TSTP Solution File: SWC389+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC389+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n016.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 20:51:11 EDT 2023
% Result : Theorem 33.46s 5.19s
% Output : Proof 118.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWC389+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 17:56:15 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.66/0.63 ________ _____
% 0.66/0.63 ___ __ \_________(_)________________________________
% 0.66/0.63 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.66/0.63 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.66/0.63 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.66/0.63
% 0.66/0.63 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.66/0.63 (2023-06-19)
% 0.66/0.63
% 0.66/0.63 (c) Philipp Rümmer, 2009-2023
% 0.66/0.63 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.66/0.63 Amanda Stjerna.
% 0.66/0.63 Free software under BSD-3-Clause.
% 0.66/0.63
% 0.66/0.63 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.66/0.63
% 0.66/0.63 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.68/0.64 Running up to 7 provers in parallel.
% 0.68/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.68/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.68/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.68/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.68/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.68/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.68/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.06/1.44 Prover 4: Preprocessing ...
% 5.06/1.44 Prover 1: Preprocessing ...
% 5.52/1.48 Prover 3: Preprocessing ...
% 5.52/1.48 Prover 0: Preprocessing ...
% 5.52/1.48 Prover 5: Preprocessing ...
% 5.52/1.48 Prover 6: Preprocessing ...
% 5.52/1.48 Prover 2: Preprocessing ...
% 14.69/2.72 Prover 2: Proving ...
% 15.58/2.82 Prover 5: Constructing countermodel ...
% 15.66/2.84 Prover 6: Proving ...
% 15.66/2.88 Prover 3: Constructing countermodel ...
% 15.66/2.89 Prover 1: Constructing countermodel ...
% 21.03/3.54 Prover 4: Constructing countermodel ...
% 21.72/3.68 Prover 0: Proving ...
% 33.46/5.19 Prover 3: proved (4536ms)
% 33.46/5.19
% 33.46/5.19 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.46/5.19
% 33.93/5.20 Prover 2: stopped
% 33.93/5.20 Prover 6: stopped
% 33.93/5.21 Prover 5: stopped
% 33.93/5.22 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 33.93/5.22 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 33.93/5.22 Prover 0: stopped
% 33.93/5.22 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 33.93/5.22 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 33.93/5.22 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 36.09/5.49 Prover 13: Preprocessing ...
% 36.09/5.51 Prover 7: Preprocessing ...
% 36.09/5.52 Prover 11: Preprocessing ...
% 36.09/5.52 Prover 8: Preprocessing ...
% 36.09/5.54 Prover 10: Preprocessing ...
% 37.32/5.68 Prover 7: Constructing countermodel ...
% 37.94/5.76 Prover 10: Constructing countermodel ...
% 38.48/5.85 Prover 8: Warning: ignoring some quantifiers
% 38.48/5.85 Prover 13: Constructing countermodel ...
% 38.48/5.86 Prover 8: Constructing countermodel ...
% 44.19/6.55 Prover 11: Constructing countermodel ...
% 72.84/10.23 Prover 13: stopped
% 72.84/10.24 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 73.48/10.37 Prover 16: Preprocessing ...
% 75.41/10.53 Prover 16: Constructing countermodel ...
% 115.10/15.77 Prover 16: stopped
% 115.10/15.77 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 116.19/15.93 Prover 19: Preprocessing ...
% 116.19/15.95 Prover 1: Found proof (size 210)
% 116.19/15.95 Prover 1: proved (15306ms)
% 116.19/15.95 Prover 8: stopped
% 116.19/15.96 Prover 10: stopped
% 116.19/15.96 Prover 11: stopped
% 116.19/15.96 Prover 4: stopped
% 116.19/15.96 Prover 7: stopped
% 117.36/16.19 Prover 19: Warning: ignoring some quantifiers
% 117.61/16.21 Prover 19: Constructing countermodel ...
% 117.61/16.22 Prover 19: stopped
% 117.61/16.22
% 117.61/16.22 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 117.61/16.22
% 117.61/16.25 % SZS output start Proof for theBenchmark
% 117.61/16.25 Assumptions after simplification:
% 117.61/16.25 ---------------------------------
% 117.61/16.25
% 117.61/16.26 (ax15)
% 117.87/16.30 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 117.87/16.30 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 117.87/16.30 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 117.87/16.30
% 117.87/16.30 (ax17)
% 117.87/16.31 ssList(nil) = 0 & $i(nil)
% 117.87/16.31
% 117.87/16.31 (ax18)
% 117.87/16.31 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (cons(v1,
% 117.87/16.31 v0) = v0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v1) =
% 117.87/16.31 v2)))
% 117.87/16.31
% 117.87/16.31 (ax20)
% 117.87/16.31 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1:
% 117.87/16.31 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 117.87/16.31 ssItem(v2) = 0 & $i(v2))))
% 117.87/16.31
% 117.87/16.31 (ax23)
% 117.87/16.31 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : (
% 117.87/16.31 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) =
% 117.87/16.31 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1))))
% 117.87/16.31
% 117.87/16.31 (ax25)
% 117.87/16.32 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : (
% 117.87/16.32 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) =
% 117.87/16.32 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0))))
% 117.87/16.32
% 117.87/16.32 (ax4)
% 117.87/16.32 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) |
% 117.87/16.32 ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2: $i]
% 117.87/16.32 : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0 | ! [v2:
% 117.87/16.32 $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 =
% 117.87/16.32 0) & ssItem(v2) = v3)))))
% 117.87/16.32
% 117.87/16.32 (ax58)
% 117.87/16.32 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(nil, v0) = v1) | ~
% 117.87/16.32 $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0
% 117.87/16.32 = nil) & ( ~ (v0 = nil) | v1 = 0)))
% 117.87/16.32
% 117.87/16.32 (ax59)
% 117.87/16.32 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 117.87/16.32 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 117.87/16.32 (v2 = 0) | v3 = 0)))
% 117.87/16.32
% 117.87/16.32 (ax61)
% 117.87/16.32 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 117.87/16.32 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 117.87/16.32 (v2 = 0) | v3 = 0)))
% 117.87/16.32
% 117.87/16.32 (ax63)
% 117.87/16.33 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 117.87/16.33 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 117.87/16.33 (v2 = 0) | v3 = 0)))
% 117.87/16.33
% 117.87/16.33 (ax65)
% 117.87/16.33 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 117.87/16.33 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 117.87/16.33 (v2 = 0) | v3 = 0)))
% 117.87/16.33
% 117.87/16.33 (ax68)
% 117.87/16.33 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 117.87/16.33 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & (
% 117.87/16.33 ~ (v2 = 0) | v3 = 0)))
% 117.87/16.33
% 117.87/16.33 (ax7)
% 117.87/16.33 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 117.87/16.33 ( ~ (segmentP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 117.87/16.33 ssList(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : ? [v4: $i] :
% 117.87/16.33 (ssList(v3) = 0 & app(v3, v1) = v4 & $i(v4) & $i(v3) & ? [v5: $i] :
% 117.87/16.33 (ssList(v5) = 0 & app(v4, v5) = v0 & $i(v5)))) & (v2 = 0 | ! [v3:
% 117.87/16.33 $i] : ! [v4: $i] : ( ~ (app(v3, v1) = v4) | ~ $i(v3) | ? [v5:
% 117.87/16.33 int] : ( ~ (v5 = 0) & ssList(v3) = v5) | ! [v5: $i] : ( ~
% 117.87/16.33 (app(v4, v5) = v0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) &
% 117.87/16.33 ssList(v5) = v6)))))))
% 117.87/16.33
% 117.87/16.33 (ax71)
% 117.87/16.33 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 117.87/16.33 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & (
% 117.87/16.33 ~ (v2 = 0) | v3 = 0)))
% 117.87/16.33
% 117.87/16.33 (ax73)
% 117.87/16.33 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 117.87/16.33 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 117.87/16.33 (v2 = 0) | v3 = 0)))
% 117.87/16.33
% 117.87/16.34 (co1)
% 117.87/16.34 $i(nil) & ? [v0: $i] : ? [v1: any] : (singletonP(v0) = v1 & ssList(v0) = 0 &
% 117.87/16.34 $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] : (segmentP(v2, v0) = v3
% 117.87/16.34 & ssList(v2) = 0 & neq(v2, nil) = v4 & $i(v2) & ( ~ (v3 = 0) | (v4 = 0 &
% 117.87/16.34 ~ (v1 = 0))) & ( ? [v5: $i] : ? [v6: $i] : (cons(v5, nil) = v6 &
% 117.87/16.34 ssItem(v5) = 0 & $i(v6) & $i(v5) & ? [v7: $i] : ? [v8: $i] :
% 117.87/16.34 (ssList(v7) = 0 & app(v7, v0) = v8 & $i(v8) & $i(v7) & ? [v9: $i] :
% 117.87/16.34 (v6 = v0 & ssList(v9) = 0 & app(v8, v9) = v2 & $i(v9) & ! [v10: $i]
% 117.87/16.34 : ( ~ (memberP(v9, v10) = 0) | ~ $i(v10) | ? [v11: any] : ?
% 117.87/16.34 [v12: any] : (lt(v10, v5) = v12 & ssItem(v10) = v11 & ( ~ (v12 =
% 117.87/16.34 0) | ~ (v11 = 0)))) & ! [v10: $i] : ( ~ (memberP(v7,
% 117.87/16.34 v10) = 0) | ~ $i(v10) | ? [v11: any] : ? [v12: any] :
% 117.87/16.34 (lt(v5, v10) = v12 & ssItem(v10) = v11 & ( ~ (v12 = 0) | ~ (v11
% 117.87/16.34 = 0))))))) | (v2 = nil & v0 = nil))))
% 117.87/16.34
% 117.87/16.34 (function-axioms)
% 117.87/16.35 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 117.87/16.35 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 117.87/16.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 117.87/16.35 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 117.87/16.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 117.87/16.35 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 117.87/16.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 117.87/16.35 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 117.87/16.35 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 117.87/16.35 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 117.87/16.35 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 117.87/16.35 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 117.87/16.35 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 117.87/16.35 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 117.87/16.35 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 117.87/16.35 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 117.87/16.35 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 117.87/16.35 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 117.87/16.35 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 117.87/16.35 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 117.87/16.35 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 117.87/16.35 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 117.87/16.35 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 117.87/16.35 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 117.87/16.35 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 117.87/16.35 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 117.87/16.35 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 117.87/16.35 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 117.87/16.35 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 117.87/16.35 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 117.87/16.35 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 117.87/16.35 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 117.87/16.35 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 117.87/16.35 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 117.87/16.35 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 117.87/16.35 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 117.87/16.35 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 117.87/16.35 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 117.87/16.35 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 117.87/16.35 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 117.87/16.35 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 117.87/16.35 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 117.87/16.35 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 117.87/16.35
% 117.87/16.35 Further assumptions not needed in the proof:
% 117.87/16.35 --------------------------------------------
% 117.87/16.35 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax19, ax2, ax21, ax22, ax24, ax26,
% 117.87/16.35 ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38,
% 117.87/16.35 ax39, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, ax50,
% 117.87/16.35 ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax6, ax60, ax62, ax64, ax66, ax67,
% 117.87/16.35 ax69, ax70, ax72, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82,
% 117.87/16.35 ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94,
% 117.87/16.35 ax95
% 117.87/16.35
% 117.87/16.35 Those formulas are unsatisfiable:
% 117.87/16.35 ---------------------------------
% 117.87/16.35
% 117.87/16.35 Begin of proof
% 117.87/16.35 |
% 117.87/16.35 | ALPHA: (ax4) implies:
% 117.87/16.35 | (1) ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) | ?
% 117.87/16.35 | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2:
% 117.87/16.35 | $i] : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0
% 117.87/16.35 | | ! [v2: $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3:
% 117.87/16.35 | int] : ( ~ (v3 = 0) & ssItem(v2) = v3)))))
% 117.87/16.35 |
% 117.87/16.35 | ALPHA: (ax17) implies:
% 117.87/16.35 | (2) ssList(nil) = 0
% 117.87/16.35 |
% 117.87/16.35 | ALPHA: (ax20) implies:
% 117.87/16.35 | (3) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 117.87/16.35 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 117.87/16.35 | ssItem(v2) = 0 & $i(v2))))
% 117.87/16.35 |
% 117.87/16.35 | ALPHA: (ax58) implies:
% 117.87/16.36 | (4) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(nil, v0) = v1) | ~ $i(v0) |
% 117.87/16.36 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | v0 =
% 117.87/16.36 | nil) & ( ~ (v0 = nil) | v1 = 0)))
% 117.87/16.36 |
% 117.87/16.36 | ALPHA: (ax59) implies:
% 117.87/16.36 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 117.87/16.36 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & (
% 117.87/16.36 | ~ (v2 = 0) | v3 = 0)))
% 117.87/16.36 |
% 117.87/16.36 | ALPHA: (ax61) implies:
% 117.87/16.36 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 117.87/16.36 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 &
% 117.87/16.36 | ( ~ (v2 = 0) | v3 = 0)))
% 117.87/16.36 |
% 117.87/16.36 | ALPHA: (ax63) implies:
% 118.35/16.36 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 118.35/16.36 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 &
% 118.35/16.36 | ( ~ (v2 = 0) | v3 = 0)))
% 118.35/16.36 |
% 118.35/16.36 | ALPHA: (ax65) implies:
% 118.35/16.36 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 118.35/16.36 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2
% 118.35/16.36 | & ( ~ (v2 = 0) | v3 = 0)))
% 118.35/16.36 |
% 118.35/16.36 | ALPHA: (ax68) implies:
% 118.35/16.36 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 118.35/16.36 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2
% 118.35/16.36 | & ( ~ (v2 = 0) | v3 = 0)))
% 118.35/16.36 |
% 118.35/16.36 | ALPHA: (ax71) implies:
% 118.35/16.36 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 118.35/16.36 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) =
% 118.35/16.36 | v2 & ( ~ (v2 = 0) | v3 = 0)))
% 118.35/16.36 |
% 118.35/16.36 | ALPHA: (ax73) implies:
% 118.35/16.36 | (11) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 118.35/16.36 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 &
% 118.35/16.36 | ( ~ (v2 = 0) | v3 = 0)))
% 118.35/16.36 |
% 118.35/16.36 | ALPHA: (co1) implies:
% 118.35/16.36 | (12) $i(nil)
% 118.35/16.37 | (13) ? [v0: $i] : ? [v1: any] : (singletonP(v0) = v1 & ssList(v0) = 0 &
% 118.35/16.37 | $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] : (segmentP(v2,
% 118.35/16.37 | v0) = v3 & ssList(v2) = 0 & neq(v2, nil) = v4 & $i(v2) & ( ~ (v3
% 118.35/16.37 | = 0) | (v4 = 0 & ~ (v1 = 0))) & ( ? [v5: $i] : ? [v6: $i] :
% 118.35/16.37 | (cons(v5, nil) = v6 & ssItem(v5) = 0 & $i(v6) & $i(v5) & ? [v7:
% 118.35/16.37 | $i] : ? [v8: $i] : (ssList(v7) = 0 & app(v7, v0) = v8 &
% 118.35/16.37 | $i(v8) & $i(v7) & ? [v9: $i] : (v6 = v0 & ssList(v9) = 0 &
% 118.35/16.37 | app(v8, v9) = v2 & $i(v9) & ! [v10: $i] : ( ~
% 118.35/16.37 | (memberP(v9, v10) = 0) | ~ $i(v10) | ? [v11: any] : ?
% 118.35/16.37 | [v12: any] : (lt(v10, v5) = v12 & ssItem(v10) = v11 & (
% 118.35/16.37 | ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v10: $i] : ( ~
% 118.35/16.37 | (memberP(v7, v10) = 0) | ~ $i(v10) | ? [v11: any] : ?
% 118.35/16.37 | [v12: any] : (lt(v5, v10) = v12 & ssItem(v10) = v11 & (
% 118.35/16.37 | ~ (v12 = 0) | ~ (v11 = 0))))))) | (v2 = nil & v0 =
% 118.35/16.37 | nil))))
% 118.35/16.37 |
% 118.35/16.37 | ALPHA: (function-axioms) implies:
% 118.35/16.37 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 118.35/16.37 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 118.35/16.37 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 118.35/16.37 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 118.35/16.37 |
% 118.35/16.37 | DELTA: instantiating (13) with fresh symbols all_93_0, all_93_1 gives:
% 118.35/16.37 | (16) singletonP(all_93_1) = all_93_0 & ssList(all_93_1) = 0 & $i(all_93_1)
% 118.35/16.37 | & ? [v0: $i] : ? [v1: any] : ? [v2: any] : (segmentP(v0, all_93_1)
% 118.35/16.37 | = v1 & ssList(v0) = 0 & neq(v0, nil) = v2 & $i(v0) & ( ~ (v1 = 0) |
% 118.35/16.37 | (v2 = 0 & ~ (all_93_0 = 0))) & ( ? [v3: $i] : ? [v4: $i] :
% 118.35/16.37 | (cons(v3, nil) = v4 & ssItem(v3) = 0 & $i(v4) & $i(v3) & ? [v5:
% 118.35/16.37 | $i] : ? [v6: $i] : (ssList(v5) = 0 & app(v5, all_93_1) = v6 &
% 118.35/16.37 | $i(v6) & $i(v5) & ? [v7: $i] : (v4 = all_93_1 & ssList(v7) =
% 118.35/16.37 | 0 & app(v6, v7) = v0 & $i(v7) & ! [v8: $i] : ( ~
% 118.35/16.37 | (memberP(v7, v8) = 0) | ~ $i(v8) | ? [v9: any] : ?
% 118.35/16.37 | [v10: any] : (lt(v8, v3) = v10 & ssItem(v8) = v9 & ( ~
% 118.35/16.37 | (v10 = 0) | ~ (v9 = 0)))) & ! [v8: $i] : ( ~
% 118.35/16.37 | (memberP(v5, v8) = 0) | ~ $i(v8) | ? [v9: any] : ?
% 118.35/16.37 | [v10: any] : (lt(v3, v8) = v10 & ssItem(v8) = v9 & ( ~
% 118.35/16.37 | (v10 = 0) | ~ (v9 = 0))))))) | (v0 = nil & all_93_1 =
% 118.35/16.37 | nil)))
% 118.35/16.37 |
% 118.35/16.37 | ALPHA: (16) implies:
% 118.35/16.37 | (17) $i(all_93_1)
% 118.35/16.37 | (18) ssList(all_93_1) = 0
% 118.35/16.37 | (19) singletonP(all_93_1) = all_93_0
% 118.35/16.37 | (20) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (segmentP(v0, all_93_1) =
% 118.35/16.37 | v1 & ssList(v0) = 0 & neq(v0, nil) = v2 & $i(v0) & ( ~ (v1 = 0) |
% 118.35/16.37 | (v2 = 0 & ~ (all_93_0 = 0))) & ( ? [v3: $i] : ? [v4: $i] :
% 118.35/16.37 | (cons(v3, nil) = v4 & ssItem(v3) = 0 & $i(v4) & $i(v3) & ? [v5:
% 118.35/16.37 | $i] : ? [v6: $i] : (ssList(v5) = 0 & app(v5, all_93_1) = v6 &
% 118.35/16.37 | $i(v6) & $i(v5) & ? [v7: $i] : (v4 = all_93_1 & ssList(v7) =
% 118.35/16.37 | 0 & app(v6, v7) = v0 & $i(v7) & ! [v8: $i] : ( ~
% 118.35/16.37 | (memberP(v7, v8) = 0) | ~ $i(v8) | ? [v9: any] : ?
% 118.35/16.37 | [v10: any] : (lt(v8, v3) = v10 & ssItem(v8) = v9 & ( ~
% 118.35/16.38 | (v10 = 0) | ~ (v9 = 0)))) & ! [v8: $i] : ( ~
% 118.35/16.38 | (memberP(v5, v8) = 0) | ~ $i(v8) | ? [v9: any] : ?
% 118.35/16.38 | [v10: any] : (lt(v3, v8) = v10 & ssItem(v8) = v9 & ( ~
% 118.35/16.38 | (v10 = 0) | ~ (v9 = 0))))))) | (v0 = nil & all_93_1 =
% 118.35/16.38 | nil)))
% 118.35/16.38 |
% 118.35/16.38 | DELTA: instantiating (20) with fresh symbols all_97_0, all_97_1, all_97_2
% 118.35/16.38 | gives:
% 118.35/16.38 | (21) segmentP(all_97_2, all_93_1) = all_97_1 & ssList(all_97_2) = 0 &
% 118.35/16.38 | neq(all_97_2, nil) = all_97_0 & $i(all_97_2) & ( ~ (all_97_1 = 0) |
% 118.35/16.38 | (all_97_0 = 0 & ~ (all_93_0 = 0))) & ( ? [v0: $i] : ? [v1: $i] :
% 118.35/16.38 | (cons(v0, nil) = v1 & ssItem(v0) = 0 & $i(v1) & $i(v0) & ? [v2: $i]
% 118.35/16.38 | : ? [v3: $i] : (ssList(v2) = 0 & app(v2, all_93_1) = v3 & $i(v3)
% 118.35/16.38 | & $i(v2) & ? [v4: $i] : (v1 = all_93_1 & ssList(v4) = 0 &
% 118.35/16.38 | app(v3, v4) = all_97_2 & $i(v4) & ! [v5: $i] : ( ~
% 118.35/16.38 | (memberP(v4, v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7:
% 118.35/16.38 | any] : (lt(v5, v0) = v7 & ssItem(v5) = v6 & ( ~ (v7 = 0) |
% 118.35/16.38 | ~ (v6 = 0)))) & ! [v5: $i] : ( ~ (memberP(v2, v5) = 0)
% 118.35/16.38 | | ~ $i(v5) | ? [v6: any] : ? [v7: any] : (lt(v0, v5) = v7
% 118.35/16.38 | & ssItem(v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0))))))) |
% 118.35/16.38 | (all_97_2 = nil & all_93_1 = nil))
% 118.35/16.38 |
% 118.35/16.38 | ALPHA: (21) implies:
% 118.35/16.38 | (22) $i(all_97_2)
% 118.35/16.38 | (23) neq(all_97_2, nil) = all_97_0
% 118.35/16.38 | (24) ssList(all_97_2) = 0
% 118.35/16.38 | (25) segmentP(all_97_2, all_93_1) = all_97_1
% 118.35/16.38 | (26) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = 0 &
% 118.35/16.38 | $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 &
% 118.35/16.38 | app(v2, all_93_1) = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (v1 =
% 118.35/16.38 | all_93_1 & ssList(v4) = 0 & app(v3, v4) = all_97_2 & $i(v4) & !
% 118.35/16.38 | [v5: $i] : ( ~ (memberP(v4, v5) = 0) | ~ $i(v5) | ? [v6: any]
% 118.35/16.38 | : ? [v7: any] : (lt(v5, v0) = v7 & ssItem(v5) = v6 & ( ~ (v7
% 118.35/16.38 | = 0) | ~ (v6 = 0)))) & ! [v5: $i] : ( ~ (memberP(v2,
% 118.35/16.38 | v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: any] :
% 118.35/16.38 | (lt(v0, v5) = v7 & ssItem(v5) = v6 & ( ~ (v7 = 0) | ~ (v6 =
% 118.35/16.38 | 0))))))) | (all_97_2 = nil & all_93_1 = nil)
% 118.35/16.38 | (27) ~ (all_97_1 = 0) | (all_97_0 = 0 & ~ (all_93_0 = 0))
% 118.35/16.38 |
% 118.35/16.38 | GROUND_INST: instantiating (ax25) with nil, simplifying with (2), (12) gives:
% 118.35/16.39 | (28) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 118.35/16.39 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) &
% 118.35/16.39 | ( ~ (v2 = 0) | v3 = nil)))
% 118.35/16.39 |
% 118.35/16.39 | GROUND_INST: instantiating (ax23) with nil, simplifying with (2), (12) gives:
% 118.35/16.39 | (29) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 118.35/16.39 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) &
% 118.35/16.39 | ( ~ (v2 = 0) | v3 = v0)))
% 118.35/16.39 |
% 118.35/16.39 | GROUND_INST: instantiating (ax18) with nil, simplifying with (2), (12) gives:
% 118.35/16.39 | (30) ! [v0: $i] : ( ~ (cons(v0, nil) = nil) | ~ $i(v0) | ? [v1: int] : (
% 118.35/16.39 | ~ (v1 = 0) & ssItem(v0) = v1))
% 118.35/16.39 |
% 118.35/16.39 | GROUND_INST: instantiating (3) with all_93_1, simplifying with (17), (18)
% 118.35/16.39 | gives:
% 118.35/16.39 | (31) all_93_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i]
% 118.35/16.39 | : (cons(v1, v0) = all_93_1 & ssItem(v1) = 0 & $i(v1)))
% 118.35/16.39 |
% 118.35/16.39 | GROUND_INST: instantiating (ax7) with all_97_2, simplifying with (22), (24)
% 118.35/16.39 | gives:
% 118.35/16.39 | (32) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(all_97_2, v0) = v1) | ~
% 118.35/16.39 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 =
% 118.35/16.39 | 0) | ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 & app(v2, v0)
% 118.35/16.39 | = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (ssList(v4) = 0 &
% 118.35/16.39 | app(v3, v4) = all_97_2 & $i(v4)))) & (v1 = 0 | ! [v2: $i] :
% 118.35/16.39 | ! [v3: $i] : ( ~ (app(v2, v0) = v3) | ~ $i(v2) | ? [v4: int]
% 118.35/16.39 | : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i] : ( ~ (app(v3,
% 118.35/16.39 | v4) = all_97_2) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 =
% 118.35/16.39 | 0) & ssList(v4) = v5))))))
% 118.35/16.39 |
% 118.35/16.39 | GROUND_INST: instantiating (ax15) with all_97_2, simplifying with (22), (24)
% 118.35/16.39 | gives:
% 118.35/16.39 | (33) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_2, v0) = v1) | ~ $i(v0)
% 118.35/16.39 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 118.35/16.39 | ~ (v0 = all_97_2)) & (v1 = 0 | v0 = all_97_2)))
% 118.35/16.39 |
% 118.35/16.39 | GROUND_INST: instantiating (1) with all_93_1, all_93_0, simplifying with (17),
% 118.35/16.39 | (19) gives:
% 118.35/16.39 | (34) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ (all_93_0
% 118.35/16.39 | = 0) | ? [v0: $i] : (cons(v0, nil) = all_93_1 & ssItem(v0) = 0
% 118.35/16.39 | & $i(v0))) & (all_93_0 = 0 | ! [v0: $i] : ( ~ (cons(v0, nil) =
% 118.35/16.39 | all_93_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 118.35/16.39 | ssItem(v0) = v1))))
% 118.35/16.39 |
% 118.35/16.39 | GROUND_INST: instantiating (33) with nil, all_97_0, simplifying with (12),
% 118.35/16.39 | (23) gives:
% 118.35/16.39 | (35) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_97_0 = 0)
% 118.35/16.39 | | ~ (all_97_2 = nil)) & (all_97_0 = 0 | all_97_2 = nil))
% 118.35/16.39 |
% 118.35/16.39 | GROUND_INST: instantiating (32) with all_93_1, all_97_1, simplifying with
% 118.35/16.39 | (17), (25) gives:
% 118.35/16.39 | (36) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ (all_97_1
% 118.35/16.39 | = 0) | ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0,
% 118.35/16.39 | all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) =
% 118.35/16.39 | 0 & app(v1, v2) = all_97_2 & $i(v2)))) & (all_97_1 = 0 | !
% 118.35/16.39 | [v0: $i] : ! [v1: $i] : ( ~ (app(v0, all_93_1) = v1) | ~ $i(v0)
% 118.35/16.40 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] :
% 118.35/16.40 | ( ~ (app(v1, v2) = all_97_2) | ~ $i(v2) | ? [v3: int] : ( ~
% 118.35/16.40 | (v3 = 0) & ssList(v2) = v3)))))
% 118.35/16.40 |
% 118.35/16.40 | BETA: splitting (26) gives:
% 118.35/16.40 |
% 118.35/16.40 | Case 1:
% 118.35/16.40 | |
% 118.35/16.40 | | (37) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = 0 &
% 118.35/16.40 | | $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 &
% 118.35/16.40 | | app(v2, all_93_1) = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (v1 =
% 118.35/16.40 | | all_93_1 & ssList(v4) = 0 & app(v3, v4) = all_97_2 & $i(v4) &
% 118.35/16.40 | | ! [v5: $i] : ( ~ (memberP(v4, v5) = 0) | ~ $i(v5) | ? [v6:
% 118.35/16.40 | | any] : ? [v7: any] : (lt(v5, v0) = v7 & ssItem(v5) = v6 &
% 118.35/16.40 | | ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v5: $i] : ( ~
% 118.35/16.40 | | (memberP(v2, v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7:
% 118.35/16.40 | | any] : (lt(v0, v5) = v7 & ssItem(v5) = v6 & ( ~ (v7 = 0) |
% 118.35/16.40 | | ~ (v6 = 0)))))))
% 118.35/16.40 | |
% 118.35/16.40 | | DELTA: instantiating (37) with fresh symbols all_298_0, all_298_1 gives:
% 118.35/16.40 | | (38) cons(all_298_1, nil) = all_298_0 & ssItem(all_298_1) = 0 &
% 118.35/16.40 | | $i(all_298_0) & $i(all_298_1) & ? [v0: $i] : ? [v1: $i] :
% 118.35/16.40 | | (ssList(v0) = 0 & app(v0, all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2:
% 118.35/16.40 | | $i] : (all_298_0 = all_93_1 & ssList(v2) = 0 & app(v1, v2) =
% 118.35/16.40 | | all_97_2 & $i(v2) & ! [v3: $i] : ( ~ (memberP(v2, v3) = 0) | ~
% 118.35/16.40 | | $i(v3) | ? [v4: any] : ? [v5: any] : (lt(v3, all_298_1) = v5
% 118.35/16.40 | | & ssItem(v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v3:
% 118.35/16.40 | | $i] : ( ~ (memberP(v0, v3) = 0) | ~ $i(v3) | ? [v4: any] :
% 118.35/16.40 | | ? [v5: any] : (lt(all_298_1, v3) = v5 & ssItem(v3) = v4 & ( ~
% 118.35/16.40 | | (v5 = 0) | ~ (v4 = 0))))))
% 118.35/16.40 | |
% 118.35/16.40 | | ALPHA: (38) implies:
% 118.35/16.40 | | (39) $i(all_298_1)
% 118.35/16.40 | | (40) ssItem(all_298_1) = 0
% 118.35/16.40 | | (41) cons(all_298_1, nil) = all_298_0
% 118.35/16.40 | | (42) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, all_93_1) = v1
% 118.35/16.40 | | & $i(v1) & $i(v0) & ? [v2: $i] : (all_298_0 = all_93_1 &
% 118.35/16.40 | | ssList(v2) = 0 & app(v1, v2) = all_97_2 & $i(v2) & ! [v3: $i] :
% 118.35/16.40 | | ( ~ (memberP(v2, v3) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5:
% 118.35/16.40 | | any] : (lt(v3, all_298_1) = v5 & ssItem(v3) = v4 & ( ~ (v5 =
% 118.35/16.40 | | 0) | ~ (v4 = 0)))) & ! [v3: $i] : ( ~ (memberP(v0, v3)
% 118.35/16.40 | | = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] :
% 118.35/16.40 | | (lt(all_298_1, v3) = v5 & ssItem(v3) = v4 & ( ~ (v5 = 0) | ~
% 118.35/16.40 | | (v4 = 0))))))
% 118.35/16.40 | |
% 118.35/16.40 | | DELTA: instantiating (42) with fresh symbols all_300_0, all_300_1 gives:
% 118.35/16.40 | | (43) ssList(all_300_1) = 0 & app(all_300_1, all_93_1) = all_300_0 &
% 118.35/16.40 | | $i(all_300_0) & $i(all_300_1) & ? [v0: $i] : (all_298_0 = all_93_1
% 118.35/16.40 | | & ssList(v0) = 0 & app(all_300_0, v0) = all_97_2 & $i(v0) & !
% 118.35/16.40 | | [v1: $i] : ( ~ (memberP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] :
% 118.35/16.40 | | ? [v3: any] : (lt(v1, all_298_1) = v3 & ssItem(v1) = v2 & ( ~
% 118.35/16.40 | | (v3 = 0) | ~ (v2 = 0)))) & ! [v1: $i] : ( ~
% 118.35/16.40 | | (memberP(all_300_1, v1) = 0) | ~ $i(v1) | ? [v2: any] : ?
% 118.35/16.40 | | [v3: any] : (lt(all_298_1, v1) = v3 & ssItem(v1) = v2 & ( ~ (v3
% 118.35/16.40 | | = 0) | ~ (v2 = 0)))))
% 118.35/16.40 | |
% 118.35/16.40 | | ALPHA: (43) implies:
% 118.35/16.40 | | (44) $i(all_300_1)
% 118.35/16.40 | | (45) app(all_300_1, all_93_1) = all_300_0
% 118.35/16.40 | | (46) ssList(all_300_1) = 0
% 118.35/16.41 | | (47) ? [v0: $i] : (all_298_0 = all_93_1 & ssList(v0) = 0 &
% 118.35/16.41 | | app(all_300_0, v0) = all_97_2 & $i(v0) & ! [v1: $i] : ( ~
% 118.35/16.41 | | (memberP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any]
% 118.35/16.41 | | : (lt(v1, all_298_1) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~
% 118.35/16.41 | | (v2 = 0)))) & ! [v1: $i] : ( ~ (memberP(all_300_1, v1) = 0)
% 118.35/16.41 | | | ~ $i(v1) | ? [v2: any] : ? [v3: any] : (lt(all_298_1, v1) =
% 118.35/16.41 | | v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 118.35/16.41 | |
% 118.35/16.41 | | DELTA: instantiating (47) with fresh symbol all_302_0 gives:
% 118.35/16.41 | | (48) all_298_0 = all_93_1 & ssList(all_302_0) = 0 & app(all_300_0,
% 118.35/16.41 | | all_302_0) = all_97_2 & $i(all_302_0) & ! [v0: $i] : ( ~
% 118.35/16.41 | | (memberP(all_302_0, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 118.35/16.41 | | any] : (lt(v0, all_298_1) = v2 & ssItem(v0) = v1 & ( ~ (v2 = 0)
% 118.35/16.41 | | | ~ (v1 = 0)))) & ! [v0: $i] : ( ~ (memberP(all_300_1, v0) =
% 118.35/16.41 | | 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (lt(all_298_1,
% 118.35/16.41 | | v0) = v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0))))
% 118.35/16.41 | |
% 118.35/16.41 | | ALPHA: (48) implies:
% 118.35/16.41 | | (49) all_298_0 = all_93_1
% 118.35/16.41 | | (50) $i(all_302_0)
% 118.35/16.41 | | (51) app(all_300_0, all_302_0) = all_97_2
% 118.35/16.41 | | (52) ssList(all_302_0) = 0
% 118.35/16.41 | |
% 118.35/16.41 | | REDUCE: (41), (49) imply:
% 118.35/16.41 | | (53) cons(all_298_1, nil) = all_93_1
% 118.35/16.41 | |
% 118.35/16.41 | | BETA: splitting (27) gives:
% 118.35/16.41 | |
% 118.35/16.41 | | Case 1:
% 118.35/16.41 | | |
% 118.35/16.41 | | | (54) ~ (all_97_1 = 0)
% 118.35/16.41 | | |
% 118.35/16.41 | | | BETA: splitting (36) gives:
% 118.35/16.41 | | |
% 118.35/16.41 | | | Case 1:
% 118.35/16.41 | | | |
% 118.35/16.41 | | | | (55) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0)
% 118.35/16.41 | | | |
% 118.35/16.41 | | | | DELTA: instantiating (55) with fresh symbol all_314_0 gives:
% 118.35/16.41 | | | | (56) ~ (all_314_0 = 0) & ssList(all_93_1) = all_314_0
% 118.35/16.41 | | | |
% 118.35/16.41 | | | | REF_CLOSE: (15), (18), (56) are inconsistent by sub-proof #2.
% 118.35/16.41 | | | |
% 118.35/16.41 | | | Case 2:
% 118.35/16.41 | | | |
% 118.35/16.41 | | | | (57) ( ~ (all_97_1 = 0) | ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0
% 118.35/16.41 | | | | & app(v0, all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2: $i] :
% 118.35/16.41 | | | | (ssList(v2) = 0 & app(v1, v2) = all_97_2 & $i(v2)))) &
% 118.35/16.41 | | | | (all_97_1 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0,
% 118.35/16.41 | | | | all_93_1) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 =
% 118.35/16.41 | | | | 0) & ssList(v0) = v2) | ! [v2: $i] : ( ~ (app(v1, v2) =
% 118.35/16.41 | | | | all_97_2) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 118.35/16.41 | | | | ssList(v2) = v3))))
% 118.35/16.41 | | | |
% 118.35/16.41 | | | | ALPHA: (57) implies:
% 118.35/16.41 | | | | (58) all_97_1 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0,
% 118.35/16.41 | | | | all_93_1) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0)
% 118.35/16.41 | | | | & ssList(v0) = v2) | ! [v2: $i] : ( ~ (app(v1, v2) =
% 118.35/16.41 | | | | all_97_2) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 118.35/16.41 | | | | ssList(v2) = v3)))
% 118.35/16.41 | | | |
% 118.35/16.41 | | | | BETA: splitting (58) gives:
% 118.35/16.41 | | | |
% 118.35/16.41 | | | | Case 1:
% 118.35/16.41 | | | | |
% 118.35/16.41 | | | | | (59) all_97_1 = 0
% 118.35/16.41 | | | | |
% 118.35/16.41 | | | | | REDUCE: (54), (59) imply:
% 118.35/16.41 | | | | | (60) $false
% 118.35/16.41 | | | | |
% 118.35/16.41 | | | | | CLOSE: (60) is inconsistent.
% 118.35/16.41 | | | | |
% 118.35/16.41 | | | | Case 2:
% 118.35/16.41 | | | | |
% 118.35/16.41 | | | | | (61) ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0, all_93_1) = v1) | ~
% 118.35/16.41 | | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | !
% 118.35/16.41 | | | | | [v2: $i] : ( ~ (app(v1, v2) = all_97_2) | ~ $i(v2) | ?
% 118.35/16.41 | | | | | [v3: int] : ( ~ (v3 = 0) & ssList(v2) = v3)))
% 118.35/16.41 | | | | |
% 118.35/16.41 | | | | | BETA: splitting (34) gives:
% 118.35/16.41 | | | | |
% 118.35/16.41 | | | | | Case 1:
% 118.35/16.41 | | | | | |
% 118.35/16.41 | | | | | | (62) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0)
% 118.35/16.41 | | | | | |
% 118.35/16.41 | | | | | | DELTA: instantiating (62) with fresh symbol all_314_0 gives:
% 118.35/16.41 | | | | | | (63) ~ (all_314_0 = 0) & ssList(all_93_1) = all_314_0
% 118.35/16.41 | | | | | |
% 118.35/16.41 | | | | | | REF_CLOSE: (15), (18), (63) are inconsistent by sub-proof #2.
% 118.35/16.41 | | | | | |
% 118.35/16.41 | | | | | Case 2:
% 118.35/16.41 | | | | | |
% 118.35/16.41 | | | | | |
% 118.35/16.41 | | | | | | GROUND_INST: instantiating (61) with all_300_1, all_300_0,
% 118.35/16.41 | | | | | | simplifying with (44), (45) gives:
% 118.35/16.41 | | | | | | (64) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_300_1) = v0) | !
% 118.35/16.41 | | | | | | [v0: $i] : ( ~ (app(all_300_0, v0) = all_97_2) | ~ $i(v0) |
% 118.35/16.41 | | | | | | ? [v1: int] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 118.35/16.41 | | | | | |
% 118.35/16.41 | | | | | | BETA: splitting (64) gives:
% 118.35/16.41 | | | | | |
% 118.35/16.41 | | | | | | Case 1:
% 118.35/16.41 | | | | | | |
% 118.35/16.41 | | | | | | | (65) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_300_1) = v0)
% 118.35/16.41 | | | | | | |
% 118.35/16.41 | | | | | | | DELTA: instantiating (65) with fresh symbol all_1026_0 gives:
% 118.35/16.41 | | | | | | | (66) ~ (all_1026_0 = 0) & ssList(all_300_1) = all_1026_0
% 118.35/16.41 | | | | | | |
% 118.35/16.41 | | | | | | | ALPHA: (66) implies:
% 118.35/16.41 | | | | | | | (67) ~ (all_1026_0 = 0)
% 118.35/16.41 | | | | | | | (68) ssList(all_300_1) = all_1026_0
% 118.35/16.41 | | | | | | |
% 118.35/16.42 | | | | | | | GROUND_INST: instantiating (15) with 0, all_1026_0, all_300_1,
% 118.35/16.42 | | | | | | | simplifying with (46), (68) gives:
% 118.35/16.42 | | | | | | | (69) all_1026_0 = 0
% 118.35/16.42 | | | | | | |
% 118.35/16.42 | | | | | | | REDUCE: (67), (69) imply:
% 118.35/16.42 | | | | | | | (70) $false
% 118.35/16.42 | | | | | | |
% 118.35/16.42 | | | | | | | CLOSE: (70) is inconsistent.
% 118.35/16.42 | | | | | | |
% 118.35/16.42 | | | | | | Case 2:
% 118.35/16.42 | | | | | | |
% 118.35/16.42 | | | | | | | (71) ! [v0: $i] : ( ~ (app(all_300_0, v0) = all_97_2) | ~
% 118.35/16.42 | | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 118.35/16.42 | | | | | | |
% 118.35/16.42 | | | | | | | GROUND_INST: instantiating (71) with all_302_0, simplifying with
% 118.35/16.42 | | | | | | | (50), (51) gives:
% 118.35/16.42 | | | | | | | (72) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_302_0) = v0)
% 118.35/16.42 | | | | | | |
% 118.35/16.42 | | | | | | | DELTA: instantiating (72) with fresh symbol all_1025_0 gives:
% 118.35/16.42 | | | | | | | (73) ~ (all_1025_0 = 0) & ssList(all_302_0) = all_1025_0
% 118.35/16.42 | | | | | | |
% 118.35/16.42 | | | | | | | ALPHA: (73) implies:
% 118.35/16.42 | | | | | | | (74) ~ (all_1025_0 = 0)
% 118.35/16.42 | | | | | | | (75) ssList(all_302_0) = all_1025_0
% 118.35/16.42 | | | | | | |
% 118.35/16.42 | | | | | | | GROUND_INST: instantiating (15) with 0, all_1025_0, all_302_0,
% 118.35/16.42 | | | | | | | simplifying with (52), (75) gives:
% 118.35/16.42 | | | | | | | (76) all_1025_0 = 0
% 118.35/16.42 | | | | | | |
% 118.35/16.42 | | | | | | | REDUCE: (74), (76) imply:
% 118.35/16.42 | | | | | | | (77) $false
% 118.35/16.42 | | | | | | |
% 118.35/16.42 | | | | | | | CLOSE: (77) is inconsistent.
% 118.35/16.42 | | | | | | |
% 118.35/16.42 | | | | | | End of split
% 118.35/16.42 | | | | | |
% 118.35/16.42 | | | | | End of split
% 118.35/16.42 | | | | |
% 118.35/16.42 | | | | End of split
% 118.35/16.42 | | | |
% 118.35/16.42 | | | End of split
% 118.35/16.42 | | |
% 118.35/16.42 | | Case 2:
% 118.35/16.42 | | |
% 118.35/16.42 | | | (78) all_97_0 = 0 & ~ (all_93_0 = 0)
% 118.35/16.42 | | |
% 118.35/16.42 | | | ALPHA: (78) implies:
% 118.35/16.42 | | | (79) ~ (all_93_0 = 0)
% 118.35/16.42 | | |
% 118.35/16.42 | | | BETA: splitting (34) gives:
% 118.35/16.42 | | |
% 118.35/16.42 | | | Case 1:
% 118.35/16.42 | | | |
% 118.35/16.42 | | | | (80) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0)
% 118.35/16.42 | | | |
% 118.35/16.42 | | | | DELTA: instantiating (80) with fresh symbol all_315_0 gives:
% 118.35/16.42 | | | | (81) ~ (all_315_0 = 0) & ssList(all_93_1) = all_315_0
% 118.35/16.42 | | | |
% 118.35/16.42 | | | | ALPHA: (81) implies:
% 118.35/16.42 | | | | (82) ~ (all_315_0 = 0)
% 118.35/16.42 | | | | (83) ssList(all_93_1) = all_315_0
% 118.35/16.42 | | | |
% 118.35/16.42 | | | | DELTA: instantiating (80) with fresh symbol all_319_0 gives:
% 118.35/16.42 | | | | (84) ~ (all_319_0 = 0) & ssList(all_93_1) = all_319_0
% 118.35/16.42 | | | |
% 118.35/16.42 | | | | ALPHA: (84) implies:
% 118.35/16.42 | | | | (85) ssList(all_93_1) = all_319_0
% 118.62/16.42 | | | |
% 118.62/16.42 | | | | GROUND_INST: instantiating (15) with 0, all_319_0, all_93_1, simplifying
% 118.62/16.42 | | | | with (18), (85) gives:
% 118.62/16.42 | | | | (86) all_319_0 = 0
% 118.62/16.42 | | | |
% 118.62/16.42 | | | | GROUND_INST: instantiating (15) with all_315_0, all_319_0, all_93_1,
% 118.62/16.42 | | | | simplifying with (83), (85) gives:
% 118.62/16.42 | | | | (87) all_319_0 = all_315_0
% 118.62/16.42 | | | |
% 118.62/16.42 | | | | COMBINE_EQS: (86), (87) imply:
% 118.62/16.42 | | | | (88) all_315_0 = 0
% 118.62/16.42 | | | |
% 118.62/16.42 | | | | REDUCE: (82), (88) imply:
% 118.62/16.42 | | | | (89) $false
% 118.62/16.42 | | | |
% 118.62/16.42 | | | | CLOSE: (89) is inconsistent.
% 118.62/16.42 | | | |
% 118.62/16.42 | | | Case 2:
% 118.62/16.42 | | | |
% 118.62/16.42 | | | | (90) ( ~ (all_93_0 = 0) | ? [v0: $i] : (cons(v0, nil) = all_93_1 &
% 118.62/16.42 | | | | ssItem(v0) = 0 & $i(v0))) & (all_93_0 = 0 | ! [v0: $i] : (
% 118.62/16.42 | | | | ~ (cons(v0, nil) = all_93_1) | ~ $i(v0) | ? [v1: int] : (
% 118.62/16.42 | | | | ~ (v1 = 0) & ssItem(v0) = v1)))
% 118.62/16.42 | | | |
% 118.62/16.42 | | | | ALPHA: (90) implies:
% 118.62/16.42 | | | | (91) all_93_0 = 0 | ! [v0: $i] : ( ~ (cons(v0, nil) = all_93_1) | ~
% 118.62/16.42 | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 118.62/16.42 | | | |
% 118.62/16.42 | | | | BETA: splitting (91) gives:
% 118.62/16.42 | | | |
% 118.62/16.42 | | | | Case 1:
% 118.62/16.42 | | | | |
% 118.62/16.42 | | | | | (92) all_93_0 = 0
% 118.62/16.42 | | | | |
% 118.62/16.42 | | | | | REDUCE: (79), (92) imply:
% 118.62/16.42 | | | | | (93) $false
% 118.62/16.42 | | | | |
% 118.62/16.42 | | | | | CLOSE: (93) is inconsistent.
% 118.62/16.42 | | | | |
% 118.62/16.42 | | | | Case 2:
% 118.62/16.42 | | | | |
% 118.62/16.42 | | | | | (94) ! [v0: $i] : ( ~ (cons(v0, nil) = all_93_1) | ~ $i(v0) | ?
% 118.62/16.42 | | | | | [v1: int] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 118.62/16.42 | | | | |
% 118.62/16.42 | | | | | BETA: splitting (31) gives:
% 118.62/16.42 | | | | |
% 118.62/16.42 | | | | | Case 1:
% 118.62/16.42 | | | | | |
% 118.62/16.42 | | | | | | (95) all_93_1 = nil
% 118.62/16.42 | | | | | |
% 118.62/16.42 | | | | | | REDUCE: (53), (95) imply:
% 118.62/16.42 | | | | | | (96) cons(all_298_1, nil) = nil
% 118.62/16.42 | | | | | |
% 118.62/16.42 | | | | | | GROUND_INST: instantiating (30) with all_298_1, simplifying with
% 118.62/16.42 | | | | | | (39), (96) gives:
% 118.62/16.42 | | | | | | (97) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_298_1) = v0)
% 118.62/16.42 | | | | | |
% 118.62/16.42 | | | | | | GROUND_INST: instantiating (28) with all_298_1, nil, simplifying
% 118.62/16.42 | | | | | | with (39), (96) gives:
% 118.62/16.42 | | | | | | (98) ? [v0: any] : ? [v1: $i] : (tl(nil) = v1 &
% 118.62/16.42 | | | | | | ssItem(all_298_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 118.62/16.42 | | | | | | nil))
% 118.62/16.42 | | | | | |
% 118.62/16.42 | | | | | | GROUND_INST: instantiating (29) with all_298_1, nil, simplifying
% 118.62/16.42 | | | | | | with (39), (96) gives:
% 118.62/16.42 | | | | | | (99) ? [v0: any] : ? [v1: $i] : (hd(nil) = v1 &
% 118.62/16.42 | | | | | | ssItem(all_298_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 118.62/16.42 | | | | | | all_298_1))
% 118.62/16.42 | | | | | |
% 118.62/16.42 | | | | | | DELTA: instantiating (97) with fresh symbol all_810_0 gives:
% 118.62/16.42 | | | | | | (100) ~ (all_810_0 = 0) & ssItem(all_298_1) = all_810_0
% 118.62/16.42 | | | | | |
% 118.62/16.42 | | | | | | ALPHA: (100) implies:
% 118.62/16.42 | | | | | | (101) ~ (all_810_0 = 0)
% 118.62/16.42 | | | | | | (102) ssItem(all_298_1) = all_810_0
% 118.62/16.42 | | | | | |
% 118.62/16.42 | | | | | | DELTA: instantiating (99) with fresh symbols all_812_0, all_812_1
% 118.62/16.42 | | | | | | gives:
% 118.62/16.42 | | | | | | (103) hd(nil) = all_812_0 & ssItem(all_298_1) = all_812_1 &
% 118.62/16.42 | | | | | | $i(all_812_0) & ( ~ (all_812_1 = 0) | all_812_0 =
% 118.62/16.42 | | | | | | all_298_1)
% 118.62/16.42 | | | | | |
% 118.62/16.42 | | | | | | ALPHA: (103) implies:
% 118.62/16.42 | | | | | | (104) ssItem(all_298_1) = all_812_1
% 118.62/16.42 | | | | | |
% 118.62/16.42 | | | | | | DELTA: instantiating (98) with fresh symbols all_814_0, all_814_1
% 118.62/16.42 | | | | | | gives:
% 118.62/16.42 | | | | | | (105) tl(nil) = all_814_0 & ssItem(all_298_1) = all_814_1 &
% 118.62/16.42 | | | | | | $i(all_814_0) & ( ~ (all_814_1 = 0) | all_814_0 = nil)
% 118.62/16.42 | | | | | |
% 118.62/16.42 | | | | | | ALPHA: (105) implies:
% 118.62/16.42 | | | | | | (106) ssItem(all_298_1) = all_814_1
% 118.62/16.42 | | | | | |
% 118.62/16.43 | | | | | | GROUND_INST: instantiating (14) with 0, all_814_1, all_298_1,
% 118.62/16.43 | | | | | | simplifying with (40), (106) gives:
% 118.62/16.43 | | | | | | (107) all_814_1 = 0
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | GROUND_INST: instantiating (14) with all_812_1, all_814_1,
% 118.62/16.43 | | | | | | all_298_1, simplifying with (104), (106) gives:
% 118.62/16.43 | | | | | | (108) all_814_1 = all_812_1
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | GROUND_INST: instantiating (14) with all_810_0, all_814_1,
% 118.62/16.43 | | | | | | all_298_1, simplifying with (102), (106) gives:
% 118.62/16.43 | | | | | | (109) all_814_1 = all_810_0
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | COMBINE_EQS: (107), (108) imply:
% 118.62/16.43 | | | | | | (110) all_812_1 = 0
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | COMBINE_EQS: (108), (109) imply:
% 118.62/16.43 | | | | | | (111) all_812_1 = all_810_0
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | COMBINE_EQS: (110), (111) imply:
% 118.62/16.43 | | | | | | (112) all_810_0 = 0
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | SIMP: (112) implies:
% 118.62/16.43 | | | | | | (113) all_810_0 = 0
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | REDUCE: (101), (113) imply:
% 118.62/16.43 | | | | | | (114) $false
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | CLOSE: (114) is inconsistent.
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | Case 2:
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | GROUND_INST: instantiating (94) with all_298_1, simplifying with
% 118.62/16.43 | | | | | | (39), (53) gives:
% 118.62/16.43 | | | | | | (115) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_298_1) = v0)
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | GROUND_INST: instantiating (28) with all_298_1, all_93_1,
% 118.62/16.43 | | | | | | simplifying with (39), (53) gives:
% 118.62/16.43 | | | | | | (116) ? [v0: any] : ? [v1: $i] : (tl(all_93_1) = v1 &
% 118.62/16.43 | | | | | | ssItem(all_298_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 118.62/16.43 | | | | | | nil))
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | GROUND_INST: instantiating (29) with all_298_1, all_93_1,
% 118.62/16.43 | | | | | | simplifying with (39), (53) gives:
% 118.62/16.43 | | | | | | (117) ? [v0: any] : ? [v1: $i] : (hd(all_93_1) = v1 &
% 118.62/16.43 | | | | | | ssItem(all_298_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 118.62/16.43 | | | | | | all_298_1))
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | GROUND_INST: instantiating (11) with all_298_1, all_93_1,
% 118.62/16.43 | | | | | | simplifying with (39), (53) gives:
% 118.62/16.43 | | | | | | (118) ? [v0: any] : ? [v1: any] : (equalelemsP(all_93_1) = v1 &
% 118.62/16.43 | | | | | | ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | GROUND_INST: instantiating (10) with all_298_1, all_93_1,
% 118.62/16.43 | | | | | | simplifying with (39), (53) gives:
% 118.62/16.43 | | | | | | (119) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_93_1) =
% 118.62/16.43 | | | | | | v1 & ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | GROUND_INST: instantiating (9) with all_298_1, all_93_1, simplifying
% 118.62/16.43 | | | | | | with (39), (53) gives:
% 118.62/16.43 | | | | | | (120) ? [v0: any] : ? [v1: any] : (strictorderedP(all_93_1) =
% 118.62/16.43 | | | | | | v1 & ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | GROUND_INST: instantiating (8) with all_298_1, all_93_1, simplifying
% 118.62/16.43 | | | | | | with (39), (53) gives:
% 118.62/16.43 | | | | | | (121) ? [v0: any] : ? [v1: any] : (totalorderedP(all_93_1) = v1
% 118.62/16.43 | | | | | | & ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | GROUND_INST: instantiating (7) with all_298_1, all_93_1, simplifying
% 118.62/16.43 | | | | | | with (39), (53) gives:
% 118.62/16.43 | | | | | | (122) ? [v0: any] : ? [v1: any] : (strictorderP(all_93_1) = v1
% 118.62/16.43 | | | | | | & ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | GROUND_INST: instantiating (6) with all_298_1, all_93_1, simplifying
% 118.62/16.43 | | | | | | with (39), (53) gives:
% 118.62/16.43 | | | | | | (123) ? [v0: any] : ? [v1: any] : (totalorderP(all_93_1) = v1 &
% 118.62/16.43 | | | | | | ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | GROUND_INST: instantiating (5) with all_298_1, all_93_1, simplifying
% 118.62/16.43 | | | | | | with (39), (53) gives:
% 118.62/16.43 | | | | | | (124) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_93_1) = v1 &
% 118.62/16.43 | | | | | | ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | DELTA: instantiating (115) with fresh symbol all_1121_0 gives:
% 118.62/16.43 | | | | | | (125) ~ (all_1121_0 = 0) & ssItem(all_298_1) = all_1121_0
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | ALPHA: (125) implies:
% 118.62/16.43 | | | | | | (126) ~ (all_1121_0 = 0)
% 118.62/16.43 | | | | | | (127) ssItem(all_298_1) = all_1121_0
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | DELTA: instantiating (124) with fresh symbols all_1123_0, all_1123_1
% 118.62/16.43 | | | | | | gives:
% 118.62/16.43 | | | | | | (128) cyclefreeP(all_93_1) = all_1123_0 & ssItem(all_298_1) =
% 118.62/16.43 | | | | | | all_1123_1 & ( ~ (all_1123_1 = 0) | all_1123_0 = 0)
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | ALPHA: (128) implies:
% 118.62/16.43 | | | | | | (129) ssItem(all_298_1) = all_1123_1
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | DELTA: instantiating (122) with fresh symbols all_1125_0, all_1125_1
% 118.62/16.43 | | | | | | gives:
% 118.62/16.43 | | | | | | (130) strictorderP(all_93_1) = all_1125_0 & ssItem(all_298_1) =
% 118.62/16.43 | | | | | | all_1125_1 & ( ~ (all_1125_1 = 0) | all_1125_0 = 0)
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | ALPHA: (130) implies:
% 118.62/16.43 | | | | | | (131) ssItem(all_298_1) = all_1125_1
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | DELTA: instantiating (121) with fresh symbols all_1127_0, all_1127_1
% 118.62/16.43 | | | | | | gives:
% 118.62/16.43 | | | | | | (132) totalorderedP(all_93_1) = all_1127_0 & ssItem(all_298_1) =
% 118.62/16.43 | | | | | | all_1127_1 & ( ~ (all_1127_1 = 0) | all_1127_0 = 0)
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | ALPHA: (132) implies:
% 118.62/16.43 | | | | | | (133) ssItem(all_298_1) = all_1127_1
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | DELTA: instantiating (123) with fresh symbols all_1129_0, all_1129_1
% 118.62/16.43 | | | | | | gives:
% 118.62/16.43 | | | | | | (134) totalorderP(all_93_1) = all_1129_0 & ssItem(all_298_1) =
% 118.62/16.43 | | | | | | all_1129_1 & ( ~ (all_1129_1 = 0) | all_1129_0 = 0)
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | ALPHA: (134) implies:
% 118.62/16.43 | | | | | | (135) ssItem(all_298_1) = all_1129_1
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | DELTA: instantiating (120) with fresh symbols all_1131_0, all_1131_1
% 118.62/16.43 | | | | | | gives:
% 118.62/16.43 | | | | | | (136) strictorderedP(all_93_1) = all_1131_0 & ssItem(all_298_1) =
% 118.62/16.43 | | | | | | all_1131_1 & ( ~ (all_1131_1 = 0) | all_1131_0 = 0)
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | ALPHA: (136) implies:
% 118.62/16.43 | | | | | | (137) ssItem(all_298_1) = all_1131_1
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | DELTA: instantiating (118) with fresh symbols all_1133_0, all_1133_1
% 118.62/16.43 | | | | | | gives:
% 118.62/16.43 | | | | | | (138) equalelemsP(all_93_1) = all_1133_0 & ssItem(all_298_1) =
% 118.62/16.43 | | | | | | all_1133_1 & ( ~ (all_1133_1 = 0) | all_1133_0 = 0)
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | ALPHA: (138) implies:
% 118.62/16.43 | | | | | | (139) ssItem(all_298_1) = all_1133_1
% 118.62/16.43 | | | | | |
% 118.62/16.43 | | | | | | DELTA: instantiating (119) with fresh symbols all_1135_0, all_1135_1
% 118.62/16.43 | | | | | | gives:
% 118.62/16.44 | | | | | | (140) duplicatefreeP(all_93_1) = all_1135_0 & ssItem(all_298_1) =
% 118.62/16.44 | | | | | | all_1135_1 & ( ~ (all_1135_1 = 0) | all_1135_0 = 0)
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | ALPHA: (140) implies:
% 118.62/16.44 | | | | | | (141) ssItem(all_298_1) = all_1135_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | DELTA: instantiating (117) with fresh symbols all_1137_0, all_1137_1
% 118.62/16.44 | | | | | | gives:
% 118.62/16.44 | | | | | | (142) hd(all_93_1) = all_1137_0 & ssItem(all_298_1) = all_1137_1
% 118.62/16.44 | | | | | | & $i(all_1137_0) & ( ~ (all_1137_1 = 0) | all_1137_0 =
% 118.62/16.44 | | | | | | all_298_1)
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | ALPHA: (142) implies:
% 118.62/16.44 | | | | | | (143) ssItem(all_298_1) = all_1137_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | DELTA: instantiating (116) with fresh symbols all_1139_0, all_1139_1
% 118.62/16.44 | | | | | | gives:
% 118.62/16.44 | | | | | | (144) tl(all_93_1) = all_1139_0 & ssItem(all_298_1) = all_1139_1
% 118.62/16.44 | | | | | | & $i(all_1139_0) & ( ~ (all_1139_1 = 0) | all_1139_0 = nil)
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | ALPHA: (144) implies:
% 118.62/16.44 | | | | | | (145) ssItem(all_298_1) = all_1139_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | GROUND_INST: instantiating (14) with all_1121_0, all_1127_1,
% 118.62/16.44 | | | | | | all_298_1, simplifying with (127), (133) gives:
% 118.62/16.44 | | | | | | (146) all_1127_1 = all_1121_0
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | GROUND_INST: instantiating (14) with all_1127_1, all_1129_1,
% 118.62/16.44 | | | | | | all_298_1, simplifying with (133), (135) gives:
% 118.62/16.44 | | | | | | (147) all_1129_1 = all_1127_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | GROUND_INST: instantiating (14) with all_1127_1, all_1133_1,
% 118.62/16.44 | | | | | | all_298_1, simplifying with (133), (139) gives:
% 118.62/16.44 | | | | | | (148) all_1133_1 = all_1127_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | GROUND_INST: instantiating (14) with all_1125_1, all_1133_1,
% 118.62/16.44 | | | | | | all_298_1, simplifying with (131), (139) gives:
% 118.62/16.44 | | | | | | (149) all_1133_1 = all_1125_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | GROUND_INST: instantiating (14) with all_1127_1, all_1135_1,
% 118.62/16.44 | | | | | | all_298_1, simplifying with (133), (141) gives:
% 118.62/16.44 | | | | | | (150) all_1135_1 = all_1127_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | GROUND_INST: instantiating (14) with all_1123_1, all_1135_1,
% 118.62/16.44 | | | | | | all_298_1, simplifying with (129), (141) gives:
% 118.62/16.44 | | | | | | (151) all_1135_1 = all_1123_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | GROUND_INST: instantiating (14) with 0, all_1137_1, all_298_1,
% 118.62/16.44 | | | | | | simplifying with (40), (143) gives:
% 118.62/16.44 | | | | | | (152) all_1137_1 = 0
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | GROUND_INST: instantiating (14) with all_1129_1, all_1137_1,
% 118.62/16.44 | | | | | | all_298_1, simplifying with (135), (143) gives:
% 118.62/16.44 | | | | | | (153) all_1137_1 = all_1129_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | GROUND_INST: instantiating (14) with all_1135_1, all_1139_1,
% 118.62/16.44 | | | | | | all_298_1, simplifying with (141), (145) gives:
% 118.62/16.44 | | | | | | (154) all_1139_1 = all_1135_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | GROUND_INST: instantiating (14) with all_1131_1, all_1139_1,
% 118.62/16.44 | | | | | | all_298_1, simplifying with (137), (145) gives:
% 118.62/16.44 | | | | | | (155) all_1139_1 = all_1131_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | COMBINE_EQS: (154), (155) imply:
% 118.62/16.44 | | | | | | (156) all_1135_1 = all_1131_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | SIMP: (156) implies:
% 118.62/16.44 | | | | | | (157) all_1135_1 = all_1131_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | COMBINE_EQS: (152), (153) imply:
% 118.62/16.44 | | | | | | (158) all_1129_1 = 0
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | SIMP: (158) implies:
% 118.62/16.44 | | | | | | (159) all_1129_1 = 0
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | COMBINE_EQS: (151), (157) imply:
% 118.62/16.44 | | | | | | (160) all_1131_1 = all_1123_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | COMBINE_EQS: (150), (157) imply:
% 118.62/16.44 | | | | | | (161) all_1131_1 = all_1127_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | COMBINE_EQS: (148), (149) imply:
% 118.62/16.44 | | | | | | (162) all_1127_1 = all_1125_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | SIMP: (162) implies:
% 118.62/16.44 | | | | | | (163) all_1127_1 = all_1125_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | COMBINE_EQS: (160), (161) imply:
% 118.62/16.44 | | | | | | (164) all_1127_1 = all_1123_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | SIMP: (164) implies:
% 118.62/16.44 | | | | | | (165) all_1127_1 = all_1123_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | COMBINE_EQS: (147), (159) imply:
% 118.62/16.44 | | | | | | (166) all_1127_1 = 0
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | SIMP: (166) implies:
% 118.62/16.44 | | | | | | (167) all_1127_1 = 0
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | COMBINE_EQS: (163), (165) imply:
% 118.62/16.44 | | | | | | (168) all_1125_1 = all_1123_1
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | COMBINE_EQS: (163), (167) imply:
% 118.62/16.44 | | | | | | (169) all_1125_1 = 0
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | COMBINE_EQS: (146), (163) imply:
% 118.62/16.44 | | | | | | (170) all_1125_1 = all_1121_0
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | COMBINE_EQS: (168), (170) imply:
% 118.62/16.44 | | | | | | (171) all_1123_1 = all_1121_0
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | COMBINE_EQS: (168), (169) imply:
% 118.62/16.44 | | | | | | (172) all_1123_1 = 0
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | COMBINE_EQS: (171), (172) imply:
% 118.62/16.44 | | | | | | (173) all_1121_0 = 0
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | SIMP: (173) implies:
% 118.62/16.44 | | | | | | (174) all_1121_0 = 0
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | REDUCE: (126), (174) imply:
% 118.62/16.44 | | | | | | (175) $false
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | CLOSE: (175) is inconsistent.
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | End of split
% 118.62/16.44 | | | | |
% 118.62/16.44 | | | | End of split
% 118.62/16.44 | | | |
% 118.62/16.44 | | | End of split
% 118.62/16.44 | | |
% 118.62/16.44 | | End of split
% 118.62/16.44 | |
% 118.62/16.44 | Case 2:
% 118.62/16.44 | |
% 118.62/16.44 | | (176) all_97_2 = nil & all_93_1 = nil
% 118.62/16.44 | |
% 118.62/16.44 | | ALPHA: (176) implies:
% 118.62/16.44 | | (177) all_93_1 = nil
% 118.62/16.44 | | (178) all_97_2 = nil
% 118.62/16.44 | |
% 118.62/16.44 | | REDUCE: (25), (177), (178) imply:
% 118.62/16.44 | | (179) segmentP(nil, nil) = all_97_1
% 118.62/16.44 | |
% 118.62/16.44 | | BETA: splitting (35) gives:
% 118.62/16.44 | |
% 118.62/16.44 | | Case 1:
% 118.62/16.44 | | |
% 118.62/16.44 | | | (180) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 118.62/16.44 | | |
% 118.62/16.44 | | | REF_CLOSE: (2), (15), (180) are inconsistent by sub-proof #1.
% 118.62/16.44 | | |
% 118.62/16.44 | | Case 2:
% 118.62/16.44 | | |
% 118.62/16.44 | | | (181) ( ~ (all_97_0 = 0) | ~ (all_97_2 = nil)) & (all_97_0 = 0 |
% 118.62/16.44 | | | all_97_2 = nil)
% 118.62/16.44 | | |
% 118.62/16.44 | | | ALPHA: (181) implies:
% 118.62/16.44 | | | (182) ~ (all_97_0 = 0) | ~ (all_97_2 = nil)
% 118.62/16.44 | | |
% 118.62/16.44 | | | BETA: splitting (182) gives:
% 118.62/16.44 | | |
% 118.62/16.44 | | | Case 1:
% 118.62/16.44 | | | |
% 118.62/16.44 | | | | (183) ~ (all_97_2 = nil)
% 118.62/16.44 | | | |
% 118.62/16.44 | | | | REDUCE: (178), (183) imply:
% 118.62/16.44 | | | | (184) $false
% 118.62/16.44 | | | |
% 118.62/16.44 | | | | CLOSE: (184) is inconsistent.
% 118.62/16.44 | | | |
% 118.62/16.44 | | | Case 2:
% 118.62/16.44 | | | |
% 118.62/16.44 | | | | (185) ~ (all_97_0 = 0)
% 118.62/16.44 | | | |
% 118.62/16.44 | | | | BETA: splitting (27) gives:
% 118.62/16.44 | | | |
% 118.62/16.44 | | | | Case 1:
% 118.62/16.44 | | | | |
% 118.62/16.44 | | | | | (186) ~ (all_97_1 = 0)
% 118.62/16.44 | | | | |
% 118.62/16.44 | | | | | GROUND_INST: instantiating (4) with nil, all_97_1, simplifying with
% 118.62/16.44 | | | | | (12), (179) gives:
% 118.62/16.44 | | | | | (187) all_97_1 = 0 | ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) =
% 118.62/16.44 | | | | | v0)
% 118.62/16.44 | | | | |
% 118.62/16.44 | | | | | BETA: splitting (187) gives:
% 118.62/16.44 | | | | |
% 118.62/16.44 | | | | | Case 1:
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | (188) all_97_1 = 0
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | REDUCE: (186), (188) imply:
% 118.62/16.44 | | | | | | (189) $false
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | CLOSE: (189) is inconsistent.
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | Case 2:
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | (190) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | | REF_CLOSE: (2), (15), (190) are inconsistent by sub-proof #1.
% 118.62/16.44 | | | | | |
% 118.62/16.44 | | | | | End of split
% 118.62/16.44 | | | | |
% 118.62/16.44 | | | | Case 2:
% 118.62/16.44 | | | | |
% 118.62/16.44 | | | | | (191) all_97_0 = 0 & ~ (all_93_0 = 0)
% 118.62/16.44 | | | | |
% 118.62/16.44 | | | | | ALPHA: (191) implies:
% 118.62/16.44 | | | | | (192) all_97_0 = 0
% 118.62/16.44 | | | | |
% 118.62/16.44 | | | | | REDUCE: (185), (192) imply:
% 118.62/16.44 | | | | | (193) $false
% 118.62/16.44 | | | | |
% 118.62/16.44 | | | | | CLOSE: (193) is inconsistent.
% 118.62/16.44 | | | | |
% 118.62/16.44 | | | | End of split
% 118.62/16.44 | | | |
% 118.62/16.44 | | | End of split
% 118.62/16.44 | | |
% 118.62/16.44 | | End of split
% 118.62/16.44 | |
% 118.62/16.45 | End of split
% 118.62/16.45 |
% 118.62/16.45 End of proof
% 118.62/16.45
% 118.62/16.45 Sub-proof #1 shows that the following formulas are inconsistent:
% 118.62/16.45 ----------------------------------------------------------------
% 118.62/16.45 (1) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 118.62/16.45 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 118.62/16.45 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 118.62/16.45 (3) ssList(nil) = 0
% 118.62/16.45
% 118.62/16.45 Begin of proof
% 118.62/16.45 |
% 118.62/16.45 | DELTA: instantiating (1) with fresh symbol all_286_0 gives:
% 118.62/16.45 | (4) ~ (all_286_0 = 0) & ssList(nil) = all_286_0
% 118.62/16.45 |
% 118.62/16.45 | ALPHA: (4) implies:
% 118.62/16.45 | (5) ~ (all_286_0 = 0)
% 118.62/16.45 | (6) ssList(nil) = all_286_0
% 118.62/16.45 |
% 118.62/16.45 | DELTA: instantiating (1) with fresh symbol all_288_0 gives:
% 118.62/16.45 | (7) ~ (all_288_0 = 0) & ssList(nil) = all_288_0
% 118.62/16.45 |
% 118.62/16.45 | ALPHA: (7) implies:
% 118.62/16.45 | (8) ssList(nil) = all_288_0
% 118.62/16.45 |
% 118.62/16.45 | GROUND_INST: instantiating (2) with 0, all_288_0, nil, simplifying with (3),
% 118.62/16.45 | (8) gives:
% 118.62/16.45 | (9) all_288_0 = 0
% 118.62/16.45 |
% 118.62/16.45 | GROUND_INST: instantiating (2) with all_286_0, all_288_0, nil, simplifying
% 118.62/16.45 | with (6), (8) gives:
% 118.62/16.45 | (10) all_288_0 = all_286_0
% 118.62/16.45 |
% 118.62/16.45 | COMBINE_EQS: (9), (10) imply:
% 118.62/16.45 | (11) all_286_0 = 0
% 118.62/16.45 |
% 118.62/16.45 | REDUCE: (5), (11) imply:
% 118.62/16.45 | (12) $false
% 118.62/16.45 |
% 118.62/16.45 | CLOSE: (12) is inconsistent.
% 118.62/16.45 |
% 118.62/16.45 End of proof
% 118.62/16.45
% 118.62/16.45 Sub-proof #2 shows that the following formulas are inconsistent:
% 118.62/16.45 ----------------------------------------------------------------
% 118.62/16.45 (1) ~ (all_314_0 = 0) & ssList(all_93_1) = all_314_0
% 118.62/16.45 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 118.62/16.45 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 118.62/16.45 (3) ssList(all_93_1) = 0
% 118.62/16.45
% 118.62/16.45 Begin of proof
% 118.62/16.45 |
% 118.62/16.45 | ALPHA: (1) implies:
% 118.62/16.45 | (4) ~ (all_314_0 = 0)
% 118.62/16.45 | (5) ssList(all_93_1) = all_314_0
% 118.62/16.45 |
% 118.62/16.45 | GROUND_INST: instantiating (2) with 0, all_314_0, all_93_1, simplifying with
% 118.62/16.45 | (3), (5) gives:
% 118.62/16.45 | (6) all_314_0 = 0
% 118.62/16.45 |
% 118.62/16.45 | REDUCE: (4), (6) imply:
% 118.62/16.45 | (7) $false
% 118.62/16.45 |
% 118.62/16.45 | CLOSE: (7) is inconsistent.
% 118.62/16.45 |
% 118.62/16.45 End of proof
% 118.62/16.45 % SZS output end Proof for theBenchmark
% 118.62/16.45
% 118.62/16.45 15819ms
%------------------------------------------------------------------------------