TSTP Solution File: SWC320+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC320+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 : n009.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 20:50:49 EDT 2023
% Result : Theorem 22.18s 3.68s
% Output : Proof 75.42s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC320+1 : TPTP v8.1.2. Released v2.4.0.
% 0.03/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 15:05:05 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.57/0.60 ________ _____
% 0.57/0.60 ___ __ \_________(_)________________________________
% 0.57/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.57/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.57/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.57/0.60
% 0.57/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.57/0.60 (2023-06-19)
% 0.57/0.60
% 0.57/0.60 (c) Philipp Rümmer, 2009-2023
% 0.57/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.57/0.60 Amanda Stjerna.
% 0.57/0.60 Free software under BSD-3-Clause.
% 0.57/0.60
% 0.57/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.57/0.60
% 0.57/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.57/0.62 Running up to 7 provers in parallel.
% 0.57/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.57/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.57/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.57/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.57/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.57/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.57/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.62/1.48 Prover 4: Preprocessing ...
% 5.62/1.49 Prover 1: Preprocessing ...
% 5.91/1.52 Prover 5: Preprocessing ...
% 5.91/1.52 Prover 3: Preprocessing ...
% 5.91/1.52 Prover 6: Preprocessing ...
% 5.91/1.52 Prover 0: Preprocessing ...
% 5.91/1.52 Prover 2: Preprocessing ...
% 14.95/2.72 Prover 2: Proving ...
% 15.20/2.76 Prover 1: Constructing countermodel ...
% 15.20/2.79 Prover 3: Constructing countermodel ...
% 15.20/2.79 Prover 6: Proving ...
% 15.20/2.79 Prover 5: Constructing countermodel ...
% 20.51/3.48 Prover 4: Constructing countermodel ...
% 20.86/3.52 Prover 0: Proving ...
% 22.18/3.68 Prover 0: proved (3057ms)
% 22.18/3.68
% 22.18/3.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.18/3.68
% 22.18/3.68 Prover 5: stopped
% 22.18/3.68 Prover 2: stopped
% 22.18/3.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 22.18/3.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.18/3.68 Prover 3: stopped
% 22.18/3.69 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.18/3.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 22.18/3.70 Prover 6: stopped
% 22.18/3.70 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.24/3.92 Prover 7: Preprocessing ...
% 24.24/3.93 Prover 10: Preprocessing ...
% 24.24/3.95 Prover 13: Preprocessing ...
% 24.48/3.98 Prover 8: Preprocessing ...
% 24.48/4.00 Prover 11: Preprocessing ...
% 25.94/4.16 Prover 10: Constructing countermodel ...
% 26.53/4.24 Prover 7: Constructing countermodel ...
% 26.77/4.29 Prover 13: Constructing countermodel ...
% 27.78/4.43 Prover 8: Warning: ignoring some quantifiers
% 27.78/4.44 Prover 8: Constructing countermodel ...
% 34.81/5.30 Prover 11: Constructing countermodel ...
% 65.62/9.29 Prover 13: stopped
% 66.33/9.31 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 66.94/9.43 Prover 16: Preprocessing ...
% 68.05/9.58 Prover 16: Constructing countermodel ...
% 74.65/10.40 Prover 1: Found proof (size 191)
% 74.65/10.40 Prover 1: proved (9776ms)
% 74.65/10.40 Prover 16: stopped
% 74.65/10.40 Prover 8: stopped
% 74.65/10.40 Prover 7: stopped
% 74.65/10.40 Prover 4: stopped
% 74.65/10.40 Prover 10: stopped
% 74.65/10.40 Prover 11: stopped
% 74.65/10.40
% 74.65/10.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 74.65/10.40
% 74.65/10.42 % SZS output start Proof for theBenchmark
% 74.65/10.42 Assumptions after simplification:
% 74.65/10.42 ---------------------------------
% 74.65/10.42
% 74.65/10.42 (ax13)
% 75.06/10.45 ! [v0: $i] : ! [v1: any] : ( ~ (duplicatefreeP(v0) = v1) | ~ $i(v0) | ?
% 75.06/10.45 [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ! [v2: $i] :
% 75.06/10.45 ( ~ (ssItem(v2) = 0) | ~ $i(v2) | ! [v3: $i] : ( ~ (ssItem(v3) = 0) |
% 75.06/10.45 ~ $i(v3) | ! [v4: $i] : ( ~ (ssList(v4) = 0) | ~ $i(v4) | ! [v5:
% 75.06/10.45 $i] : ! [v6: $i] : ! [v7: $i] : ( ~ (cons(v2, v5) = v6) | ~
% 75.06/10.45 (app(v4, v6) = v7) | ~ $i(v5) | ? [v8: int] : ( ~ (v8 = 0) &
% 75.06/10.45 ssList(v5) = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ (v3 = v2) |
% 75.06/10.45 ~ (cons(v2, v8) = v9) | ~ (app(v7, v9) = v0) | ~ $i(v8) |
% 75.06/10.45 ? [v10: int] : ( ~ (v10 = 0) & ssList(v8) = v10))))))) & (v1 =
% 75.06/10.45 0 | ? [v2: $i] : (ssItem(v2) = 0 & $i(v2) & ? [v3: $i] : (ssItem(v3) =
% 75.06/10.45 0 & $i(v3) & ? [v4: $i] : (ssList(v4) = 0 & $i(v4) & ? [v5: $i] :
% 75.06/10.45 ? [v6: $i] : ? [v7: $i] : (ssList(v5) = 0 & cons(v2, v5) = v6 &
% 75.06/10.45 app(v4, v6) = v7 & $i(v7) & $i(v6) & $i(v5) & ? [v8: $i] : ?
% 75.06/10.45 [v9: $i] : (v3 = v2 & ssList(v8) = 0 & cons(v2, v8) = v9 &
% 75.06/10.45 app(v7, v9) = v0 & $i(v9) & $i(v8)))))))))
% 75.06/10.45
% 75.06/10.45 (ax15)
% 75.06/10.45 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 75.06/10.45 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 75.06/10.45 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 75.06/10.45
% 75.06/10.45 (ax16)
% 75.06/10.46 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : (
% 75.06/10.46 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: any] :
% 75.06/10.46 (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))))
% 75.06/10.46
% 75.06/10.46 (ax17)
% 75.06/10.46 ssList(nil) = 0 & $i(nil)
% 75.06/10.46
% 75.06/10.46 (ax2)
% 75.06/10.46 ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ( ~ (v1 = v0) &
% 75.06/10.46 ssItem(v1) = 0 & $i(v1)))
% 75.06/10.46
% 75.06/10.46 (ax20)
% 75.06/10.46 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1:
% 75.06/10.46 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 75.06/10.46 ssItem(v2) = 0 & $i(v2))))
% 75.06/10.46
% 75.06/10.46 (ax23)
% 75.06/10.46 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : (
% 75.06/10.46 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) =
% 75.06/10.46 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1))))
% 75.06/10.46
% 75.06/10.46 (ax25)
% 75.06/10.46 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : (
% 75.06/10.46 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) =
% 75.06/10.46 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0))))
% 75.06/10.46
% 75.06/10.46 (ax59)
% 75.06/10.46 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 75.06/10.46 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 75.06/10.46 (v2 = 0) | v3 = 0)))
% 75.06/10.46
% 75.06/10.46 (ax61)
% 75.06/10.46 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 75.06/10.46 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 75.06/10.46 (v2 = 0) | v3 = 0)))
% 75.06/10.46
% 75.06/10.46 (ax63)
% 75.06/10.46 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 75.06/10.46 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 75.06/10.46 (v2 = 0) | v3 = 0)))
% 75.06/10.46
% 75.06/10.46 (ax65)
% 75.06/10.46 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 75.06/10.46 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 75.06/10.46 (v2 = 0) | v3 = 0)))
% 75.06/10.46
% 75.06/10.46 (ax68)
% 75.06/10.46 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 75.06/10.46 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & (
% 75.06/10.46 ~ (v2 = 0) | v3 = 0)))
% 75.06/10.46
% 75.06/10.46 (ax71)
% 75.06/10.46 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 75.06/10.46 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & (
% 75.06/10.46 ~ (v2 = 0) | v3 = 0)))
% 75.06/10.46
% 75.06/10.46 (ax72)
% 75.06/10.46 duplicatefreeP(nil) = 0 & $i(nil)
% 75.06/10.46
% 75.06/10.46 (ax73)
% 75.06/10.46 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 75.06/10.46 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 75.06/10.46 (v2 = 0) | v3 = 0)))
% 75.06/10.46
% 75.06/10.46 (ax81)
% 75.06/10.47 $i(nil) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : !
% 75.06/10.47 [v2: $i] : ! [v3: $i] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) |
% 75.06/10.47 ~ $i(v1) | ? [v4: any] : ? [v5: $i] : (cons(v1, v0) = v5 & ssItem(v1) =
% 75.06/10.47 v4 & $i(v5) & ( ~ (v4 = 0) | v5 = v3))))
% 75.06/10.47
% 75.06/10.47 (co1)
% 75.06/10.47 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any]
% 75.06/10.47 : (ssList(v1) = 0 & neq(v1, nil) = v2 & $i(v1) & ( ~ (v2 = 0) | ? [v3: $i]
% 75.06/10.47 : ? [v4: $i] : (cons(v3, nil) = v4 & ssItem(v3) = 0 & $i(v4) & $i(v3) &
% 75.06/10.47 ? [v5: $i] : (ssList(v5) = 0 & app(v5, v4) = v1 & app(v4, v5) = v0 &
% 75.06/10.47 $i(v5)))) & ( ~ (v1 = nil) | v0 = nil) & ((v2 = 0 & ! [v3: $i] : !
% 75.06/10.47 [v4: $i] : ( ~ (cons(v3, nil) = v4) | ~ $i(v3) | ? [v5: int] : ( ~
% 75.06/10.47 (v5 = 0) & ssItem(v3) = v5) | ! [v5: $i] : ( ~ (app(v4, v5) = v0)
% 75.06/10.47 | ~ $i(v5) | ? [v6: any] : ? [v7: $i] : (ssList(v5) = v6 &
% 75.06/10.47 app(v5, v4) = v7 & $i(v7) & ( ~ (v7 = v1) | ~ (v6 = 0)))))) |
% 75.06/10.47 (v1 = nil & ~ (v0 = nil)))))
% 75.06/10.47
% 75.06/10.47 (function-axioms)
% 75.06/10.47 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 75.06/10.47 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 75.06/10.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 75.06/10.47 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 75.06/10.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 75.06/10.47 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 75.06/10.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 75.06/10.47 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 75.06/10.47 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 75.06/10.47 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 75.06/10.47 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 75.06/10.47 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 75.06/10.47 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 75.06/10.47 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 75.06/10.47 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 75.06/10.47 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 75.06/10.47 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 75.06/10.47 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 75.06/10.47 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 75.06/10.47 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 75.06/10.47 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 75.06/10.47 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 75.06/10.47 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 75.06/10.47 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 75.06/10.47 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 75.06/10.47 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 75.06/10.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 75.06/10.47 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 75.06/10.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 75.06/10.47 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 75.06/10.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 75.06/10.47 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 75.06/10.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 75.06/10.47 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 75.06/10.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 75.06/10.47 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 75.06/10.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 75.06/10.47 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 75.06/10.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 75.06/10.47 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 75.06/10.47 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 75.06/10.47 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 75.06/10.47 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 75.06/10.47
% 75.06/10.47 Further assumptions not needed in the proof:
% 75.06/10.47 --------------------------------------------
% 75.06/10.47 ax1, ax10, ax11, ax12, ax14, ax18, ax19, ax21, ax22, ax24, ax26, ax27, ax28,
% 75.06/10.47 ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax4,
% 75.06/10.47 ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51,
% 75.06/10.47 ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax6, ax60, ax62, ax64, ax66, ax67,
% 75.06/10.47 ax69, ax7, ax70, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax82, ax83,
% 75.06/10.47 ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 75.06/10.47
% 75.06/10.47 Those formulas are unsatisfiable:
% 75.06/10.47 ---------------------------------
% 75.06/10.47
% 75.06/10.47 Begin of proof
% 75.06/10.48 |
% 75.06/10.48 | ALPHA: (ax17) implies:
% 75.06/10.48 | (1) ssList(nil) = 0
% 75.06/10.48 |
% 75.06/10.48 | ALPHA: (ax20) implies:
% 75.06/10.48 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 75.06/10.48 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 75.06/10.48 | ssItem(v2) = 0 & $i(v2))))
% 75.06/10.48 |
% 75.06/10.48 | ALPHA: (ax59) implies:
% 75.06/10.48 | (3) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 75.06/10.48 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & (
% 75.06/10.48 | ~ (v2 = 0) | v3 = 0)))
% 75.06/10.48 |
% 75.06/10.48 | ALPHA: (ax61) implies:
% 75.06/10.48 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 75.06/10.48 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 &
% 75.06/10.48 | ( ~ (v2 = 0) | v3 = 0)))
% 75.06/10.48 |
% 75.06/10.48 | ALPHA: (ax63) implies:
% 75.06/10.48 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 75.06/10.48 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 &
% 75.06/10.48 | ( ~ (v2 = 0) | v3 = 0)))
% 75.06/10.48 |
% 75.06/10.48 | ALPHA: (ax65) implies:
% 75.06/10.48 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 75.06/10.48 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2
% 75.06/10.48 | & ( ~ (v2 = 0) | v3 = 0)))
% 75.06/10.48 |
% 75.06/10.48 | ALPHA: (ax68) implies:
% 75.06/10.48 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 75.06/10.48 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2
% 75.06/10.48 | & ( ~ (v2 = 0) | v3 = 0)))
% 75.06/10.48 |
% 75.06/10.48 | ALPHA: (ax71) implies:
% 75.06/10.48 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 75.06/10.48 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2
% 75.06/10.48 | & ( ~ (v2 = 0) | v3 = 0)))
% 75.06/10.48 |
% 75.06/10.48 | ALPHA: (ax72) implies:
% 75.06/10.48 | (9) duplicatefreeP(nil) = 0
% 75.06/10.48 |
% 75.06/10.48 | ALPHA: (ax73) implies:
% 75.06/10.48 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 75.06/10.48 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 &
% 75.06/10.48 | ( ~ (v2 = 0) | v3 = 0)))
% 75.06/10.48 |
% 75.06/10.48 | ALPHA: (ax81) implies:
% 75.06/10.48 | (11) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2:
% 75.06/10.48 | $i] : ! [v3: $i] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) =
% 75.06/10.48 | v3) | ~ $i(v1) | ? [v4: any] : ? [v5: $i] : (cons(v1, v0) =
% 75.06/10.48 | v5 & ssItem(v1) = v4 & $i(v5) & ( ~ (v4 = 0) | v5 = v3))))
% 75.06/10.48 |
% 75.06/10.48 | ALPHA: (co1) implies:
% 75.06/10.48 | (12) $i(nil)
% 75.06/10.49 | (13) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] :
% 75.06/10.49 | (ssList(v1) = 0 & neq(v1, nil) = v2 & $i(v1) & ( ~ (v2 = 0) | ?
% 75.06/10.49 | [v3: $i] : ? [v4: $i] : (cons(v3, nil) = v4 & ssItem(v3) = 0 &
% 75.06/10.49 | $i(v4) & $i(v3) & ? [v5: $i] : (ssList(v5) = 0 & app(v5, v4)
% 75.06/10.49 | = v1 & app(v4, v5) = v0 & $i(v5)))) & ( ~ (v1 = nil) | v0 =
% 75.06/10.49 | nil) & ((v2 = 0 & ! [v3: $i] : ! [v4: $i] : ( ~ (cons(v3, nil)
% 75.06/10.49 | = v4) | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) &
% 75.06/10.49 | ssItem(v3) = v5) | ! [v5: $i] : ( ~ (app(v4, v5) = v0) |
% 75.06/10.49 | ~ $i(v5) | ? [v6: any] : ? [v7: $i] : (ssList(v5) = v6 &
% 75.06/10.49 | app(v5, v4) = v7 & $i(v7) & ( ~ (v7 = v1) | ~ (v6 =
% 75.06/10.49 | 0)))))) | (v1 = nil & ~ (v0 = nil)))))
% 75.06/10.49 |
% 75.06/10.49 | ALPHA: (function-axioms) implies:
% 75.06/10.49 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 75.06/10.49 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 75.06/10.49 | (15) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 75.06/10.49 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 75.06/10.49 | (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 75.06/10.49 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 75.06/10.49 |
% 75.06/10.49 | DELTA: instantiating (ax2) with fresh symbol all_91_0 gives:
% 75.06/10.49 | (17) ssItem(all_91_0) = 0 & $i(all_91_0) & ? [v0: any] : ( ~ (v0 =
% 75.06/10.49 | all_91_0) & ssItem(v0) = 0 & $i(v0))
% 75.06/10.49 |
% 75.06/10.49 | ALPHA: (17) implies:
% 75.06/10.49 | (18) $i(all_91_0)
% 75.06/10.49 | (19) ssItem(all_91_0) = 0
% 75.06/10.49 |
% 75.06/10.49 | DELTA: instantiating (13) with fresh symbol all_93_0 gives:
% 75.06/10.49 | (20) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : ? [v1: any] :
% 75.06/10.49 | (ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ( ~ (v1 = 0) | ? [v2:
% 75.06/10.49 | $i] : ? [v3: $i] : (cons(v2, nil) = v3 & ssItem(v2) = 0 &
% 75.06/10.49 | $i(v3) & $i(v2) & ? [v4: $i] : (ssList(v4) = 0 & app(v4, v3) =
% 75.06/10.49 | v0 & app(v3, v4) = all_93_0 & $i(v4)))) & ( ~ (v0 = nil) |
% 75.06/10.49 | all_93_0 = nil) & ((v1 = 0 & ! [v2: $i] : ! [v3: $i] : ( ~
% 75.06/10.49 | (cons(v2, nil) = v3) | ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0)
% 75.06/10.49 | & ssItem(v2) = v4) | ! [v4: $i] : ( ~ (app(v3, v4) =
% 75.06/10.49 | all_93_0) | ~ $i(v4) | ? [v5: any] : ? [v6: $i] :
% 75.06/10.49 | (ssList(v4) = v5 & app(v4, v3) = v6 & $i(v6) & ( ~ (v6 = v0)
% 75.06/10.49 | | ~ (v5 = 0)))))) | (v0 = nil & ~ (all_93_0 = nil))))
% 75.06/10.49 |
% 75.06/10.49 | ALPHA: (20) implies:
% 75.06/10.49 | (21) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 75.06/10.49 | $i(v0) & ( ~ (v1 = 0) | ? [v2: $i] : ? [v3: $i] : (cons(v2, nil) =
% 75.06/10.49 | v3 & ssItem(v2) = 0 & $i(v3) & $i(v2) & ? [v4: $i] :
% 75.06/10.49 | (ssList(v4) = 0 & app(v4, v3) = v0 & app(v3, v4) = all_93_0 &
% 75.06/10.49 | $i(v4)))) & ( ~ (v0 = nil) | all_93_0 = nil) & ((v1 = 0 & !
% 75.06/10.49 | [v2: $i] : ! [v3: $i] : ( ~ (cons(v2, nil) = v3) | ~ $i(v2) |
% 75.06/10.49 | ? [v4: int] : ( ~ (v4 = 0) & ssItem(v2) = v4) | ! [v4: $i] :
% 75.06/10.49 | ( ~ (app(v3, v4) = all_93_0) | ~ $i(v4) | ? [v5: any] : ?
% 75.06/10.49 | [v6: $i] : (ssList(v4) = v5 & app(v4, v3) = v6 & $i(v6) & (
% 75.06/10.49 | ~ (v6 = v0) | ~ (v5 = 0)))))) | (v0 = nil & ~
% 75.06/10.49 | (all_93_0 = nil))))
% 75.06/10.49 |
% 75.06/10.49 | DELTA: instantiating (21) with fresh symbols all_97_0, all_97_1 gives:
% 75.06/10.50 | (22) ssList(all_97_1) = 0 & neq(all_97_1, nil) = all_97_0 & $i(all_97_1) &
% 75.06/10.50 | ( ~ (all_97_0 = 0) | ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 &
% 75.06/10.50 | ssItem(v0) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 &
% 75.06/10.50 | app(v2, v1) = all_97_1 & app(v1, v2) = all_93_0 & $i(v2)))) & (
% 75.06/10.50 | ~ (all_97_1 = nil) | all_93_0 = nil) & ((all_97_0 = 0 & ! [v0: $i]
% 75.06/10.50 | : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ? [v2:
% 75.06/10.50 | int] : ( ~ (v2 = 0) & ssItem(v0) = v2) | ! [v2: $i] : ( ~
% 75.06/10.50 | (app(v1, v2) = all_93_0) | ~ $i(v2) | ? [v3: any] : ? [v4:
% 75.06/10.50 | $i] : (ssList(v2) = v3 & app(v2, v1) = v4 & $i(v4) & ( ~ (v4
% 75.06/10.50 | = all_97_1) | ~ (v3 = 0)))))) | (all_97_1 = nil & ~
% 75.06/10.50 | (all_93_0 = nil)))
% 75.06/10.50 |
% 75.06/10.50 | ALPHA: (22) implies:
% 75.06/10.50 | (23) $i(all_97_1)
% 75.06/10.50 | (24) neq(all_97_1, nil) = all_97_0
% 75.06/10.50 | (25) ssList(all_97_1) = 0
% 75.06/10.50 | (26) (all_97_0 = 0 & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) |
% 75.06/10.50 | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v0) = v2) | !
% 75.06/10.50 | [v2: $i] : ( ~ (app(v1, v2) = all_93_0) | ~ $i(v2) | ? [v3: any]
% 75.06/10.50 | : ? [v4: $i] : (ssList(v2) = v3 & app(v2, v1) = v4 & $i(v4) & (
% 75.06/10.50 | ~ (v4 = all_97_1) | ~ (v3 = 0)))))) | (all_97_1 = nil & ~
% 75.06/10.50 | (all_93_0 = nil))
% 75.06/10.50 | (27) ~ (all_97_1 = nil) | all_93_0 = nil
% 75.06/10.50 | (28) ~ (all_97_0 = 0) | ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 &
% 75.06/10.50 | ssItem(v0) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 &
% 75.06/10.50 | app(v2, v1) = all_97_1 & app(v1, v2) = all_93_0 & $i(v2)))
% 75.06/10.50 |
% 75.06/10.50 | GROUND_INST: instantiating (ax25) with nil, simplifying with (1), (12) gives:
% 75.06/10.50 | (29) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 75.06/10.50 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) &
% 75.06/10.50 | ( ~ (v2 = 0) | v3 = nil)))
% 75.06/10.50 |
% 75.06/10.50 | GROUND_INST: instantiating (ax23) with nil, simplifying with (1), (12) gives:
% 75.06/10.50 | (30) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 75.06/10.50 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) &
% 75.06/10.50 | ( ~ (v2 = 0) | v3 = v0)))
% 75.06/10.50 |
% 75.06/10.50 | GROUND_INST: instantiating (ax16) with nil, simplifying with (1), (12) gives:
% 75.06/10.50 | (31) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 75.06/10.50 | [v2: any] : ? [v3: any] : (ssList(v1) = v3 & ssItem(v0) = v2 & ( ~
% 75.06/10.50 | (v2 = 0) | v3 = 0)))
% 75.06/10.50 |
% 75.06/10.50 | GROUND_INST: instantiating (2) with all_97_1, simplifying with (23), (25)
% 75.06/10.50 | gives:
% 75.06/10.50 | (32) all_97_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i]
% 75.06/10.50 | : (cons(v1, v0) = all_97_1 & ssItem(v1) = 0 & $i(v1)))
% 75.06/10.50 |
% 75.06/10.50 | GROUND_INST: instantiating (ax15) with all_97_1, simplifying with (23), (25)
% 75.06/10.50 | gives:
% 75.06/10.50 | (33) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_1, v0) = v1) | ~ $i(v0)
% 75.06/10.50 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 75.06/10.50 | ~ (v0 = all_97_1)) & (v1 = 0 | v0 = all_97_1)))
% 75.06/10.50 |
% 75.06/10.50 | GROUND_INST: instantiating (ax13) with nil, 0, simplifying with (9), (12)
% 75.06/10.50 | gives:
% 75.06/10.50 | (34) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0: $i] : ( ~
% 75.06/10.50 | (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1) = 0) |
% 75.06/10.50 | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) = 0) | ~ $i(v2) | !
% 75.06/10.50 | [v3: $i] : ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v0, v3) = v4) |
% 75.06/10.50 | ~ (app(v2, v4) = v5) | ~ $i(v3) | ? [v6: int] : ( ~ (v6 =
% 75.06/10.50 | 0) & ssList(v3) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~
% 75.06/10.50 | (v1 = v0) | ~ (cons(v0, v6) = v7) | ~ (app(v5, v7) = nil)
% 75.06/10.50 | | ~ $i(v6) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v6) =
% 75.06/10.50 | v8))))))
% 75.06/10.50 |
% 75.06/10.50 | GROUND_INST: instantiating (33) with nil, all_97_0, simplifying with (12),
% 75.06/10.50 | (24) gives:
% 75.06/10.51 | (35) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_97_0 = 0)
% 75.06/10.51 | | ~ (all_97_1 = nil)) & (all_97_0 = 0 | all_97_1 = nil))
% 75.06/10.51 |
% 75.06/10.51 | BETA: splitting (34) gives:
% 75.06/10.51 |
% 75.06/10.51 | Case 1:
% 75.06/10.51 | |
% 75.06/10.51 | | (36) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 75.06/10.51 | |
% 75.06/10.51 | | REF_CLOSE: (1), (15), (36) are inconsistent by sub-proof #1.
% 75.06/10.51 | |
% 75.06/10.51 | Case 2:
% 75.06/10.51 | |
% 75.06/10.51 | | (37) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~
% 75.06/10.51 | | (ssItem(v1) = 0) | ~ $i(v1) | ! [v2: $i] : ( ~ (ssList(v2) =
% 75.06/10.51 | | 0) | ~ $i(v2) | ! [v3: $i] : ! [v4: $i] : ! [v5: $i] : (
% 75.06/10.51 | | ~ (cons(v0, v3) = v4) | ~ (app(v2, v4) = v5) | ~ $i(v3) |
% 75.06/10.51 | | ? [v6: int] : ( ~ (v6 = 0) & ssList(v3) = v6) | ! [v6: $i]
% 75.06/10.51 | | : ! [v7: $i] : ( ~ (v1 = v0) | ~ (cons(v0, v6) = v7) | ~
% 75.06/10.51 | | (app(v5, v7) = nil) | ~ $i(v6) | ? [v8: int] : ( ~ (v8 =
% 75.06/10.51 | | 0) & ssList(v6) = v8))))))
% 75.06/10.51 | |
% 75.06/10.51 | | BETA: splitting (26) gives:
% 75.06/10.51 | |
% 75.06/10.51 | | Case 1:
% 75.06/10.51 | | |
% 75.06/10.51 | | | (38) all_97_0 = 0 & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) =
% 75.06/10.51 | | | v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v0) =
% 75.06/10.51 | | | v2) | ! [v2: $i] : ( ~ (app(v1, v2) = all_93_0) | ~ $i(v2) |
% 75.06/10.51 | | | ? [v3: any] : ? [v4: $i] : (ssList(v2) = v3 & app(v2, v1) =
% 75.06/10.51 | | | v4 & $i(v4) & ( ~ (v4 = all_97_1) | ~ (v3 = 0)))))
% 75.06/10.51 | | |
% 75.06/10.51 | | | ALPHA: (38) implies:
% 75.06/10.51 | | | (39) all_97_0 = 0
% 75.06/10.51 | | | (40) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 75.06/10.51 | | | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v0) = v2) | ! [v2: $i] : (
% 75.06/10.51 | | | ~ (app(v1, v2) = all_93_0) | ~ $i(v2) | ? [v3: any] : ?
% 75.06/10.51 | | | [v4: $i] : (ssList(v2) = v3 & app(v2, v1) = v4 & $i(v4) & ( ~
% 75.06/10.51 | | | (v4 = all_97_1) | ~ (v3 = 0)))))
% 75.06/10.51 | | |
% 75.06/10.51 | | | BETA: splitting (35) gives:
% 75.06/10.51 | | |
% 75.06/10.51 | | | Case 1:
% 75.06/10.51 | | | |
% 75.06/10.51 | | | | (41) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 75.06/10.51 | | | |
% 75.06/10.51 | | | | REF_CLOSE: (1), (15), (41) are inconsistent by sub-proof #1.
% 75.06/10.51 | | | |
% 75.06/10.51 | | | Case 2:
% 75.06/10.51 | | | |
% 75.06/10.51 | | | | (42) ( ~ (all_97_0 = 0) | ~ (all_97_1 = nil)) & (all_97_0 = 0 |
% 75.06/10.51 | | | | all_97_1 = nil)
% 75.06/10.51 | | | |
% 75.06/10.51 | | | | ALPHA: (42) implies:
% 75.06/10.51 | | | | (43) ~ (all_97_0 = 0) | ~ (all_97_1 = nil)
% 75.06/10.51 | | | |
% 75.06/10.51 | | | | BETA: splitting (28) gives:
% 75.06/10.51 | | | |
% 75.06/10.51 | | | | Case 1:
% 75.06/10.51 | | | | |
% 75.06/10.51 | | | | | (44) ~ (all_97_0 = 0)
% 75.06/10.51 | | | | |
% 75.06/10.51 | | | | | REDUCE: (39), (44) imply:
% 75.06/10.51 | | | | | (45) $false
% 75.06/10.51 | | | | |
% 75.06/10.51 | | | | | CLOSE: (45) is inconsistent.
% 75.06/10.51 | | | | |
% 75.06/10.51 | | | | Case 2:
% 75.06/10.51 | | | | |
% 75.06/10.51 | | | | | (46) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) =
% 75.06/10.51 | | | | | 0 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) = 0 &
% 75.06/10.51 | | | | | app(v2, v1) = all_97_1 & app(v1, v2) = all_93_0 & $i(v2)))
% 75.06/10.51 | | | | |
% 75.06/10.51 | | | | | DELTA: instantiating (46) with fresh symbols all_301_0, all_301_1
% 75.06/10.51 | | | | | gives:
% 75.06/10.51 | | | | | (47) cons(all_301_1, nil) = all_301_0 & ssItem(all_301_1) = 0 &
% 75.06/10.51 | | | | | $i(all_301_0) & $i(all_301_1) & ? [v0: $i] : (ssList(v0) = 0
% 75.06/10.51 | | | | | & app(v0, all_301_0) = all_97_1 & app(all_301_0, v0) =
% 75.06/10.51 | | | | | all_93_0 & $i(v0))
% 75.06/10.51 | | | | |
% 75.06/10.51 | | | | | ALPHA: (47) implies:
% 75.06/10.51 | | | | | (48) $i(all_301_1)
% 75.06/10.51 | | | | | (49) ssItem(all_301_1) = 0
% 75.06/10.51 | | | | | (50) cons(all_301_1, nil) = all_301_0
% 75.06/10.51 | | | | | (51) ? [v0: $i] : (ssList(v0) = 0 & app(v0, all_301_0) = all_97_1
% 75.06/10.51 | | | | | & app(all_301_0, v0) = all_93_0 & $i(v0))
% 75.06/10.51 | | | | |
% 75.06/10.51 | | | | | DELTA: instantiating (51) with fresh symbol all_303_0 gives:
% 75.06/10.51 | | | | | (52) ssList(all_303_0) = 0 & app(all_303_0, all_301_0) = all_97_1 &
% 75.06/10.51 | | | | | app(all_301_0, all_303_0) = all_93_0 & $i(all_303_0)
% 75.06/10.51 | | | | |
% 75.06/10.51 | | | | | ALPHA: (52) implies:
% 75.06/10.51 | | | | | (53) $i(all_303_0)
% 75.06/10.51 | | | | | (54) app(all_301_0, all_303_0) = all_93_0
% 75.06/10.51 | | | | | (55) app(all_303_0, all_301_0) = all_97_1
% 75.06/10.51 | | | | | (56) ssList(all_303_0) = 0
% 75.06/10.51 | | | | |
% 75.06/10.51 | | | | | BETA: splitting (43) gives:
% 75.06/10.51 | | | | |
% 75.06/10.51 | | | | | Case 1:
% 75.06/10.51 | | | | | |
% 75.06/10.51 | | | | | | (57) ~ (all_97_1 = nil)
% 75.06/10.51 | | | | | |
% 75.06/10.51 | | | | | | BETA: splitting (32) gives:
% 75.06/10.51 | | | | | |
% 75.06/10.51 | | | | | | Case 1:
% 75.06/10.51 | | | | | | |
% 75.06/10.51 | | | | | | | (58) all_97_1 = nil
% 75.06/10.51 | | | | | | |
% 75.06/10.51 | | | | | | | REDUCE: (57), (58) imply:
% 75.06/10.51 | | | | | | | (59) $false
% 75.06/10.51 | | | | | | |
% 75.06/10.51 | | | | | | | CLOSE: (59) is inconsistent.
% 75.06/10.51 | | | | | | |
% 75.06/10.51 | | | | | | Case 2:
% 75.06/10.51 | | | | | | |
% 75.06/10.51 | | | | | | | (60) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] :
% 75.06/10.52 | | | | | | | (cons(v1, v0) = all_97_1 & ssItem(v1) = 0 & $i(v1)))
% 75.06/10.52 | | | | | | |
% 75.06/10.52 | | | | | | | DELTA: instantiating (60) with fresh symbol all_313_0 gives:
% 75.06/10.52 | | | | | | | (61) ssList(all_313_0) = 0 & $i(all_313_0) & ? [v0: $i] :
% 75.06/10.52 | | | | | | | (cons(v0, all_313_0) = all_97_1 & ssItem(v0) = 0 & $i(v0))
% 75.06/10.52 | | | | | | |
% 75.06/10.52 | | | | | | | ALPHA: (61) implies:
% 75.06/10.52 | | | | | | | (62) $i(all_313_0)
% 75.06/10.52 | | | | | | | (63) ssList(all_313_0) = 0
% 75.06/10.52 | | | | | | | (64) ? [v0: $i] : (cons(v0, all_313_0) = all_97_1 & ssItem(v0)
% 75.06/10.52 | | | | | | | = 0 & $i(v0))
% 75.06/10.52 | | | | | | |
% 75.06/10.52 | | | | | | | DELTA: instantiating (64) with fresh symbol all_315_0 gives:
% 75.06/10.52 | | | | | | | (65) cons(all_315_0, all_313_0) = all_97_1 & ssItem(all_315_0)
% 75.06/10.52 | | | | | | | = 0 & $i(all_315_0)
% 75.06/10.52 | | | | | | |
% 75.06/10.52 | | | | | | | ALPHA: (65) implies:
% 75.06/10.52 | | | | | | | (66) $i(all_315_0)
% 75.06/10.52 | | | | | | | (67) ssItem(all_315_0) = 0
% 75.06/10.52 | | | | | | | (68) cons(all_315_0, all_313_0) = all_97_1
% 75.06/10.52 | | | | | | |
% 75.06/10.52 | | | | | | | GROUND_INST: instantiating (37) with all_301_1, simplifying with
% 75.06/10.52 | | | | | | | (48), (49) gives:
% 75.06/10.52 | | | | | | | (69) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1:
% 75.06/10.52 | | | | | | | $i] : ( ~ (ssList(v1) = 0) | ~ $i(v1) | ! [v2: $i] :
% 75.06/10.52 | | | | | | | ! [v3: $i] : ! [v4: $i] : ( ~ (cons(all_301_1, v2) =
% 75.06/10.52 | | | | | | | v3) | ~ (app(v1, v3) = v4) | ~ $i(v2) | ? [v5:
% 75.06/10.52 | | | | | | | int] : ( ~ (v5 = 0) & ssList(v2) = v5) | ! [v5:
% 75.06/10.52 | | | | | | | $i] : ! [v6: $i] : ( ~ (v0 = all_301_1) | ~
% 75.06/10.52 | | | | | | | (cons(all_301_1, v5) = v6) | ~ (app(v4, v6) =
% 75.06/10.52 | | | | | | | nil) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 = 0) &
% 75.06/10.52 | | | | | | | ssList(v5) = v7)))))
% 75.06/10.52 | | | | | | |
% 75.06/10.52 | | | | | | | GROUND_INST: instantiating (29) with all_301_1, all_301_0,
% 75.06/10.52 | | | | | | | simplifying with (48), (50) gives:
% 75.06/10.52 | | | | | | | (70) ? [v0: any] : ? [v1: $i] : (tl(all_301_0) = v1 &
% 75.06/10.52 | | | | | | | ssItem(all_301_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 75.06/10.52 | | | | | | | nil))
% 75.06/10.52 | | | | | | |
% 75.06/10.52 | | | | | | | GROUND_INST: instantiating (30) with all_301_1, all_301_0,
% 75.06/10.52 | | | | | | | simplifying with (48), (50) gives:
% 75.42/10.52 | | | | | | | (71) ? [v0: any] : ? [v1: $i] : (hd(all_301_0) = v1 &
% 75.42/10.52 | | | | | | | ssItem(all_301_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 75.42/10.52 | | | | | | | all_301_1))
% 75.42/10.52 | | | | | | |
% 75.42/10.52 | | | | | | | GROUND_INST: instantiating (10) with all_301_1, all_301_0,
% 75.42/10.52 | | | | | | | simplifying with (48), (50) gives:
% 75.42/10.52 | | | | | | | (72) ? [v0: any] : ? [v1: any] : (equalelemsP(all_301_0) = v1
% 75.42/10.52 | | | | | | | & ssItem(all_301_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 75.42/10.52 | | | | | | |
% 75.42/10.52 | | | | | | | GROUND_INST: instantiating (8) with all_301_1, all_301_0,
% 75.42/10.52 | | | | | | | simplifying with (48), (50) gives:
% 75.42/10.52 | | | | | | | (73) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_301_0) =
% 75.42/10.52 | | | | | | | v1 & ssItem(all_301_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 75.42/10.52 | | | | | | |
% 75.42/10.52 | | | | | | | GROUND_INST: instantiating (7) with all_301_1, all_301_0,
% 75.42/10.52 | | | | | | | simplifying with (48), (50) gives:
% 75.42/10.52 | | | | | | | (74) ? [v0: any] : ? [v1: any] : (strictorderedP(all_301_0) =
% 75.42/10.52 | | | | | | | v1 & ssItem(all_301_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 75.42/10.52 | | | | | | |
% 75.42/10.52 | | | | | | | GROUND_INST: instantiating (6) with all_301_1, all_301_0,
% 75.42/10.52 | | | | | | | simplifying with (48), (50) gives:
% 75.42/10.52 | | | | | | | (75) ? [v0: any] : ? [v1: any] : (totalorderedP(all_301_0) =
% 75.42/10.52 | | | | | | | v1 & ssItem(all_301_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 75.42/10.52 | | | | | | |
% 75.42/10.52 | | | | | | | GROUND_INST: instantiating (5) with all_301_1, all_301_0,
% 75.42/10.52 | | | | | | | simplifying with (48), (50) gives:
% 75.42/10.52 | | | | | | | (76) ? [v0: any] : ? [v1: any] : (strictorderP(all_301_0) =
% 75.42/10.52 | | | | | | | v1 & ssItem(all_301_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 75.42/10.52 | | | | | | |
% 75.42/10.52 | | | | | | | GROUND_INST: instantiating (4) with all_301_1, all_301_0,
% 75.42/10.52 | | | | | | | simplifying with (48), (50) gives:
% 75.42/10.52 | | | | | | | (77) ? [v0: any] : ? [v1: any] : (totalorderP(all_301_0) = v1
% 75.42/10.52 | | | | | | | & ssItem(all_301_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 75.42/10.52 | | | | | | |
% 75.42/10.52 | | | | | | | GROUND_INST: instantiating (3) with all_301_1, all_301_0,
% 75.42/10.52 | | | | | | | simplifying with (48), (50) gives:
% 75.42/10.52 | | | | | | | (78) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_301_0) = v1
% 75.42/10.52 | | | | | | | & ssItem(all_301_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 75.42/10.52 | | | | | | |
% 75.42/10.52 | | | | | | | GROUND_INST: instantiating (31) with all_301_1, all_301_0,
% 75.42/10.52 | | | | | | | simplifying with (48), (50) gives:
% 75.42/10.52 | | | | | | | (79) ? [v0: any] : ? [v1: any] : (ssList(all_301_0) = v1 &
% 75.42/10.52 | | | | | | | ssItem(all_301_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 75.42/10.52 | | | | | | |
% 75.42/10.52 | | | | | | | GROUND_INST: instantiating (40) with all_301_1, all_301_0,
% 75.42/10.52 | | | | | | | simplifying with (48), (50) gives:
% 75.42/10.52 | | | | | | | (80) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_301_1) = v0) | !
% 75.42/10.52 | | | | | | | [v0: $i] : ( ~ (app(all_301_0, v0) = all_93_0) | ~ $i(v0)
% 75.42/10.52 | | | | | | | | ? [v1: any] : ? [v2: $i] : (ssList(v0) = v1 &
% 75.42/10.52 | | | | | | | app(v0, all_301_0) = v2 & $i(v2) & ( ~ (v2 = all_97_1)
% 75.42/10.52 | | | | | | | | ~ (v1 = 0))))
% 75.42/10.52 | | | | | | |
% 75.42/10.52 | | | | | | | GROUND_INST: instantiating (11) with all_303_0, simplifying with
% 75.42/10.52 | | | | | | | (53), (56) gives:
% 75.42/10.52 | | | | | | | (81) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v0,
% 75.42/10.52 | | | | | | | nil) = v1) | ~ (app(v1, all_303_0) = v2) | ~
% 75.42/10.52 | | | | | | | $i(v0) | ? [v3: any] : ? [v4: $i] : (cons(v0,
% 75.42/10.52 | | | | | | | all_303_0) = v4 & ssItem(v0) = v3 & $i(v4) & ( ~ (v3
% 75.42/10.52 | | | | | | | = 0) | v4 = v2)))
% 75.42/10.52 | | | | | | |
% 75.42/10.52 | | | | | | | GROUND_INST: instantiating (ax25) with all_313_0, simplifying with
% 75.42/10.52 | | | | | | | (62), (63) gives:
% 75.42/10.52 | | | | | | | (82) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, all_313_0) = v1)
% 75.42/10.52 | | | | | | | | ~ $i(v0) | ? [v2: any] : ? [v3: $i] : (tl(v1) = v3
% 75.42/10.52 | | | | | | | & ssItem(v0) = v2 & $i(v3) & ( ~ (v2 = 0) | v3 =
% 75.42/10.52 | | | | | | | all_313_0)))
% 75.42/10.52 | | | | | | |
% 75.42/10.52 | | | | | | | GROUND_INST: instantiating (81) with all_301_1, all_301_0,
% 75.42/10.52 | | | | | | | all_93_0, simplifying with (48), (50), (54) gives:
% 75.42/10.53 | | | | | | | (83) ? [v0: any] : ? [v1: $i] : (cons(all_301_1, all_303_0) =
% 75.42/10.53 | | | | | | | v1 & ssItem(all_301_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1
% 75.42/10.53 | | | | | | | = all_93_0))
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | GROUND_INST: instantiating (82) with all_315_0, all_97_1,
% 75.42/10.53 | | | | | | | simplifying with (66), (68) gives:
% 75.42/10.53 | | | | | | | (84) ? [v0: any] : ? [v1: $i] : (tl(all_97_1) = v1 &
% 75.42/10.53 | | | | | | | ssItem(all_315_0) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 75.42/10.53 | | | | | | | all_313_0))
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | GROUND_INST: instantiating (69) with all_91_0, simplifying with
% 75.42/10.53 | | | | | | | (18), (19) gives:
% 75.42/10.53 | | | | | | | (85) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1:
% 75.42/10.53 | | | | | | | $i] : ! [v2: $i] : ! [v3: $i] : ( ~ (cons(all_301_1,
% 75.42/10.53 | | | | | | | v1) = v2) | ~ (app(v0, v2) = v3) | ~ $i(v1) | ?
% 75.42/10.53 | | | | | | | [v4: int] : ( ~ (v4 = 0) & ssList(v1) = v4) | ! [v4:
% 75.42/10.53 | | | | | | | $i] : ! [v5: $i] : ( ~ (all_301_1 = all_91_0) | ~
% 75.42/10.53 | | | | | | | (cons(all_91_0, v4) = v5) | ~ (app(v3, v5) = nil) |
% 75.42/10.53 | | | | | | | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) & ssList(v4)
% 75.42/10.53 | | | | | | | = v6))))
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | GROUND_INST: instantiating (85) with all_303_0, simplifying with
% 75.42/10.53 | | | | | | | (53), (56) gives:
% 75.42/10.53 | | | | | | | (86) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ( ~
% 75.42/10.53 | | | | | | | (cons(all_301_1, v0) = v1) | ~ (app(all_303_0, v1) =
% 75.42/10.53 | | | | | | | v2) | ~ $i(v0) | ? [v3: int] : ( ~ (v3 = 0) &
% 75.42/10.53 | | | | | | | ssList(v0) = v3) | ! [v3: $i] : ! [v4: $i] : ( ~
% 75.42/10.53 | | | | | | | (all_301_1 = all_91_0) | ~ (cons(all_91_0, v3) = v4)
% 75.42/10.53 | | | | | | | | ~ (app(v2, v4) = nil) | ~ $i(v3) | ? [v5: int] :
% 75.42/10.53 | | | | | | | ( ~ (v5 = 0) & ssList(v3) = v5)))
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | GROUND_INST: instantiating (86) with nil, all_301_0, all_97_1,
% 75.42/10.53 | | | | | | | simplifying with (12), (50), (55) gives:
% 75.42/10.53 | | | | | | | (87) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | ! [v0:
% 75.42/10.53 | | | | | | | $i] : ! [v1: $i] : ( ~ (all_301_1 = all_91_0) | ~
% 75.42/10.53 | | | | | | | (cons(all_91_0, v0) = v1) | ~ (app(all_97_1, v1) = nil)
% 75.42/10.53 | | | | | | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) =
% 75.42/10.53 | | | | | | | v2))
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | DELTA: instantiating (79) with fresh symbols all_845_0, all_845_1
% 75.42/10.53 | | | | | | | gives:
% 75.42/10.53 | | | | | | | (88) ssList(all_301_0) = all_845_0 & ssItem(all_301_1) =
% 75.42/10.53 | | | | | | | all_845_1 & ( ~ (all_845_1 = 0) | all_845_0 = 0)
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | ALPHA: (88) implies:
% 75.42/10.53 | | | | | | | (89) ssItem(all_301_1) = all_845_1
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | DELTA: instantiating (78) with fresh symbols all_847_0, all_847_1
% 75.42/10.53 | | | | | | | gives:
% 75.42/10.53 | | | | | | | (90) cyclefreeP(all_301_0) = all_847_0 & ssItem(all_301_1) =
% 75.42/10.53 | | | | | | | all_847_1 & ( ~ (all_847_1 = 0) | all_847_0 = 0)
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | ALPHA: (90) implies:
% 75.42/10.53 | | | | | | | (91) ssItem(all_301_1) = all_847_1
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | DELTA: instantiating (75) with fresh symbols all_849_0, all_849_1
% 75.42/10.53 | | | | | | | gives:
% 75.42/10.53 | | | | | | | (92) totalorderedP(all_301_0) = all_849_0 & ssItem(all_301_1) =
% 75.42/10.53 | | | | | | | all_849_1 & ( ~ (all_849_1 = 0) | all_849_0 = 0)
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | ALPHA: (92) implies:
% 75.42/10.53 | | | | | | | (93) ssItem(all_301_1) = all_849_1
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | DELTA: instantiating (74) with fresh symbols all_851_0, all_851_1
% 75.42/10.53 | | | | | | | gives:
% 75.42/10.53 | | | | | | | (94) strictorderedP(all_301_0) = all_851_0 & ssItem(all_301_1)
% 75.42/10.53 | | | | | | | = all_851_1 & ( ~ (all_851_1 = 0) | all_851_0 = 0)
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | ALPHA: (94) implies:
% 75.42/10.53 | | | | | | | (95) ssItem(all_301_1) = all_851_1
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | DELTA: instantiating (73) with fresh symbols all_853_0, all_853_1
% 75.42/10.53 | | | | | | | gives:
% 75.42/10.53 | | | | | | | (96) duplicatefreeP(all_301_0) = all_853_0 & ssItem(all_301_1)
% 75.42/10.53 | | | | | | | = all_853_1 & ( ~ (all_853_1 = 0) | all_853_0 = 0)
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | ALPHA: (96) implies:
% 75.42/10.53 | | | | | | | (97) ssItem(all_301_1) = all_853_1
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | DELTA: instantiating (72) with fresh symbols all_855_0, all_855_1
% 75.42/10.53 | | | | | | | gives:
% 75.42/10.53 | | | | | | | (98) equalelemsP(all_301_0) = all_855_0 & ssItem(all_301_1) =
% 75.42/10.53 | | | | | | | all_855_1 & ( ~ (all_855_1 = 0) | all_855_0 = 0)
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | ALPHA: (98) implies:
% 75.42/10.53 | | | | | | | (99) ssItem(all_301_1) = all_855_1
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | DELTA: instantiating (77) with fresh symbols all_857_0, all_857_1
% 75.42/10.53 | | | | | | | gives:
% 75.42/10.53 | | | | | | | (100) totalorderP(all_301_0) = all_857_0 & ssItem(all_301_1) =
% 75.42/10.53 | | | | | | | all_857_1 & ( ~ (all_857_1 = 0) | all_857_0 = 0)
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | ALPHA: (100) implies:
% 75.42/10.53 | | | | | | | (101) ssItem(all_301_1) = all_857_1
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | DELTA: instantiating (76) with fresh symbols all_859_0, all_859_1
% 75.42/10.53 | | | | | | | gives:
% 75.42/10.53 | | | | | | | (102) strictorderP(all_301_0) = all_859_0 & ssItem(all_301_1) =
% 75.42/10.53 | | | | | | | all_859_1 & ( ~ (all_859_1 = 0) | all_859_0 = 0)
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | ALPHA: (102) implies:
% 75.42/10.53 | | | | | | | (103) ssItem(all_301_1) = all_859_1
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | DELTA: instantiating (71) with fresh symbols all_861_0, all_861_1
% 75.42/10.53 | | | | | | | gives:
% 75.42/10.53 | | | | | | | (104) hd(all_301_0) = all_861_0 & ssItem(all_301_1) = all_861_1
% 75.42/10.53 | | | | | | | & $i(all_861_0) & ( ~ (all_861_1 = 0) | all_861_0 =
% 75.42/10.53 | | | | | | | all_301_1)
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | ALPHA: (104) implies:
% 75.42/10.53 | | | | | | | (105) ssItem(all_301_1) = all_861_1
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | DELTA: instantiating (70) with fresh symbols all_863_0, all_863_1
% 75.42/10.53 | | | | | | | gives:
% 75.42/10.53 | | | | | | | (106) tl(all_301_0) = all_863_0 & ssItem(all_301_1) = all_863_1
% 75.42/10.53 | | | | | | | & $i(all_863_0) & ( ~ (all_863_1 = 0) | all_863_0 = nil)
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | ALPHA: (106) implies:
% 75.42/10.53 | | | | | | | (107) ssItem(all_301_1) = all_863_1
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | DELTA: instantiating (83) with fresh symbols all_865_0, all_865_1
% 75.42/10.53 | | | | | | | gives:
% 75.42/10.53 | | | | | | | (108) cons(all_301_1, all_303_0) = all_865_0 &
% 75.42/10.53 | | | | | | | ssItem(all_301_1) = all_865_1 & $i(all_865_0) & ( ~
% 75.42/10.53 | | | | | | | (all_865_1 = 0) | all_865_0 = all_93_0)
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | ALPHA: (108) implies:
% 75.42/10.53 | | | | | | | (109) ssItem(all_301_1) = all_865_1
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | DELTA: instantiating (84) with fresh symbols all_869_0, all_869_1
% 75.42/10.53 | | | | | | | gives:
% 75.42/10.53 | | | | | | | (110) tl(all_97_1) = all_869_0 & ssItem(all_315_0) = all_869_1
% 75.42/10.53 | | | | | | | & $i(all_869_0) & ( ~ (all_869_1 = 0) | all_869_0 =
% 75.42/10.53 | | | | | | | all_313_0)
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | ALPHA: (110) implies:
% 75.42/10.53 | | | | | | | (111) ssItem(all_315_0) = all_869_1
% 75.42/10.53 | | | | | | | (112) ~ (all_869_1 = 0) | all_869_0 = all_313_0
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | BETA: splitting (87) gives:
% 75.42/10.53 | | | | | | |
% 75.42/10.53 | | | | | | | Case 1:
% 75.42/10.53 | | | | | | | |
% 75.42/10.53 | | | | | | | | (113) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 75.42/10.53 | | | | | | | |
% 75.42/10.53 | | | | | | | | REF_CLOSE: (1), (15), (113) are inconsistent by sub-proof #1.
% 75.42/10.53 | | | | | | | |
% 75.42/10.53 | | | | | | | Case 2:
% 75.42/10.53 | | | | | | | |
% 75.42/10.53 | | | | | | | |
% 75.42/10.53 | | | | | | | | GROUND_INST: instantiating (14) with all_849_1, all_851_1,
% 75.42/10.53 | | | | | | | | all_301_1, simplifying with (93), (95) gives:
% 75.42/10.53 | | | | | | | | (114) all_851_1 = all_849_1
% 75.42/10.53 | | | | | | | |
% 75.42/10.53 | | | | | | | | GROUND_INST: instantiating (14) with all_847_1, all_851_1,
% 75.42/10.53 | | | | | | | | all_301_1, simplifying with (91), (95) gives:
% 75.42/10.53 | | | | | | | | (115) all_851_1 = all_847_1
% 75.42/10.53 | | | | | | | |
% 75.42/10.53 | | | | | | | | GROUND_INST: instantiating (14) with all_849_1, all_853_1,
% 75.42/10.53 | | | | | | | | all_301_1, simplifying with (93), (97) gives:
% 75.42/10.53 | | | | | | | | (116) all_853_1 = all_849_1
% 75.42/10.53 | | | | | | | |
% 75.42/10.53 | | | | | | | | GROUND_INST: instantiating (14) with all_857_1, all_861_1,
% 75.42/10.53 | | | | | | | | all_301_1, simplifying with (101), (105) gives:
% 75.42/10.53 | | | | | | | | (117) all_861_1 = all_857_1
% 75.42/10.53 | | | | | | | |
% 75.42/10.53 | | | | | | | | GROUND_INST: instantiating (14) with all_855_1, all_861_1,
% 75.42/10.53 | | | | | | | | all_301_1, simplifying with (99), (105) gives:
% 75.42/10.53 | | | | | | | | (118) all_861_1 = all_855_1
% 75.42/10.53 | | | | | | | |
% 75.42/10.53 | | | | | | | | GROUND_INST: instantiating (14) with all_853_1, all_861_1,
% 75.42/10.53 | | | | | | | | all_301_1, simplifying with (97), (105) gives:
% 75.42/10.53 | | | | | | | | (119) all_861_1 = all_853_1
% 75.42/10.53 | | | | | | | |
% 75.42/10.53 | | | | | | | | GROUND_INST: instantiating (14) with all_857_1, all_863_1,
% 75.42/10.53 | | | | | | | | all_301_1, simplifying with (101), (107) gives:
% 75.42/10.53 | | | | | | | | (120) all_863_1 = all_857_1
% 75.42/10.53 | | | | | | | |
% 75.42/10.54 | | | | | | | | GROUND_INST: instantiating (14) with all_845_1, all_863_1,
% 75.42/10.54 | | | | | | | | all_301_1, simplifying with (89), (107) gives:
% 75.42/10.54 | | | | | | | | (121) all_863_1 = all_845_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | GROUND_INST: instantiating (14) with 0, all_865_1, all_301_1,
% 75.42/10.54 | | | | | | | | simplifying with (49), (109) gives:
% 75.42/10.54 | | | | | | | | (122) all_865_1 = 0
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | GROUND_INST: instantiating (14) with all_859_1, all_865_1,
% 75.42/10.54 | | | | | | | | all_301_1, simplifying with (103), (109) gives:
% 75.42/10.54 | | | | | | | | (123) all_865_1 = all_859_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | GROUND_INST: instantiating (14) with all_851_1, all_865_1,
% 75.42/10.54 | | | | | | | | all_301_1, simplifying with (95), (109) gives:
% 75.42/10.54 | | | | | | | | (124) all_865_1 = all_851_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | GROUND_INST: instantiating (14) with 0, all_869_1, all_315_0,
% 75.42/10.54 | | | | | | | | simplifying with (67), (111) gives:
% 75.42/10.54 | | | | | | | | (125) all_869_1 = 0
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | COMBINE_EQS: (123), (124) imply:
% 75.42/10.54 | | | | | | | | (126) all_859_1 = all_851_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | COMBINE_EQS: (122), (123) imply:
% 75.42/10.54 | | | | | | | | (127) all_859_1 = 0
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | COMBINE_EQS: (120), (121) imply:
% 75.42/10.54 | | | | | | | | (128) all_857_1 = all_845_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | SIMP: (128) implies:
% 75.42/10.54 | | | | | | | | (129) all_857_1 = all_845_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | COMBINE_EQS: (117), (118) imply:
% 75.42/10.54 | | | | | | | | (130) all_857_1 = all_855_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | SIMP: (130) implies:
% 75.42/10.54 | | | | | | | | (131) all_857_1 = all_855_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | COMBINE_EQS: (118), (119) imply:
% 75.42/10.54 | | | | | | | | (132) all_855_1 = all_853_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | COMBINE_EQS: (126), (127) imply:
% 75.42/10.54 | | | | | | | | (133) all_851_1 = 0
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | SIMP: (133) implies:
% 75.42/10.54 | | | | | | | | (134) all_851_1 = 0
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | COMBINE_EQS: (129), (131) imply:
% 75.42/10.54 | | | | | | | | (135) all_855_1 = all_845_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | SIMP: (135) implies:
% 75.42/10.54 | | | | | | | | (136) all_855_1 = all_845_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | COMBINE_EQS: (132), (136) imply:
% 75.42/10.54 | | | | | | | | (137) all_853_1 = all_845_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | SIMP: (137) implies:
% 75.42/10.54 | | | | | | | | (138) all_853_1 = all_845_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | COMBINE_EQS: (116), (138) imply:
% 75.42/10.54 | | | | | | | | (139) all_849_1 = all_845_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | SIMP: (139) implies:
% 75.42/10.54 | | | | | | | | (140) all_849_1 = all_845_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | COMBINE_EQS: (114), (115) imply:
% 75.42/10.54 | | | | | | | | (141) all_849_1 = all_847_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | SIMP: (141) implies:
% 75.42/10.54 | | | | | | | | (142) all_849_1 = all_847_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | COMBINE_EQS: (115), (134) imply:
% 75.42/10.54 | | | | | | | | (143) all_847_1 = 0
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | COMBINE_EQS: (140), (142) imply:
% 75.42/10.54 | | | | | | | | (144) all_847_1 = all_845_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | SIMP: (144) implies:
% 75.42/10.54 | | | | | | | | (145) all_847_1 = all_845_1
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | COMBINE_EQS: (143), (145) imply:
% 75.42/10.54 | | | | | | | | (146) all_845_1 = 0
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | BETA: splitting (80) gives:
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | | Case 1:
% 75.42/10.54 | | | | | | | | |
% 75.42/10.54 | | | | | | | | | (147) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_301_1) = v0)
% 75.42/10.54 | | | | | | | | |
% 75.42/10.54 | | | | | | | | | DELTA: instantiating (147) with fresh symbol all_946_0 gives:
% 75.42/10.54 | | | | | | | | | (148) ~ (all_946_0 = 0) & ssItem(all_301_1) = all_946_0
% 75.42/10.54 | | | | | | | | |
% 75.42/10.54 | | | | | | | | | ALPHA: (148) implies:
% 75.42/10.54 | | | | | | | | | (149) ~ (all_946_0 = 0)
% 75.42/10.54 | | | | | | | | | (150) ssItem(all_301_1) = all_946_0
% 75.42/10.54 | | | | | | | | |
% 75.42/10.54 | | | | | | | | | BETA: splitting (112) gives:
% 75.42/10.54 | | | | | | | | |
% 75.42/10.54 | | | | | | | | | Case 1:
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | (151) ~ (all_869_1 = 0)
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | REDUCE: (125), (151) imply:
% 75.42/10.54 | | | | | | | | | | (152) $false
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | CLOSE: (152) is inconsistent.
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | Case 2:
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | DELTA: instantiating (147) with fresh symbol all_955_0
% 75.42/10.54 | | | | | | | | | | gives:
% 75.42/10.54 | | | | | | | | | | (153) ~ (all_955_0 = 0) & ssItem(all_301_1) = all_955_0
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | ALPHA: (153) implies:
% 75.42/10.54 | | | | | | | | | | (154) ssItem(all_301_1) = all_955_0
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | GROUND_INST: instantiating (14) with 0, all_955_0, all_301_1,
% 75.42/10.54 | | | | | | | | | | simplifying with (49), (154) gives:
% 75.42/10.54 | | | | | | | | | | (155) all_955_0 = 0
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | GROUND_INST: instantiating (14) with all_946_0, all_955_0,
% 75.42/10.54 | | | | | | | | | | all_301_1, simplifying with (150), (154) gives:
% 75.42/10.54 | | | | | | | | | | (156) all_955_0 = all_946_0
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | COMBINE_EQS: (155), (156) imply:
% 75.42/10.54 | | | | | | | | | | (157) all_946_0 = 0
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | REDUCE: (149), (157) imply:
% 75.42/10.54 | | | | | | | | | | (158) $false
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | CLOSE: (158) is inconsistent.
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | End of split
% 75.42/10.54 | | | | | | | | |
% 75.42/10.54 | | | | | | | | Case 2:
% 75.42/10.54 | | | | | | | | |
% 75.42/10.54 | | | | | | | | | (159) ! [v0: $i] : ( ~ (app(all_301_0, v0) = all_93_0) |
% 75.42/10.54 | | | | | | | | | ~ $i(v0) | ? [v1: any] : ? [v2: $i] : (ssList(v0)
% 75.42/10.54 | | | | | | | | | = v1 & app(v0, all_301_0) = v2 & $i(v2) & ( ~ (v2
% 75.42/10.54 | | | | | | | | | = all_97_1) | ~ (v1 = 0))))
% 75.42/10.54 | | | | | | | | |
% 75.42/10.54 | | | | | | | | | GROUND_INST: instantiating (159) with all_303_0, simplifying
% 75.42/10.54 | | | | | | | | | with (53), (54) gives:
% 75.42/10.54 | | | | | | | | | (160) ? [v0: any] : ? [v1: $i] : (ssList(all_303_0) = v0
% 75.42/10.54 | | | | | | | | | & app(all_303_0, all_301_0) = v1 & $i(v1) & ( ~ (v1
% 75.42/10.54 | | | | | | | | | = all_97_1) | ~ (v0 = 0)))
% 75.42/10.54 | | | | | | | | |
% 75.42/10.54 | | | | | | | | | DELTA: instantiating (160) with fresh symbols all_947_0,
% 75.42/10.54 | | | | | | | | | all_947_1 gives:
% 75.42/10.54 | | | | | | | | | (161) ssList(all_303_0) = all_947_1 & app(all_303_0,
% 75.42/10.54 | | | | | | | | | all_301_0) = all_947_0 & $i(all_947_0) & ( ~
% 75.42/10.54 | | | | | | | | | (all_947_0 = all_97_1) | ~ (all_947_1 = 0))
% 75.42/10.54 | | | | | | | | |
% 75.42/10.54 | | | | | | | | | ALPHA: (161) implies:
% 75.42/10.54 | | | | | | | | | (162) app(all_303_0, all_301_0) = all_947_0
% 75.42/10.54 | | | | | | | | | (163) ssList(all_303_0) = all_947_1
% 75.42/10.54 | | | | | | | | | (164) ~ (all_947_0 = all_97_1) | ~ (all_947_1 = 0)
% 75.42/10.54 | | | | | | | | |
% 75.42/10.54 | | | | | | | | | GROUND_INST: instantiating (16) with all_97_1, all_947_0,
% 75.42/10.54 | | | | | | | | | all_301_0, all_303_0, simplifying with (55), (162)
% 75.42/10.54 | | | | | | | | | gives:
% 75.42/10.54 | | | | | | | | | (165) all_947_0 = all_97_1
% 75.42/10.54 | | | | | | | | |
% 75.42/10.54 | | | | | | | | | GROUND_INST: instantiating (15) with 0, all_947_1, all_303_0,
% 75.42/10.54 | | | | | | | | | simplifying with (56), (163) gives:
% 75.42/10.54 | | | | | | | | | (166) all_947_1 = 0
% 75.42/10.54 | | | | | | | | |
% 75.42/10.54 | | | | | | | | | BETA: splitting (164) gives:
% 75.42/10.54 | | | | | | | | |
% 75.42/10.54 | | | | | | | | | Case 1:
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | (167) ~ (all_947_1 = 0)
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | REDUCE: (166), (167) imply:
% 75.42/10.54 | | | | | | | | | | (168) $false
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | CLOSE: (168) is inconsistent.
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | Case 2:
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | (169) ~ (all_947_0 = all_97_1)
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | REDUCE: (165), (169) imply:
% 75.42/10.54 | | | | | | | | | | (170) $false
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | | CLOSE: (170) is inconsistent.
% 75.42/10.54 | | | | | | | | | |
% 75.42/10.54 | | | | | | | | | End of split
% 75.42/10.54 | | | | | | | | |
% 75.42/10.54 | | | | | | | | End of split
% 75.42/10.54 | | | | | | | |
% 75.42/10.54 | | | | | | | End of split
% 75.42/10.54 | | | | | | |
% 75.42/10.54 | | | | | | End of split
% 75.42/10.54 | | | | | |
% 75.42/10.54 | | | | | Case 2:
% 75.42/10.54 | | | | | |
% 75.42/10.54 | | | | | | (171) ~ (all_97_0 = 0)
% 75.42/10.54 | | | | | |
% 75.42/10.54 | | | | | | REDUCE: (39), (171) imply:
% 75.42/10.54 | | | | | | (172) $false
% 75.42/10.54 | | | | | |
% 75.42/10.54 | | | | | | CLOSE: (172) is inconsistent.
% 75.42/10.54 | | | | | |
% 75.42/10.54 | | | | | End of split
% 75.42/10.54 | | | | |
% 75.42/10.54 | | | | End of split
% 75.42/10.54 | | | |
% 75.42/10.54 | | | End of split
% 75.42/10.54 | | |
% 75.42/10.54 | | Case 2:
% 75.42/10.54 | | |
% 75.42/10.54 | | | (173) all_97_1 = nil & ~ (all_93_0 = nil)
% 75.42/10.54 | | |
% 75.42/10.54 | | | ALPHA: (173) implies:
% 75.42/10.54 | | | (174) all_97_1 = nil
% 75.42/10.54 | | | (175) ~ (all_93_0 = nil)
% 75.42/10.54 | | |
% 75.42/10.54 | | | BETA: splitting (27) gives:
% 75.42/10.54 | | |
% 75.42/10.54 | | | Case 1:
% 75.42/10.54 | | | |
% 75.42/10.54 | | | | (176) ~ (all_97_1 = nil)
% 75.42/10.54 | | | |
% 75.42/10.54 | | | | REDUCE: (174), (176) imply:
% 75.42/10.54 | | | | (177) $false
% 75.42/10.54 | | | |
% 75.42/10.54 | | | | CLOSE: (177) is inconsistent.
% 75.42/10.54 | | | |
% 75.42/10.54 | | | Case 2:
% 75.42/10.54 | | | |
% 75.42/10.54 | | | | (178) all_93_0 = nil
% 75.42/10.54 | | | |
% 75.42/10.54 | | | | REDUCE: (175), (178) imply:
% 75.42/10.54 | | | | (179) $false
% 75.42/10.54 | | | |
% 75.42/10.54 | | | | CLOSE: (179) is inconsistent.
% 75.42/10.54 | | | |
% 75.42/10.54 | | | End of split
% 75.42/10.54 | | |
% 75.42/10.54 | | End of split
% 75.42/10.54 | |
% 75.42/10.54 | End of split
% 75.42/10.54 |
% 75.42/10.54 End of proof
% 75.42/10.55
% 75.42/10.55 Sub-proof #1 shows that the following formulas are inconsistent:
% 75.42/10.55 ----------------------------------------------------------------
% 75.42/10.55 (1) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 75.42/10.55 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 75.42/10.55 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 75.42/10.55 (3) ssList(nil) = 0
% 75.42/10.55
% 75.42/10.55 Begin of proof
% 75.42/10.55 |
% 75.42/10.55 | DELTA: instantiating (1) with fresh symbol all_274_0 gives:
% 75.42/10.55 | (4) ~ (all_274_0 = 0) & ssList(nil) = all_274_0
% 75.42/10.55 |
% 75.42/10.55 | ALPHA: (4) implies:
% 75.42/10.55 | (5) ~ (all_274_0 = 0)
% 75.42/10.55 | (6) ssList(nil) = all_274_0
% 75.42/10.55 |
% 75.42/10.55 | DELTA: instantiating (1) with fresh symbol all_276_0 gives:
% 75.42/10.55 | (7) ~ (all_276_0 = 0) & ssList(nil) = all_276_0
% 75.42/10.55 |
% 75.42/10.55 | ALPHA: (7) implies:
% 75.42/10.55 | (8) ssList(nil) = all_276_0
% 75.42/10.55 |
% 75.42/10.55 | GROUND_INST: instantiating (2) with 0, all_276_0, nil, simplifying with (3),
% 75.42/10.55 | (8) gives:
% 75.42/10.55 | (9) all_276_0 = 0
% 75.42/10.55 |
% 75.42/10.55 | GROUND_INST: instantiating (2) with all_274_0, all_276_0, nil, simplifying
% 75.42/10.55 | with (6), (8) gives:
% 75.42/10.55 | (10) all_276_0 = all_274_0
% 75.42/10.55 |
% 75.42/10.55 | COMBINE_EQS: (9), (10) imply:
% 75.42/10.55 | (11) all_274_0 = 0
% 75.42/10.55 |
% 75.42/10.55 | REDUCE: (5), (11) imply:
% 75.42/10.55 | (12) $false
% 75.42/10.55 |
% 75.42/10.55 | CLOSE: (12) is inconsistent.
% 75.42/10.55 |
% 75.42/10.55 End of proof
% 75.42/10.55 % SZS output end Proof for theBenchmark
% 75.42/10.55
% 75.42/10.55 9942ms
%------------------------------------------------------------------------------