq(v6,
% 11.63/2.38 | v2) = v9 & leq(v6, v1) = 0 & leq(v6, v0) = 0) | (leq(v2, v1)
% 11.63/2.38 | = v5 & leq(v2, v0) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))))
% 11.63/2.38 | (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: int] :
% 11.63/2.38 | (v4 = 0 | ~ (ismeet(v2, v0, v1) = 0) | ~ (leq(v3, v2) = v4) | ~
% 11.76/2.38 | $i(v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6:
% 11.76/2.38 | any] : (leq(v3, v1) = v6 & leq(v3, v0) = v5 & ( ~ (v6 = 0) | ~ (v5
% 11.76/2.38 | = 0))))
% 11.76/2.38 |
% 11.76/2.38 | ALPHA: (ismeetu) implies:
% 11.76/2.38 | (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 11.76/2.38 | (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v0) = 0) | ~ $i(v3) | ~
% 11.76/2.38 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 11.76/2.38 | (leq(v3, v2) = v5 & leq(v3, v1) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 11.76/2.38 | (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ( ~
% 11.76/2.38 | (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v1) = 0) | ~ $i(v3) | ~
% 11.76/2.38 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v4: any] : ? [v5: any] :
% 11.76/2.38 | (leq(v3, v2) = v5 & leq(v3, v0) = v4 & ( ~ (v4 = 0) | v5 = 0)))
% 11.76/2.39 | (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: int] : (v3 = 0 | ~
% 11.76/2.39 | (ismeetu(v2, v0, v1) = v3) | ~ $i(v2) | ~ $i(v1) | ~ $i(v0) | ?
% 11.76/2.39 | [v4: $i] : ? [v5: any] : ? [v6: any] : ? [v7: any] : (leq(v4, v2)
% 11.76/2.39 | = v7 & leq(v4, v1) = v6 & leq(v4, v0) = v5 & $i(v4) & ( ~ (v7 = 0)
% 11.76/2.39 | | ~ (v6 = 0) | ~ (v5 = 0)) & (v7 = 0 | (v6 = 0 & v5 = 0))))
% 11.76/2.39 | (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 11.76/2.39 | ( ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v0) = v4) | ~ $i(v3) | ~
% 11.76/2.39 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 11.76/2.39 | (leq(v3, v2) = v5 & leq(v3, v1) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 =
% 11.76/2.39 | 0))))
% 11.76/2.39 | (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : ! [v4: any] :
% 11.76/2.39 | ( ~ (ismeetu(v2, v0, v1) = 0) | ~ (leq(v3, v1) = v4) | ~ $i(v3) | ~
% 11.76/2.39 | $i(v2) | ~ $i(v1) | ~ $i(v0) | ? [v5: any] : ? [v6: any] :
% 11.76/2.39 | (leq(v3, v2) = v5 & leq(v3, v0) = v6 & ( ~ (v5 = 0) | (v6 = 0 & v4 =
% 11.76/2.39 | 0))))
% 11.76/2.39 |
% 11.76/2.39 | ALPHA: (function-axioms) implies:
% 11.76/2.39 | (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 11.76/2.39 | (addition(v3, v2) = v1) | ~ (addition(v3, v2) = v0))
% 11.76/2.39 | (16) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 11.76/2.39 | : ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) =
% 11.76/2.39 | v0))
% 11.76/2.39 |
% 11.76/2.39 | DELTA: instantiating (goals) with fresh symbols all_18_0, all_18_1, all_18_2,
% 11.76/2.39 | all_18_3, all_18_4 gives:
% 11.76/2.39 | (17) ismeetu(all_18_4, all_18_3, all_18_2) = all_18_0 & ismeet(all_18_4,
% 11.76/2.39 | all_18_3, all_18_2) = all_18_1 & $i(all_18_2) & $i(all_18_3) &
% 11.76/2.39 | $i(all_18_4) & ((all_18_0 = 0 & ~ (all_18_1 = 0)) | (all_18_1 = 0 &
% 11.76/2.39 | ~ (all_18_0 = 0)))
% 11.76/2.39 |
% 11.76/2.39 | ALPHA: (17) implies:
% 11.76/2.39 | (18) $i(all_18_4)
% 11.76/2.39 | (19) $i(all_18_3)
% 11.76/2.39 | (20) $i(all_18_2)
% 11.76/2.39 | (21) ismeet(all_18_4, all_18_3, all_18_2) = all_18_1
% 11.76/2.39 | (22) ismeetu(all_18_4, all_18_3, all_18_2) = all_18_0
% 11.76/2.39 | (23) (all_18_0 = 0 & ~ (all_18_1 = 0)) | (all_18_1 = 0 & ~ (all_18_0 =
% 11.76/2.39 | 0))
% 11.76/2.39 |
% 11.76/2.39 | GROUND_INST: instantiating (8) with all_18_3, all_18_2, all_18_4, all_18_1,
% 11.76/2.39 | simplifying with (18), (19), (20), (21) gives:
% 11.76/2.40 | (24) all_18_1 = 0 | ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3:
% 11.76/2.40 | int] : ? [v4: int] : ? [v5: int] : ($i(v2) & ((v4 = 0 & v3 = 0 &
% 11.76/2.40 | ~ (v5 = 0) & leq(v2, all_18_2) = 0 & leq(v2, all_18_3) = 0 &
% 11.76/2.40 | leq(v2, all_18_4) = v5) | (leq(all_18_4, all_18_2) = v1 &
% 11.76/2.40 | leq(all_18_4, all_18_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))))
% 11.76/2.40 |
% 11.76/2.40 | GROUND_INST: instantiating (12) with all_18_3, all_18_2, all_18_4, all_18_0,
% 11.76/2.40 | simplifying with (18), (19), (20), (22) gives:
% 11.76/2.40 | (25) all_18_0 = 0 | ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3:
% 11.76/2.40 | any] : (leq(v0, all_18_2) = v2 & leq(v0, all_18_3) = v1 & leq(v0,
% 11.76/2.40 | all_18_4) = v3 & $i(v0) & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 =
% 11.76/2.40 | 0)) & (v3 = 0 | (v2 = 0 & v1 = 0)))
% 11.76/2.40 |
% 11.76/2.40 | BETA: splitting (23) gives:
% 11.76/2.40 |
% 11.76/2.40 | Case 1:
% 11.76/2.40 | |
% 11.76/2.40 | | (26) all_18_0 = 0 & ~ (all_18_1 = 0)
% 11.76/2.40 | |
% 11.76/2.40 | | ALPHA: (26) implies:
% 11.76/2.40 | | (27) all_18_0 = 0
% 11.76/2.40 | | (28) ~ (all_18_1 = 0)
% 11.76/2.40 | |
% 11.76/2.40 | | REDUCE: (22), (27) imply:
% 11.76/2.40 | | (29) ismeetu(all_18_4, all_18_3, all_18_2) = 0
% 11.76/2.40 | |
% 11.76/2.40 | | BETA: splitting (24) gives:
% 11.76/2.40 | |
% 11.76/2.40 | | Case 1:
% 11.76/2.40 | | |
% 11.76/2.40 | | | (30) all_18_1 = 0
% 11.76/2.40 | | |
% 11.76/2.40 | | | REDUCE: (28), (30) imply:
% 11.76/2.40 | | | (31) $false
% 11.76/2.40 | | |
% 11.76/2.40 | | | CLOSE: (31) is inconsistent.
% 11.76/2.40 | | |
% 11.76/2.40 | | Case 2:
% 11.76/2.40 | | |
% 11.76/2.40 | | | (32) ? [v0: any] : ? [v1: any] : ? [v2: $i] : ? [v3: int] : ? [v4:
% 11.76/2.40 | | | int] : ? [v5: int] : ($i(v2) & ((v4 = 0 & v3 = 0 & ~ (v5 = 0)
% 11.76/2.40 | | | & leq(v2, all_18_2) = 0 & leq(v2, all_18_3) = 0 & leq(v2,
% 11.76/2.40 | | | all_18_4) = v5) | (leq(all_18_4, all_18_2) = v1 &
% 11.76/2.40 | | | leq(all_18_4, all_18_3) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 11.76/2.40 | | | 0)))))
% 11.76/2.40 | | |
% 11.76/2.40 | | | DELTA: instantiating (32) with fresh symbols all_31_0, all_31_1, all_31_2,
% 11.76/2.40 | | | all_31_3, all_31_4, all_31_5 gives:
% 11.76/2.40 | | | (33) $i(all_31_3) & ((all_31_1 = 0 & all_31_2 = 0 & ~ (all_31_0 = 0) &
% 11.76/2.40 | | | leq(all_31_3, all_18_2) = 0 & leq(all_31_3, all_18_3) = 0 &
% 11.76/2.40 | | | leq(all_31_3, all_18_4) = all_31_0) | (leq(all_18_4, all_18_2)
% 11.76/2.40 | | | = all_31_4 & leq(all_18_4, all_18_3) = all_31_5 & ( ~
% 11.76/2.40 | | | (all_31_4 = 0) | ~ (all_31_5 = 0))))
% 11.76/2.40 | | |
% 11.76/2.40 | | | ALPHA: (33) implies:
% 11.76/2.40 | | | (34) $i(all_31_3)
% 11.76/2.40 | | | (35) (all_31_1 = 0 & all_31_2 = 0 & ~ (all_31_0 = 0) & leq(all_31_3,
% 11.76/2.40 | | | all_18_2) = 0 & leq(all_31_3, all_18_3) = 0 & leq(all_31_3,
% 11.76/2.40 | | | all_18_4) = all_31_0) | (leq(all_18_4, all_18_2) = all_31_4 &
% 11.76/2.40 | | | leq(all_18_4, all_18_3) = all_31_5 & ( ~ (all_31_4 = 0) | ~
% 11.76/2.40 | | | (all_31_5 = 0)))
% 11.76/2.40 | | |
% 11.76/2.40 | | | BETA: splitting (35) gives:
% 11.76/2.40 | | |
% 11.76/2.40 | | | Case 1:
% 11.76/2.40 | | | |
% 11.76/2.40 | | | | (36) all_31_1 = 0 & all_31_2 = 0 & ~ (all_31_0 = 0) & leq(all_31_3,
% 11.76/2.40 | | | | all_18_2) = 0 & leq(all_31_3, all_18_3) = 0 & leq(all_31_3,
% 11.76/2.40 | | | | all_18_4) = all_31_0
% 11.76/2.40 | | | |
% 11.76/2.40 | | | | ALPHA: (36) implies:
% 11.76/2.40 | | | | (37) ~ (all_31_0 = 0)
% 11.76/2.40 | | | | (38) leq(all_31_3, all_18_4) = all_31_0
% 11.76/2.40 | | | | (39) leq(all_31_3, all_18_3) = 0
% 11.76/2.40 | | | | (40) leq(all_31_3, all_18_2) = 0
% 11.76/2.40 | | | |
% 11.76/2.40 | | | | GROUND_INST: instantiating (10) with all_18_3, all_18_2, all_18_4,
% 11.76/2.40 | | | | all_31_3, simplifying with (18), (19), (20), (29), (34),
% 11.76/2.40 | | | | (39) gives:
% 11.76/2.41 | | | | (41) ? [v0: any] : ? [v1: any] : (leq(all_31_3, all_18_2) = v0 &
% 11.76/2.41 | | | | leq(all_31_3, all_18_4) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 11.76/2.41 | | | |
% 11.76/2.41 | | | | GROUND_INST: instantiating (11) with all_18_3, all_18_2, all_18_4,
% 11.76/2.41 | | | | all_31_3, simplifying with (18), (19), (20), (29), (34),
% 11.76/2.41 | | | | (40) gives:
% 11.76/2.41 | | | | (42) ? [v0: any] : ? [v1: any] : (leq(all_31_3, all_18_3) = v0 &
% 11.76/2.41 | | | | leq(all_31_3, all_18_4) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 11.76/2.41 | | | |
% 11.76/2.41 | | | | DELTA: instantiating (41) with fresh symbols all_46_0, all_46_1 gives:
% 11.76/2.41 | | | | (43) leq(all_31_3, all_18_2) = all_46_1 & leq(all_31_3, all_18_4) =
% 11.76/2.41 | | | | all_46_0 & ( ~ (all_46_1 = 0) | all_46_0 = 0)
% 11.76/2.41 | | | |
% 11.76/2.41 | | | | ALPHA: (43) implies:
% 11.76/2.41 | | | | (44) leq(all_31_3, all_18_4) = all_46_0
% 11.76/2.41 | | | | (45) leq(all_31_3, all_18_2) = all_46_1
% 11.76/2.41 | | | | (46) ~ (all_46_1 = 0) | all_46_0 = 0
% 11.76/2.41 | | | |
% 11.76/2.41 | | | | DELTA: instantiating (42) with fresh symbols all_48_0, all_48_1 gives:
% 11.76/2.41 | | | | (47) leq(all_31_3, all_18_3) = all_48_1 & leq(all_31_3, all_18_4) =
% 11.76/2.41 | | | | all_48_0 & ( ~ (all_48_1 = 0) | all_48_0 = 0)
% 11.76/2.41 | | | |
% 11.76/2.41 | | | | ALPHA: (47) implies:
% 11.76/2.41 | | | | (48) leq(all_31_3, all_18_4) = all_48_0
% 11.76/2.41 | | | |
% 11.76/2.41 | | | | GROUND_INST: instantiating (16) with all_31_0, all_48_0, all_18_4,
% 11.76/2.41 | | | | all_31_3, simplifying with (38), (48) gives:
% 11.76/2.41 | | | | (49) all_48_0 = all_31_0
% 11.76/2.41 | | | |
% 11.76/2.41 | | | | GROUND_INST: instantiating (16) with all_46_0, all_48_0, all_18_4,
% 11.76/2.41 | | | | all_31_3, simplifying with (44), (48) gives:
% 11.76/2.41 | | | | (50) all_48_0 = all_46_0
% 11.76/2.41 | | | |
% 11.76/2.41 | | | | GROUND_INST: instantiating (16) with 0, all_46_1, all_18_2, all_31_3,
% 11.76/2.41 | | | | simplifying with (40), (45) gives:
% 11.76/2.41 | | | | (51) all_46_1 = 0
% 11.76/2.41 | | | |
% 11.76/2.41 | | | | COMBINE_EQS: (49), (50) imply:
% 11.76/2.41 | | | | (52) all_46_0 = all_31_0
% 11.76/2.41 | | | |
% 11.76/2.41 | | | | BETA: splitting (46) gives:
% 11.76/2.41 | | | |
% 11.76/2.41 | | | | Case 1:
% 11.76/2.41 | | | | |
% 11.76/2.41 | | | | | (53) ~ (all_46_1 = 0)
% 11.76/2.41 | | | | |
% 11.76/2.41 | | | | | REDUCE: (51), (53) imply:
% 11.76/2.41 | | | | | (54) $false
% 11.76/2.41 | | | | |
% 11.76/2.41 | | | | | CLOSE: (54) is inconsistent.
% 11.76/2.41 | | | | |
% 11.76/2.41 | | | | Case 2:
% 11.76/2.41 | | | | |
% 11.76/2.41 | | | | | (55) all_46_0 = 0
% 11.76/2.41 | | | | |
% 11.76/2.41 | | | | | COMBINE_EQS: (52), (55) imply:
% 11.76/2.41 | | | | | (56) all_31_0 = 0
% 11.76/2.41 | | | | |
% 11.76/2.41 | | | | | SIMP: (56) implies:
% 11.76/2.41 | | | | | (57) all_31_0 = 0
% 11.76/2.41 | | | | |
% 11.76/2.41 | | | | | REDUCE: (37), (57) imply:
% 11.76/2.41 | | | | | (58) $false
% 11.76/2.41 | | | | |
% 11.76/2.41 | | | | | CLOSE: (58) is inconsistent.
% 11.76/2.41 | | | | |
% 11.76/2.41 | | | | End of split
% 11.76/2.41 | | | |
% 11.76/2.41 | | | Case 2:
% 11.76/2.41 | | | |
% 11.76/2.41 | | | | (59) leq(all_18_4, all_18_2) = all_31_4 & leq(all_18_4, all_18_3) =
% 11.76/2.41 | | | | all_31_5 & ( ~ (all_31_4 = 0) | ~ (all_31_5 = 0))
% 11.76/2.41 | | | |
% 11.76/2.41 | | | | ALPHA: (59) implies:
% 11.76/2.41 | | | | (60) leq(all_18_4, all_18_3) = all_31_5
% 11.76/2.41 | | | | (61) leq(all_18_4, all_18_2) = all_31_4
% 11.76/2.41 | | | | (62) ~ (all_31_4 = 0) | ~ (all_31_5 = 0)
% 11.76/2.41 | | | |
% 11.76/2.41 | | | | GROUND_INST: instantiating (13) with all_18_3, all_18_2, all_18_4,
% 11.76/2.41 | | | | all_18_4, all_31_5, simplifying with (18), (19), (20),
% 11.76/2.41 | | | | (29), (60) gives:
% 11.76/2.41 | | | | (63) ? [v0: any] : ? [v1: any] : (leq(all_18_4, all_18_2) = v1 &
% 11.76/2.41 | | | | leq(all_18_4, all_18_4) = v0 & ( ~ (v0 = 0) | (v1 = 0 &
% 11.76/2.41 | | | | all_31_5 = 0)))
% 11.76/2.41 | | | |
% 11.76/2.42 | | | | GROUND_INST: instantiating (14) with all_18_3, all_18_2, all_18_4,
% 11.76/2.42 | | | | all_18_4, all_31_4, simplifying with (18), (19), (20),
% 11.76/2.42 | | | | (29), (61) gives:
% 11.76/2.42 | | | | (64) ? [v0: any] : ? [v1: any] : (leq(all_18_4, all_18_3) = v1 &
% 11.76/2.42 | | | | leq(all_18_4, all_18_4) = v0 & ( ~ (v0 = 0) | (v1 = 0 &
% 11.76/2.42 | | | | all_31_4 = 0)))
% 11.76/2.42 | | | |
% 11.76/2.42 | | | | DELTA: instantiating (64) with fresh symbols all_45_0, all_45_1 gives:
% 11.76/2.42 | | | | (65) leq(all_18_4, all_18_3) = all_45_0 & leq(all_18_4, all_18_4) =
% 11.76/2.42 | | | | all_45_1 & ( ~ (all_45_1 = 0) | (all_45_0 = 0 & all_31_4 = 0))
% 11.76/2.42 | | | |
% 11.76/2.42 | | | | ALPHA: (65) implies:
% 11.76/2.42 | | | | (66) leq(all_18_4, all_18_4) = all_45_1
% 11.76/2.42 | | | | (67) leq(all_18_4, all_18_3) = all_45_0
% 11.76/2.42 | | | | (68) ~ (all_45_1 = 0) | (all_45_0 = 0 & all_31_4 = 0)
% 11.76/2.42 | | | |
% 11.76/2.42 | | | | DELTA: instantiating (63) with fresh symbols all_47_0, all_47_1 gives:
% 11.76/2.42 | | | | (69) leq(all_18_4, all_18_2) = all_47_0 & leq(all_18_4, all_18_4) =
% 11.76/2.42 | | | | all_47_1 & ( ~ (all_47_1 = 0) | (all_47_0 = 0 & all_31_5 = 0))
% 11.76/2.42 | | | |
% 11.76/2.42 | | | | ALPHA: (69) implies:
% 11.76/2.42 | | | | (70) leq(all_18_4, all_18_4) = all_47_1
% 11.76/2.42 | | | |
% 11.76/2.42 | | | | GROUND_INST: instantiating (16) with all_45_1, all_47_1, all_18_4,
% 11.76/2.42 | | | | all_18_4, simplifying with (66), (70) gives:
% 11.76/2.42 | | | | (71) all_47_1 = all_45_1
% 11.76/2.42 | | | |
% 11.76/2.42 | | | | GROUND_INST: instantiating (16) with all_31_5, all_45_0, all_18_3,
% 11.76/2.42 | | | | all_18_4, simplifying with (60), (67) gives:
% 11.76/2.42 | | | | (72) all_45_0 = all_31_5
% 11.76/2.42 | | | |
% 11.76/2.42 | | | | GROUND_INST: instantiating (4) with all_18_4, all_18_4, all_45_1,
% 11.76/2.42 | | | | simplifying with (18), (66) gives:
% 11.76/2.42 | | | | (73) all_45_1 = 0 | ? [v0: any] : ( ~ (v0 = all_18_4) &
% 11.76/2.42 | | | | addition(all_18_4, all_18_4) = v0 & $i(v0))
% 11.76/2.42 | | | |
% 11.76/2.42 | | | | BETA: splitting (62) gives:
% 11.76/2.42 | | | |
% 11.76/2.42 | | | | Case 1:
% 11.76/2.42 | | | | |
% 11.76/2.42 | | | | | (74) ~ (all_31_4 = 0)
% 11.76/2.42 | | | | |
% 11.76/2.42 | | | | | BETA: splitting (68) gives:
% 11.76/2.42 | | | | |
% 11.76/2.42 | | | | | Case 1:
% 11.76/2.42 | | | | | |
% 11.76/2.42 | | | | | | (75) ~ (all_45_1 = 0)
% 11.76/2.42 | | | | | |
% 11.76/2.42 | | | | | | REF_CLOSE: (18), (73), (75), (additive_idempotence) are inconsistent
% 11.76/2.42 | | | | | | by sub-proof #2.
% 11.76/2.42 | | | | | |
% 11.76/2.42 | | | | | Case 2:
% 11.76/2.42 | | | | | |
% 11.94/2.42 | | | | | | (76) all_45_0 = 0 & all_31_4 = 0
% 11.94/2.42 | | | | | |
% 11.94/2.42 | | | | | | ALPHA: (76) implies:
% 11.94/2.42 | | | | | | (77) all_31_4 = 0
% 11.94/2.42 | | | | | |
% 11.94/2.42 | | | | | | REDUCE: (74), (77) imply:
% 11.94/2.42 | | | | | | (78) $false
% 11.94/2.42 | | | | | |
% 11.94/2.42 | | | | | | CLOSE: (78) is inconsistent.
% 11.94/2.42 | | | | | |
% 11.94/2.42 | | | | | End of split
% 11.94/2.42 | | | | |
% 11.94/2.42 | | | | Case 2:
% 11.94/2.42 | | | | |
% 11.94/2.42 | | | | | (79) ~ (all_31_5 = 0)
% 11.94/2.42 | | | | |
% 11.94/2.42 | | | | | BETA: splitting (68) gives:
% 11.94/2.42 | | | | |
% 11.94/2.42 | | | | | Case 1:
% 11.94/2.42 | | | | | |
% 11.94/2.42 | | | | | | (80) ~ (all_45_1 = 0)
% 11.94/2.42 | | | | | |
% 11.94/2.42 | | | | | | REF_CLOSE: (18), (73), (80), (additive_idempotence) are inconsistent
% 11.94/2.42 | | | | | | by sub-proof #2.
% 11.94/2.42 | | | | | |
% 11.94/2.42 | | | | | Case 2:
% 11.94/2.42 | | | | | |
% 11.94/2.42 | | | | | | (81) all_45_0 = 0 & all_31_4 = 0
% 11.94/2.42 | | | | | |
% 11.94/2.42 | | | | | | ALPHA: (81) implies:
% 11.94/2.42 | | | | | | (82) all_45_0 = 0
% 11.94/2.42 | | | | | |
% 11.94/2.42 | | | | | | COMBINE_EQS: (72), (82) imply:
% 11.94/2.42 | | | | | | (83) all_31_5 = 0
% 11.94/2.42 | | | | | |
% 11.94/2.42 | | | | | | SIMP: (83) implies:
% 11.94/2.42 | | | | | | (84) all_31_5 = 0
% 11.94/2.42 | | | | | |
% 11.94/2.42 | | | | | | REDUCE: (79), (84) imply:
% 11.94/2.42 | | | | | | (85) $false
% 11.94/2.42 | | | | | |
% 11.94/2.42 | | | | | | CLOSE: (85) is inconsistent.
% 11.94/2.42 | | | | | |
% 11.94/2.42 | | | | | End of split
% 11.94/2.42 | | | | |
% 11.94/2.42 | | | | End of split
% 11.94/2.42 | | | |
% 11.94/2.42 | | | End of split
% 11.94/2.42 | | |
% 11.94/2.42 | | End of split
% 11.94/2.42 | |
% 11.94/2.42 | Case 2:
% 11.94/2.42 | |
% 11.94/2.42 | | (86) all_18_1 = 0 & ~ (all_18_0 = 0)
% 11.94/2.42 | |
% 11.94/2.42 | | ALPHA: (86) implies:
% 11.94/2.42 | | (87) all_18_1 = 0
% 11.94/2.42 | | (88) ~ (all_18_0 = 0)
% 11.94/2.42 | |
% 11.94/2.42 | | REDUCE: (21), (87) imply:
% 11.94/2.42 | | (89) ismeet(all_18_4, all_18_3, all_18_2) = 0
% 11.94/2.42 | |
% 11.94/2.42 | | BETA: splitting (25) gives:
% 11.94/2.42 | |
% 11.94/2.42 | | Case 1:
% 11.94/2.42 | | |
% 11.94/2.42 | | | (90) all_18_0 = 0
% 11.94/2.42 | | |
% 11.94/2.42 | | | REDUCE: (88), (90) imply:
% 11.94/2.42 | | | (91) $false
% 11.94/2.42 | | |
% 11.94/2.42 | | | CLOSE: (91) is inconsistent.
% 11.94/2.42 | | |
% 11.94/2.42 | | Case 2:
% 11.94/2.42 | | |
% 11.94/2.42 | | | (92) ? [v0: $i] : ? [v1: any] : ? [v2: any] : ? [v3: any] :
% 11.94/2.42 | | | (leq(v0, all_18_2) = v2 & leq(v0, all_18_3) = v1 & leq(v0,
% 11.94/2.42 | | | all_18_4) = v3 & $i(v0) & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1
% 11.94/2.42 | | | = 0)) & (v3 = 0 | (v2 = 0 & v1 = 0)))
% 11.94/2.42 | | |
% 11.94/2.42 | | | DELTA: instantiating (92) with fresh symbols all_31_0, all_31_1, all_31_2,
% 11.94/2.42 | | | all_31_3 gives:
% 11.94/2.43 | | | (93) leq(all_31_3, all_18_2) = all_31_1 & leq(all_31_3, all_18_3) =
% 11.94/2.43 | | | all_31_2 & leq(all_31_3, all_18_4) = all_31_0 & $i(all_31_3) & ( ~
% 11.94/2.43 | | | (all_31_0 = 0) | ~ (all_31_1 = 0) | ~ (all_31_2 = 0)) &
% 11.94/2.43 | | | (all_31_0 = 0 | (all_31_1 = 0 & all_31_2 = 0))
% 11.94/2.43 | | |
% 11.94/2.43 | | | ALPHA: (93) implies:
% 11.94/2.43 | | | (94) $i(all_31_3)
% 11.94/2.43 | | | (95) leq(all_31_3, all_18_4) = all_31_0
% 11.94/2.43 | | | (96) leq(all_31_3, all_18_3) = all_31_2
% 11.94/2.43 | | | (97) leq(all_31_3, all_18_2) = all_31_1
% 11.94/2.43 | | | (98) all_31_0 = 0 | (all_31_1 = 0 & all_31_2 = 0)
% 11.94/2.43 | | | (99) ~ (all_31_0 = 0) | ~ (all_31_1 = 0) | ~ (all_31_2 = 0)
% 11.94/2.43 | | |
% 11.94/2.43 | | | GROUND_INST: instantiating (4) with all_31_3, all_18_3, all_31_2,
% 11.94/2.43 | | | simplifying with (19), (94), (96) gives:
% 11.94/2.43 | | | (100) all_31_2 = 0 | ? [v0: any] : ( ~ (v0 = all_18_3) &
% 11.94/2.43 | | | addition(all_31_3, all_18_3) = v0 & $i(v0))
% 11.94/2.43 | | |
% 11.94/2.43 | | | GROUND_INST: instantiating (4) with all_31_3, all_18_2, all_31_1,
% 11.94/2.43 | | | simplifying with (20), (94), (97) gives:
% 11.94/2.43 | | | (101) all_31_1 = 0 | ? [v0: any] : ( ~ (v0 = all_18_2) &
% 11.94/2.43 | | | addition(all_31_3, all_18_2) = v0 & $i(v0))
% 11.94/2.43 | | |
% 11.94/2.43 | | | GROUND_INST: instantiating (9) with all_18_3, all_18_2, all_18_4,
% 11.94/2.43 | | | all_31_3, all_31_0, simplifying with (18), (19), (20), (89),
% 11.94/2.43 | | | (94), (95) gives:
% 11.94/2.43 | | | (102) all_31_0 = 0 | ? [v0: any] : ? [v1: any] : (leq(all_31_3,
% 11.94/2.43 | | | all_18_2) = v1 & leq(all_31_3, all_18_3) = v0 & ( ~ (v1 = 0)
% 11.94/2.43 | | | | ~ (v0 = 0)))
% 11.94/2.43 | | |
% 11.94/2.43 | | | GROUND_INST: instantiating (5) with all_18_3, all_18_2, all_18_4,
% 11.94/2.43 | | | simplifying with (18), (19), (20), (89) gives:
% 11.94/2.43 | | | (103) leq(all_18_4, all_18_2) = 0 & leq(all_18_4, all_18_3) = 0
% 11.94/2.43 | | |
% 11.94/2.43 | | | ALPHA: (103) implies:
% 11.94/2.43 | | | (104) leq(all_18_4, all_18_3) = 0
% 11.94/2.43 | | | (105) leq(all_18_4, all_18_2) = 0
% 11.94/2.43 | | |
% 11.94/2.43 | | | GROUND_INST: instantiating (6) with all_18_3, all_18_2, all_18_4,
% 11.94/2.43 | | | all_18_4, simplifying with (18), (19), (20), (89), (104)
% 11.94/2.43 | | | gives:
% 11.94/2.43 | | | (106) ? [v0: any] : ? [v1: any] : (leq(all_18_4, all_18_2) = v0 &
% 11.94/2.43 | | | leq(all_18_4, all_18_4) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 11.94/2.43 | | |
% 11.94/2.43 | | | GROUND_INST: instantiating (3) with all_18_4, all_18_3, simplifying with
% 11.94/2.43 | | | (18), (19), (104) gives:
% 11.94/2.43 | | | (107) addition(all_18_4, all_18_3) = all_18_3
% 11.94/2.43 | | |
% 11.94/2.43 | | | GROUND_INST: instantiating (7) with all_18_3, all_18_2, all_18_4,
% 11.94/2.43 | | | all_18_4, simplifying with (18), (19), (20), (89), (105)
% 11.94/2.43 | | | gives:
% 11.94/2.43 | | | (108) ? [v0: any] : ? [v1: any] : (leq(all_18_4, all_18_3) = v0 &
% 11.94/2.43 | | | leq(all_18_4, all_18_4) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 11.94/2.43 | | |
% 11.94/2.43 | | | GROUND_INST: instantiating (3) with all_18_4, all_18_2, simplifying with
% 11.94/2.43 | | | (18), (20), (105) gives:
% 11.94/2.43 | | | (109) addition(all_18_4, all_18_2) = all_18_2
% 11.94/2.43 | | |
% 11.94/2.43 | | | DELTA: instantiating (108) with fresh symbols all_45_0, all_45_1 gives:
% 11.94/2.43 | | | (110) leq(all_18_4, all_18_3) = all_45_1 & leq(all_18_4, all_18_4) =
% 11.94/2.43 | | | all_45_0 & ( ~ (all_45_1 = 0) | all_45_0 = 0)
% 11.94/2.43 | | |
% 11.94/2.43 | | | ALPHA: (110) implies:
% 11.94/2.43 | | | (111) leq(all_18_4, all_18_4) = all_45_0
% 11.94/2.43 | | |
% 11.94/2.43 | | | DELTA: instantiating (106) with fresh symbols all_47_0, all_47_1 gives:
% 11.94/2.43 | | | (112) leq(all_18_4, all_18_2) = all_47_1 & leq(all_18_4, all_18_4) =
% 11.94/2.43 | | | all_47_0 & ( ~ (all_47_1 = 0) | all_47_0 = 0)
% 11.94/2.43 | | |
% 11.94/2.43 | | | ALPHA: (112) implies:
% 11.94/2.43 | | | (113) leq(all_18_4, all_18_4) = all_47_0
% 11.94/2.43 | | | (114) leq(all_18_4, all_18_2) = all_47_1
% 11.94/2.43 | | | (115) ~ (all_47_1 = 0) | all_47_0 = 0
% 11.94/2.43 | | |
% 11.94/2.43 | | | GROUND_INST: instantiating (16) with all_45_0, all_47_0, all_18_4,
% 11.94/2.43 | | | all_18_4, simplifying with (111), (113) gives:
% 11.94/2.43 | | | (116) all_47_0 = all_45_0
% 11.94/2.43 | | |
% 11.94/2.43 | | | GROUND_INST: instantiating (16) with 0, all_47_1, all_18_2, all_18_4,
% 11.94/2.43 | | | simplifying with (105), (114) gives:
% 11.94/2.43 | | | (117) all_47_1 = 0
% 11.94/2.43 | | |
% 11.94/2.43 | | | BETA: splitting (115) gives:
% 11.94/2.43 | | |
% 11.94/2.43 | | | Case 1:
% 11.94/2.43 | | | |
% 11.94/2.43 | | | | (118) ~ (all_47_1 = 0)
% 11.94/2.43 | | | |
% 11.94/2.43 | | | | REDUCE: (117), (118) imply:
% 11.94/2.43 | | | | (119) $false
% 11.94/2.43 | | | |
% 11.94/2.43 | | | | CLOSE: (119) is inconsistent.
% 11.94/2.43 | | | |
% 11.94/2.43 | | | Case 2:
% 11.94/2.43 | | | |
% 11.94/2.43 | | | | (120) all_47_0 = 0
% 11.94/2.43 | | | |
% 11.94/2.43 | | | | COMBINE_EQS: (116), (120) imply:
% 11.94/2.43 | | | | (121) all_45_0 = 0
% 11.94/2.43 | | | |
% 11.94/2.43 | | | | REDUCE: (111), (121) imply:
% 11.94/2.43 | | | | (122) leq(all_18_4, all_18_4) = 0
% 11.94/2.43 | | | |
% 12.01/2.43 | | | | GROUND_INST: instantiating (1) with all_18_3, all_18_4, all_18_4,
% 12.01/2.43 | | | | all_18_3, all_18_3, simplifying with (18), (19), (107)
% 12.01/2.44 | | | | gives:
% 12.01/2.44 | | | | (123) ? [v0: $i] : (addition(v0, all_18_3) = all_18_3 &
% 12.01/2.44 | | | | addition(all_18_4, all_18_4) = v0 & $i(v0))
% 12.01/2.44 | | | |
% 12.01/2.44 | | | | GROUND_INST: instantiating (1) with all_18_2, all_18_4, all_18_4,
% 12.01/2.44 | | | | all_18_2, all_18_2, simplifying with (18), (20), (109)
% 12.01/2.44 | | | | gives:
% 12.01/2.44 | | | | (124) ? [v0: $i] : (addition(v0, all_18_2) = all_18_2 &
% 12.01/2.44 | | | | addition(all_18_4, all_18_4) = v0 & $i(v0))
% 12.01/2.44 | | | |
% 12.01/2.44 | | | | GROUND_INST: instantiating (3) with all_18_4, all_18_4, simplifying with
% 12.01/2.44 | | | | (18), (122) gives:
% 12.01/2.44 | | | | (125) addition(all_18_4, all_18_4) = all_18_4
% 12.01/2.44 | | | |
% 12.01/2.44 | | | | DELTA: instantiating (124) with fresh symbol all_63_0 gives:
% 12.01/2.44 | | | | (126) addition(all_63_0, all_18_2) = all_18_2 & addition(all_18_4,
% 12.01/2.44 | | | | all_18_4) = all_63_0 & $i(all_63_0)
% 12.01/2.44 | | | |
% 12.01/2.44 | | | | ALPHA: (126) implies:
% 12.01/2.44 | | | | (127) $i(all_63_0)
% 12.01/2.44 | | | | (128) addition(all_18_4, all_18_4) = all_63_0
% 12.01/2.44 | | | | (129) addition(all_63_0, all_18_2) = all_18_2
% 12.01/2.44 | | | |
% 12.01/2.44 | | | | DELTA: instantiating (123) with fresh symbol all_65_0 gives:
% 12.01/2.44 | | | | (130) addition(all_65_0, all_18_3) = all_18_3 & addition(all_18_4,
% 12.01/2.44 | | | | all_18_4) = all_65_0 & $i(all_65_0)
% 12.01/2.44 | | | |
% 12.01/2.44 | | | | ALPHA: (130) implies:
% 12.01/2.44 | | | | (131) addition(all_18_4, all_18_4) = all_65_0
% 12.01/2.44 | | | | (132) addition(all_65_0, all_18_3) = all_18_3
% 12.01/2.44 | | | |
% 12.01/2.44 | | | | GROUND_INST: instantiating (15) with all_63_0, all_65_0, all_18_4,
% 12.01/2.44 | | | | all_18_4, simplifying with (128), (131) gives:
% 12.01/2.44 | | | | (133) all_65_0 = all_63_0
% 12.01/2.44 | | | |
% 12.01/2.44 | | | | GROUND_INST: instantiating (15) with all_18_4, all_65_0, all_18_4,
% 12.01/2.44 | | | | all_18_4, simplifying with (125), (131) gives:
% 12.01/2.44 | | | | (134) all_65_0 = all_18_4
% 12.01/2.44 | | | |
% 12.01/2.44 | | | | COMBINE_EQS: (133), (134) imply:
% 12.01/2.44 | | | | (135) all_63_0 = all_18_4
% 12.01/2.44 | | | |
% 12.01/2.44 | | | | SIMP: (135) implies:
% 12.01/2.44 | | | | (136) all_63_0 = all_18_4
% 12.01/2.44 | | | |
% 12.01/2.44 | | | | BETA: splitting (98) gives:
% 12.01/2.44 | | | |
% 12.01/2.44 | | | | Case 1:
% 12.01/2.44 | | | | |
% 12.01/2.44 | | | | | (137) all_31_0 = 0
% 12.01/2.44 | | | | |
% 12.01/2.44 | | | | | REDUCE: (95), (137) imply:
% 12.01/2.44 | | | | | (138) leq(all_31_3, all_18_4) = 0
% 12.01/2.44 | | | | |
% 12.01/2.44 | | | | | GROUND_INST: instantiating (3) with all_31_3, all_18_4, simplifying
% 12.01/2.44 | | | | | with (18), (94), (138) gives:
% 12.01/2.44 | | | | | (139) addition(all_31_3, all_18_4) = all_18_4
% 12.01/2.44 | | | | |
% 12.01/2.44 | | | | | GROUND_INST: instantiating (2) with all_18_2, all_18_4, all_31_3,
% 12.01/2.44 | | | | | all_18_4, all_18_2, simplifying with (18), (20), (94),
% 12.01/2.44 | | | | | (109), (139) gives:
% 12.01/2.44 | | | | | (140) ? [v0: $i] : (addition(all_31_3, v0) = all_18_2 &
% 12.01/2.44 | | | | | addition(all_18_4, all_18_2) = v0 & $i(v0))
% 12.01/2.44 | | | | |
% 12.01/2.44 | | | | | GROUND_INST: instantiating (2) with all_18_3, all_18_4, all_31_3,
% 12.01/2.44 | | | | | all_18_4, all_18_3, simplifying with (18), (19), (94),
% 12.01/2.44 | | | | | (107), (139) gives:
% 12.01/2.44 | | | | | (141) ? [v0: $i] : (addition(all_31_3, v0) = all_18_3 &
% 12.01/2.44 | | | | | addition(all_18_4, all_18_3) = v0 & $i(v0))
% 12.01/2.44 | | | | |
% 12.01/2.44 | | | | | DELTA: instantiating (141) with fresh symbol all_94_0 gives:
% 12.01/2.44 | | | | | (142) addition(all_31_3, all_94_0) = all_18_3 & addition(all_18_4,
% 12.01/2.44 | | | | | all_18_3) = all_94_0 & $i(all_94_0)
% 12.01/2.44 | | | | |
% 12.01/2.44 | | | | | ALPHA: (142) implies:
% 12.01/2.44 | | | | | (143) addition(all_18_4, all_18_3) = all_94_0
% 12.01/2.44 | | | | | (144) addition(all_31_3, all_94_0) = all_18_3
% 12.01/2.44 | | | | |
% 12.01/2.44 | | | | | DELTA: instantiating (140) with fresh symbol all_96_0 gives:
% 12.01/2.44 | | | | | (145) addition(all_31_3, all_96_0) = all_18_2 & addition(all_18_4,
% 12.01/2.44 | | | | | all_18_2) = all_96_0 & $i(all_96_0)
% 12.01/2.44 | | | | |
% 12.01/2.44 | | | | | ALPHA: (145) implies:
% 12.01/2.44 | | | | | (146) addition(all_18_4, all_18_2) = all_96_0
% 12.01/2.44 | | | | | (147) addition(all_31_3, all_96_0) = all_18_2
% 12.01/2.44 | | | | |
% 12.01/2.44 | | | | | GROUND_INST: instantiating (15) with all_18_3, all_94_0, all_18_3,
% 12.01/2.44 | | | | | all_18_4, simplifying with (107), (143) gives:
% 12.01/2.44 | | | | | (148) all_94_0 = all_18_3
% 12.01/2.44 | | | | |
% 12.01/2.44 | | | | | GROUND_INST: instantiating (15) with all_18_2, all_96_0, all_18_2,
% 12.01/2.44 | | | | | all_18_4, simplifying with (109), (146) gives:
% 12.01/2.44 | | | | | (149) all_96_0 = all_18_2
% 12.01/2.44 | | | | |
% 12.01/2.44 | | | | | REDUCE: (147), (149) imply:
% 12.01/2.44 | | | | | (150) addition(all_31_3, all_18_2) = all_18_2
% 12.01/2.44 | | | | |
% 12.01/2.44 | | | | | REDUCE: (144), (148) imply:
% 12.01/2.44 | | | | | (151) addition(all_31_3, all_18_3) = all_18_3
% 12.01/2.44 | | | | |
% 12.01/2.44 | | | | | BETA: splitting (101) gives:
% 12.01/2.44 | | | | |
% 12.01/2.44 | | | | | Case 1:
% 12.01/2.44 | | | | | |
% 12.01/2.44 | | | | | | (152) all_31_1 = 0
% 12.01/2.44 | | | | | |
% 12.01/2.44 | | | | | | REDUCE: (97), (152) imply:
% 12.01/2.44 | | | | | | (153) leq(all_31_3, all_18_2) = 0
% 12.01/2.44 | | | | | |
% 12.01/2.44 | | | | | | BETA: splitting (100) gives:
% 12.01/2.44 | | | | | |
% 12.01/2.44 | | | | | | Case 1:
% 12.01/2.44 | | | | | | |
% 12.01/2.44 | | | | | | | (154) all_31_2 = 0
% 12.01/2.44 | | | | | | |
% 12.01/2.44 | | | | | | | REDUCE: (96), (154) imply:
% 12.01/2.44 | | | | | | | (155) leq(all_31_3, all_18_3) = 0
% 12.01/2.44 | | | | | | |
% 12.01/2.44 | | | | | | | BETA: splitting (99) gives:
% 12.01/2.44 | | | | | | |
% 12.01/2.44 | | | | | | | Case 1:
% 12.01/2.44 | | | | | | | |
% 12.01/2.44 | | | | | | | | (156) ~ (all_31_0 = 0)
% 12.01/2.44 | | | | | | | |
% 12.01/2.44 | | | | | | | | REF_CLOSE: (16), (102), (153), (155), (156) are inconsistent by
% 12.01/2.44 | | | | | | | | sub-proof #1.
% 12.01/2.44 | | | | | | | |
% 12.01/2.44 | | | | | | | Case 2:
% 12.01/2.44 | | | | | | | |
% 12.01/2.44 | | | | | | | | (157) ~ (all_31_1 = 0) | ~ (all_31_2 = 0)
% 12.01/2.44 | | | | | | | |
% 12.01/2.44 | | | | | | | | BETA: splitting (157) gives:
% 12.01/2.44 | | | | | | | |
% 12.01/2.44 | | | | | | | | Case 1:
% 12.01/2.44 | | | | | | | | |
% 12.01/2.44 | | | | | | | | | (158) ~ (all_31_1 = 0)
% 12.01/2.44 | | | | | | | | |
% 12.01/2.44 | | | | | | | | | REDUCE: (152), (158) imply:
% 12.01/2.44 | | | | | | | | | (159) $false
% 12.01/2.44 | | | | | | | | |
% 12.01/2.44 | | | | | | | | | CLOSE: (159) is inconsistent.
% 12.01/2.44 | | | | | | | | |
% 12.01/2.44 | | | | | | | | Case 2:
% 12.01/2.44 | | | | | | | | |
% 12.01/2.44 | | | | | | | | | (160) ~ (all_31_2 = 0)
% 12.01/2.44 | | | | | | | | |
% 12.01/2.45 | | | | | | | | | REDUCE: (154), (160) imply:
% 12.01/2.45 | | | | | | | | | (161) $false
% 12.01/2.45 | | | | | | | | |
% 12.01/2.45 | | | | | | | | | CLOSE: (161) is inconsistent.
% 12.01/2.45 | | | | | | | | |
% 12.01/2.45 | | | | | | | | End of split
% 12.01/2.45 | | | | | | | |
% 12.01/2.45 | | | | | | | End of split
% 12.01/2.45 | | | | | | |
% 12.01/2.45 | | | | | | Case 2:
% 12.01/2.45 | | | | | | |
% 12.01/2.45 | | | | | | | (162) ? [v0: any] : ( ~ (v0 = all_18_3) & addition(all_31_3,
% 12.01/2.45 | | | | | | | all_18_3) = v0 & $i(v0))
% 12.01/2.45 | | | | | | |
% 12.01/2.45 | | | | | | | DELTA: instantiating (162) with fresh symbol all_114_0 gives:
% 12.01/2.45 | | | | | | | (163) ~ (all_114_0 = all_18_3) & addition(all_31_3, all_18_3)
% 12.01/2.45 | | | | | | | = all_114_0 & $i(all_114_0)
% 12.01/2.45 | | | | | | |
% 12.01/2.45 | | | | | | | ALPHA: (163) implies:
% 12.01/2.45 | | | | | | | (164) ~ (all_114_0 = all_18_3)
% 12.01/2.45 | | | | | | | (165) addition(all_31_3, all_18_3) = all_114_0
% 12.01/2.45 | | | | | | |
% 12.01/2.45 | | | | | | | GROUND_INST: instantiating (15) with all_18_3, all_114_0,
% 12.01/2.45 | | | | | | | all_18_3, all_31_3, simplifying with (151), (165)
% 12.01/2.45 | | | | | | | gives:
% 12.01/2.45 | | | | | | | (166) all_114_0 = all_18_3
% 12.01/2.45 | | | | | | |
% 12.01/2.45 | | | | | | | REDUCE: (164), (166) imply:
% 12.01/2.45 | | | | | | | (167) $false
% 12.01/2.45 | | | | | | |
% 12.01/2.45 | | | | | | | CLOSE: (167) is inconsistent.
% 12.01/2.45 | | | | | | |
% 12.01/2.45 | | | | | | End of split
% 12.01/2.45 | | | | | |
% 12.01/2.45 | | | | | Case 2:
% 12.01/2.45 | | | | | |
% 12.01/2.45 | | | | | | (168) ? [v0: any] : ( ~ (v0 = all_18_2) & addition(all_31_3,
% 12.01/2.45 | | | | | | all_18_2) = v0 & $i(v0))
% 12.01/2.45 | | | | | |
% 12.01/2.45 | | | | | | DELTA: instantiating (168) with fresh symbol all_110_0 gives:
% 12.01/2.45 | | | | | | (169) ~ (all_110_0 = all_18_2) & addition(all_31_3, all_18_2) =
% 12.01/2.45 | | | | | | all_110_0 & $i(all_110_0)
% 12.01/2.45 | | | | | |
% 12.01/2.45 | | | | | | ALPHA: (169) implies:
% 12.01/2.45 | | | | | | (170) ~ (all_110_0 = all_18_2)
% 12.01/2.45 | | | | | | (171) addition(all_31_3, all_18_2) = all_110_0
% 12.01/2.45 | | | | | |
% 12.01/2.45 | | | | | | GROUND_INST: instantiating (15) with all_18_2, all_110_0, all_18_2,
% 12.01/2.45 | | | | | | all_31_3, simplifying with (150), (171) gives:
% 12.01/2.45 | | | | | | (172) all_110_0 = all_18_2
% 12.01/2.45 | | | | | |
% 12.01/2.45 | | | | | | REDUCE: (170), (172) imply:
% 12.01/2.45 | | | | | | (173) $false
% 12.01/2.45 | | | | | |
% 12.01/2.45 | | | | | | CLOSE: (173) is inconsistent.
% 12.01/2.45 | | | | | |
% 12.01/2.45 | | | | | End of split
% 12.01/2.45 | | | | |
% 12.01/2.45 | | | | Case 2:
% 12.01/2.45 | | | | |
% 12.01/2.45 | | | | | (174) ~ (all_31_0 = 0)
% 12.01/2.45 | | | | | (175) all_31_1 = 0 & all_31_2 = 0
% 12.01/2.45 | | | | |
% 12.01/2.45 | | | | | ALPHA: (175) implies:
% 12.01/2.45 | | | | | (176) all_31_2 = 0
% 12.01/2.45 | | | | | (177) all_31_1 = 0
% 12.01/2.45 | | | | |
% 12.01/2.45 | | | | | REDUCE: (97), (177) imply:
% 12.01/2.45 | | | | | (178) leq(all_31_3, all_18_2) = 0
% 12.01/2.45 | | | | |
% 12.01/2.45 | | | | | REDUCE: (96), (176) imply:
% 12.01/2.45 | | | | | (179) leq(all_31_3, all_18_3) = 0
% 12.01/2.45 | | | | |
% 12.01/2.45 | | | | | REF_CLOSE: (16), (102), (174), (178), (179) are inconsistent by
% 12.01/2.45 | | | | | sub-proof #1.
% 12.01/2.45 | | | | |
% 12.01/2.45 | | | | End of split
% 12.01/2.45 | | | |
% 12.01/2.45 | | | End of split
% 12.01/2.45 | | |
% 12.01/2.45 | | End of split
% 12.01/2.45 | |
% 12.01/2.45 | End of split
% 12.01/2.45 |
% 12.01/2.45 End of proof
% 12.01/2.45
% 12.01/2.45 Sub-proof #1 shows that the following formulas are inconsistent:
% 12.01/2.45 ----------------------------------------------------------------
% 12.01/2.45 (1) leq(all_31_3, all_18_2) = 0
% 12.01/2.45 (2) all_31_0 = 0 | ? [v0: any] : ? [v1: any] : (leq(all_31_3, all_18_2) =
% 12.01/2.45 v1 & leq(all_31_3, all_18_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 12.01/2.45 (3) leq(all_31_3, all_18_3) = 0
% 12.01/2.45 (4) ~ (all_31_0 = 0)
% 12.01/2.45 (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.01/2.45 ! [v3: $i] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 12.01/2.45
% 12.01/2.45 Begin of proof
% 12.01/2.45 |
% 12.01/2.45 | BETA: splitting (2) gives:
% 12.01/2.45 |
% 12.01/2.45 | Case 1:
% 12.01/2.45 | |
% 12.01/2.45 | | (6) all_31_0 = 0
% 12.01/2.45 | |
% 12.01/2.45 | | REDUCE: (4), (6) imply:
% 12.01/2.45 | | (7) $false
% 12.01/2.45 | |
% 12.01/2.45 | | CLOSE: (7) is inconsistent.
% 12.01/2.45 | |
% 12.01/2.45 | Case 2:
% 12.01/2.45 | |
% 12.01/2.45 | | (8) ? [v0: any] : ? [v1: any] : (leq(all_31_3, all_18_2) = v1 &
% 12.01/2.45 | | leq(all_31_3, all_18_3) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 12.01/2.45 | |
% 12.01/2.45 | | DELTA: instantiating (8) with fresh symbols all_82_0, all_82_1 gives:
% 12.01/2.45 | | (9) leq(all_31_3, all_18_2) = all_82_0 & leq(all_31_3, all_18_3) =
% 12.01/2.45 | | all_82_1 & ( ~ (all_82_0 = 0) | ~ (all_82_1 = 0))
% 12.01/2.45 | |
% 12.01/2.45 | | ALPHA: (9) implies:
% 12.01/2.45 | | (10) leq(all_31_3, all_18_3) = all_82_1
% 12.01/2.45 | | (11) leq(all_31_3, all_18_2) = all_82_0
% 12.01/2.45 | | (12) ~ (all_82_0 = 0) | ~ (all_82_1 = 0)
% 12.01/2.45 | |
% 12.01/2.45 | | GROUND_INST: instantiating (5) with 0, all_82_1, all_18_3, all_31_3,
% 12.01/2.45 | | simplifying with (3), (10) gives:
% 12.01/2.45 | | (13) all_82_1 = 0
% 12.01/2.45 | |
% 12.01/2.45 | | GROUND_INST: instantiating (5) with 0, all_82_0, all_18_2, all_31_3,
% 12.01/2.45 | | simplifying with (1), (11) gives:
% 12.01/2.45 | | (14) all_82_0 = 0
% 12.01/2.45 | |
% 12.01/2.45 | | BETA: splitting (12) gives:
% 12.01/2.45 | |
% 12.01/2.45 | | Case 1:
% 12.01/2.45 | | |
% 12.01/2.45 | | | (15) ~ (all_82_0 = 0)
% 12.01/2.45 | | |
% 12.01/2.45 | | | REDUCE: (14), (15) imply:
% 12.01/2.45 | | | (16) $false
% 12.01/2.45 | | |
% 12.01/2.45 | | | CLOSE: (16) is inconsistent.
% 12.01/2.45 | | |
% 12.01/2.45 | | Case 2:
% 12.01/2.45 | | |
% 12.01/2.45 | | | (17) ~ (all_82_1 = 0)
% 12.01/2.45 | | |
% 12.01/2.45 | | | REDUCE: (13), (17) imply:
% 12.01/2.45 | | | (18) $false
% 12.01/2.45 | | |
% 12.01/2.45 | | | CLOSE: (18) is inconsistent.
% 12.01/2.45 | | |
% 12.01/2.45 | | End of split
% 12.01/2.45 | |
% 12.01/2.45 | End of split
% 12.01/2.45 |
% 12.01/2.45 End of proof
% 12.01/2.45
% 12.01/2.45 Sub-proof #2 shows that the following formulas are inconsistent:
% 12.01/2.45 ----------------------------------------------------------------
% 12.01/2.45 (1) all_45_1 = 0 | ? [v0: any] : ( ~ (v0 = all_18_4) & addition(all_18_4,
% 12.01/2.45 all_18_4) = v0 & $i(v0))
% 12.01/2.45 (2) ~ (all_45_1 = 0)
% 12.01/2.46 (3) ! [v0: $i] : ! [v1: $i] : (v1 = v0 | ~ (addition(v0, v0) = v1) | ~
% 12.01/2.46 $i(v0))
% 12.01/2.46 (4) $i(all_18_4)
% 12.01/2.46
% 12.01/2.46 Begin of proof
% 12.01/2.46 |
% 12.01/2.46 | BETA: splitting (1) gives:
% 12.01/2.46 |
% 12.01/2.46 | Case 1:
% 12.01/2.46 | |
% 12.01/2.46 | | (5) all_45_1 = 0
% 12.01/2.46 | |
% 12.01/2.46 | | REDUCE: (2), (5) imply:
% 12.01/2.46 | | (6) $false
% 12.01/2.46 | |
% 12.01/2.46 | | CLOSE: (6) is inconsistent.
% 12.01/2.46 | |
% 12.01/2.46 | Case 2:
% 12.01/2.46 | |
% 12.01/2.46 | | (7) ? [v0: any] : ( ~ (v0 = all_18_4) & addition(all_18_4, all_18_4) =
% 12.01/2.46 | | v0 & $i(v0))
% 12.01/2.46 | |
% 12.01/2.46 | | DELTA: instantiating (7) with fresh symbol all_73_0 gives:
% 12.01/2.46 | | (8) ~ (all_73_0 = all_18_4) & addition(all_18_4, all_18_4) = all_73_0 &
% 12.01/2.46 | | $i(all_73_0)
% 12.01/2.46 | |
% 12.01/2.46 | | ALPHA: (8) implies:
% 12.01/2.46 | | (9) ~ (all_73_0 = all_18_4)
% 12.01/2.46 | | (10) addition(all_18_4, all_18_4) = all_73_0
% 12.01/2.46 | |
% 12.01/2.46 | | GROUND_INST: instantiating (3) with all_18_4, all_73_0, simplifying with
% 12.01/2.46 | | (4), (10) gives:
% 12.01/2.46 | | (11) all_73_0 = all_18_4
% 12.01/2.46 | |
% 12.01/2.46 | | REDUCE: (9), (11) imply:
% 12.01/2.46 | | (12) $false
% 12.01/2.46 | |
% 12.01/2.46 | | CLOSE: (12) is inconsistent.
% 12.01/2.46 | |
% 12.01/2.46 | End of split
% 12.01/2.46 |
% 12.01/2.46 End of proof
% 12.01/2.46 % SZS output end Proof for theBenchmark
% 12.01/2.46
% 12.01/2.46 1855ms
%------------------------------------------------------------------------------