TSTP Solution File: SWC384+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC384+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 : n025.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 20:51:09 EDT 2023
% Result : Theorem 44.06s 6.69s
% Output : Proof 109.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWC384+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n025.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 18:04:39 EDT 2023
% 0.12/0.33 % CPUTime :
% 0.19/0.66 ________ _____
% 0.19/0.66 ___ __ \_________(_)________________________________
% 0.19/0.66 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.66 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.66 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.66
% 0.19/0.66 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.66 (2023-06-19)
% 0.19/0.66
% 0.19/0.66 (c) Philipp Rümmer, 2009-2023
% 0.19/0.66 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.66 Amanda Stjerna.
% 0.19/0.66 Free software under BSD-3-Clause.
% 0.19/0.66
% 0.19/0.66 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.66
% 0.19/0.66 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.67 Running up to 7 provers in parallel.
% 0.19/0.68 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.68 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.68 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.69 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.69 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.69 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.69 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 6.05/1.66 Prover 4: Preprocessing ...
% 6.58/1.69 Prover 1: Preprocessing ...
% 6.58/1.72 Prover 5: Preprocessing ...
% 6.58/1.72 Prover 0: Preprocessing ...
% 6.58/1.72 Prover 3: Preprocessing ...
% 6.58/1.72 Prover 2: Preprocessing ...
% 6.58/1.72 Prover 6: Preprocessing ...
% 16.80/3.07 Prover 2: Proving ...
% 16.80/3.09 Prover 5: Constructing countermodel ...
% 16.80/3.14 Prover 1: Constructing countermodel ...
% 17.42/3.16 Prover 6: Proving ...
% 18.09/3.24 Prover 3: Constructing countermodel ...
% 23.61/4.05 Prover 4: Constructing countermodel ...
% 24.38/4.15 Prover 0: Proving ...
% 44.06/6.68 Prover 3: proved (6005ms)
% 44.06/6.69
% 44.06/6.69 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 44.06/6.69
% 44.06/6.69 Prover 2: stopped
% 44.40/6.69 Prover 0: stopped
% 44.40/6.70 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 44.40/6.70 Prover 5: stopped
% 44.40/6.71 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 44.40/6.71 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 44.40/6.71 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 44.40/6.74 Prover 6: stopped
% 44.88/6.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 45.71/6.92 Prover 11: Preprocessing ...
% 45.71/6.93 Prover 7: Preprocessing ...
% 45.71/6.94 Prover 13: Preprocessing ...
% 45.71/6.94 Prover 8: Preprocessing ...
% 45.71/6.97 Prover 10: Preprocessing ...
% 47.68/7.13 Prover 7: Constructing countermodel ...
% 47.68/7.14 Prover 10: Constructing countermodel ...
% 48.69/7.27 Prover 13: Constructing countermodel ...
% 48.89/7.28 Prover 8: Warning: ignoring some quantifiers
% 48.89/7.29 Prover 8: Constructing countermodel ...
% 53.65/7.95 Prover 11: Constructing countermodel ...
% 81.05/11.43 Prover 13: stopped
% 81.05/11.44 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 81.21/11.50 Prover 16: Preprocessing ...
% 82.09/11.60 Prover 16: Constructing countermodel ...
% 108.96/15.09 Prover 1: Found proof (size 176)
% 108.96/15.09 Prover 1: proved (14410ms)
% 108.96/15.09 Prover 8: stopped
% 108.96/15.09 Prover 11: stopped
% 108.96/15.09 Prover 7: stopped
% 108.96/15.09 Prover 16: stopped
% 108.96/15.09 Prover 4: stopped
% 108.96/15.09 Prover 10: stopped
% 108.96/15.09
% 108.96/15.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 108.96/15.09
% 109.23/15.11 % SZS output start Proof for theBenchmark
% 109.23/15.11 Assumptions after simplification:
% 109.23/15.11 ---------------------------------
% 109.23/15.11
% 109.23/15.11 (ax15)
% 109.23/15.14 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 109.23/15.14 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 109.23/15.14 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 109.23/15.14
% 109.23/15.14 (ax17)
% 109.23/15.14 ssList(nil) = 0 & $i(nil)
% 109.23/15.14
% 109.23/15.14 (ax20)
% 109.23/15.15 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1:
% 109.23/15.15 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 109.23/15.15 ssItem(v2) = 0 & $i(v2))))
% 109.23/15.15
% 109.23/15.15 (ax23)
% 109.23/15.15 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : (
% 109.23/15.15 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) =
% 109.23/15.15 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1))))
% 109.23/15.15
% 109.23/15.15 (ax25)
% 109.23/15.15 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : (
% 109.23/15.15 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) =
% 109.23/15.15 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0))))
% 109.23/15.15
% 109.23/15.15 (ax4)
% 109.23/15.15 $i(nil) & ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) |
% 109.23/15.15 ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2: $i]
% 109.23/15.15 : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0 | ! [v2:
% 109.23/15.15 $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 =
% 109.23/15.15 0) & ssItem(v2) = v3)))))
% 109.23/15.15
% 109.23/15.15 (ax59)
% 109.23/15.16 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 109.23/15.16 ? [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 109.23/15.16 (v2 = 0) | v3 = 0)))
% 109.23/15.16
% 109.23/15.16 (ax61)
% 109.23/15.16 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 109.23/15.16 ? [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 109.23/15.16 (v2 = 0) | v3 = 0)))
% 109.23/15.16
% 109.23/15.16 (ax63)
% 109.23/15.16 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 109.23/15.16 ? [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 109.23/15.16 (v2 = 0) | v3 = 0)))
% 109.23/15.16
% 109.23/15.16 (ax65)
% 109.23/15.16 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 109.23/15.16 ? [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 109.23/15.16 (v2 = 0) | v3 = 0)))
% 109.23/15.16
% 109.23/15.16 (ax68)
% 109.23/15.16 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 109.23/15.16 ? [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & (
% 109.23/15.16 ~ (v2 = 0) | v3 = 0)))
% 109.23/15.16
% 109.23/15.16 (ax7)
% 109.23/15.16 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 109.23/15.16 ( ~ (segmentP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 109.23/15.16 ssList(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : ? [v4: $i] :
% 109.23/15.16 (ssList(v3) = 0 & app(v3, v1) = v4 & $i(v4) & $i(v3) & ? [v5: $i] :
% 109.23/15.16 (ssList(v5) = 0 & app(v4, v5) = v0 & $i(v5)))) & (v2 = 0 | ! [v3:
% 109.23/15.16 $i] : ! [v4: $i] : ( ~ (app(v3, v1) = v4) | ~ $i(v3) | ? [v5:
% 109.23/15.16 int] : ( ~ (v5 = 0) & ssList(v3) = v5) | ! [v5: $i] : ( ~
% 109.23/15.16 (app(v4, v5) = v0) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0) &
% 109.23/15.16 ssList(v5) = v6)))))))
% 109.23/15.16
% 109.23/15.16 (ax71)
% 109.23/15.17 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 109.23/15.17 ? [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & (
% 109.23/15.17 ~ (v2 = 0) | v3 = 0)))
% 109.23/15.17
% 109.23/15.17 (ax73)
% 109.23/15.17 $i(nil) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) |
% 109.23/15.17 ? [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~
% 109.23/15.17 (v2 = 0) | v3 = 0)))
% 109.23/15.17
% 109.23/15.17 (co1)
% 109.23/15.17 $i(nil) & ? [v0: $i] : ? [v1: any] : (singletonP(v0) = v1 & ssList(v0) = 0 &
% 109.23/15.17 $i(v0) & ? [v2: $i] : ? [v3: any] : (segmentP(v2, v0) = v3 & ssList(v2) =
% 109.23/15.17 0 & neq(v2, nil) = 0 & $i(v2) & ( ~ (v3 = 0) | ~ (v1 = 0)) & ( ? [v4: $i]
% 109.23/15.17 : ? [v5: $i] : (cons(v4, nil) = v5 & ssItem(v4) = 0 & $i(v5) & $i(v4) &
% 109.23/15.17 ? [v6: $i] : ? [v7: $i] : (ssList(v6) = 0 & app(v6, v0) = v7 &
% 109.23/15.17 $i(v7) & $i(v6) & ? [v8: $i] : (v5 = v0 & ssList(v8) = 0 & app(v7,
% 109.23/15.17 v8) = v2 & $i(v8) & ! [v9: $i] : ( ~ (memberP(v8, v9) = 0) | ~
% 109.23/15.17 $i(v9) | ? [v10: any] : ? [v11: any] : (lt(v9, v4) = v11 &
% 109.23/15.17 ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v9:
% 109.23/15.17 $i] : ( ~ (memberP(v6, v9) = 0) | ~ $i(v9) | ? [v10: any] : ?
% 109.23/15.17 [v11: any] : (lt(v4, v9) = v11 & ssItem(v9) = v10 & ( ~ (v11 =
% 109.23/15.17 0) | ~ (v10 = 0))))))) | (v2 = nil & v0 = nil))))
% 109.23/15.17
% 109.23/15.17 (function-axioms)
% 109.23/15.18 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 109.23/15.18 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 109.23/15.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 109.23/15.18 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 109.23/15.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 109.23/15.18 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 109.23/15.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 109.23/15.18 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 109.23/15.18 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 109.23/15.18 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 109.23/15.18 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 109.23/15.18 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 109.23/15.18 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 109.23/15.18 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 109.23/15.18 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 109.23/15.18 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 109.23/15.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 109.23/15.18 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 109.23/15.18 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 109.23/15.18 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 109.23/15.18 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 109.23/15.18 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 109.23/15.18 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 109.23/15.18 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 109.23/15.18 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 109.23/15.18 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 109.23/15.18 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 109.23/15.18 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 109.23/15.18 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 109.23/15.18 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 109.23/15.18 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 109.23/15.18 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 109.23/15.18 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 109.23/15.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 109.23/15.18 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 109.23/15.18 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 109.23/15.18
% 109.23/15.18 Further assumptions not needed in the proof:
% 109.23/15.18 --------------------------------------------
% 109.23/15.18 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax21, ax22, ax24,
% 109.23/15.18 ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37,
% 109.23/15.18 ax38, ax39, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5,
% 109.23/15.18 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax6, ax60, ax62, ax64,
% 109.23/15.18 ax66, ax67, ax69, ax70, ax72, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80,
% 109.23/15.18 ax81, ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92,
% 109.23/15.18 ax93, ax94, ax95
% 109.23/15.18
% 109.23/15.18 Those formulas are unsatisfiable:
% 109.23/15.18 ---------------------------------
% 109.23/15.18
% 109.23/15.18 Begin of proof
% 109.23/15.18 |
% 109.23/15.18 | ALPHA: (ax4) implies:
% 109.23/15.18 | (1) ! [v0: $i] : ! [v1: any] : ( ~ (singletonP(v0) = v1) | ~ $i(v0) | ?
% 109.23/15.18 | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ? [v2:
% 109.23/15.18 | $i] : (cons(v2, nil) = v0 & ssItem(v2) = 0 & $i(v2))) & (v1 = 0
% 109.23/15.18 | | ! [v2: $i] : ( ~ (cons(v2, nil) = v0) | ~ $i(v2) | ? [v3:
% 109.23/15.18 | int] : ( ~ (v3 = 0) & ssItem(v2) = v3)))))
% 109.23/15.18 |
% 109.23/15.18 | ALPHA: (ax17) implies:
% 109.23/15.18 | (2) ssList(nil) = 0
% 109.23/15.18 |
% 109.23/15.18 | ALPHA: (ax20) implies:
% 109.23/15.19 | (3) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 109.23/15.19 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 109.23/15.19 | ssItem(v2) = 0 & $i(v2))))
% 109.23/15.19 |
% 109.23/15.19 | ALPHA: (ax59) implies:
% 109.23/15.19 | (4) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 109.23/15.19 | [v2: any] : ? [v3: any] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & (
% 109.23/15.19 | ~ (v2 = 0) | v3 = 0)))
% 109.23/15.19 |
% 109.23/15.19 | ALPHA: (ax61) implies:
% 109.23/15.19 | (5) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 109.23/15.19 | [v2: any] : ? [v3: any] : (totalorderP(v1) = v3 & ssItem(v0) = v2 &
% 109.23/15.19 | ( ~ (v2 = 0) | v3 = 0)))
% 109.23/15.19 |
% 109.23/15.19 | ALPHA: (ax63) implies:
% 109.23/15.19 | (6) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 109.23/15.19 | [v2: any] : ? [v3: any] : (strictorderP(v1) = v3 & ssItem(v0) = v2 &
% 109.23/15.19 | ( ~ (v2 = 0) | v3 = 0)))
% 109.23/15.19 |
% 109.23/15.19 | ALPHA: (ax65) implies:
% 109.23/15.19 | (7) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 109.23/15.19 | [v2: any] : ? [v3: any] : (totalorderedP(v1) = v3 & ssItem(v0) = v2
% 109.23/15.19 | & ( ~ (v2 = 0) | v3 = 0)))
% 109.23/15.19 |
% 109.23/15.19 | ALPHA: (ax68) implies:
% 109.23/15.19 | (8) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 109.23/15.19 | [v2: any] : ? [v3: any] : (strictorderedP(v1) = v3 & ssItem(v0) = v2
% 109.23/15.19 | & ( ~ (v2 = 0) | v3 = 0)))
% 109.23/15.19 |
% 109.23/15.19 | ALPHA: (ax71) implies:
% 109.23/15.19 | (9) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 109.23/15.19 | [v2: any] : ? [v3: any] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2
% 109.23/15.19 | & ( ~ (v2 = 0) | v3 = 0)))
% 109.23/15.19 |
% 109.23/15.19 | ALPHA: (ax73) implies:
% 109.23/15.19 | (10) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 109.23/15.19 | [v2: any] : ? [v3: any] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 &
% 109.23/15.19 | ( ~ (v2 = 0) | v3 = 0)))
% 109.23/15.19 |
% 109.23/15.19 | ALPHA: (co1) implies:
% 109.23/15.19 | (11) $i(nil)
% 109.23/15.20 | (12) ? [v0: $i] : ? [v1: any] : (singletonP(v0) = v1 & ssList(v0) = 0 &
% 109.23/15.20 | $i(v0) & ? [v2: $i] : ? [v3: any] : (segmentP(v2, v0) = v3 &
% 109.23/15.20 | ssList(v2) = 0 & neq(v2, nil) = 0 & $i(v2) & ( ~ (v3 = 0) | ~ (v1
% 109.23/15.20 | = 0)) & ( ? [v4: $i] : ? [v5: $i] : (cons(v4, nil) = v5 &
% 109.23/15.20 | ssItem(v4) = 0 & $i(v5) & $i(v4) & ? [v6: $i] : ? [v7: $i] :
% 109.23/15.20 | (ssList(v6) = 0 & app(v6, v0) = v7 & $i(v7) & $i(v6) & ? [v8:
% 109.23/15.20 | $i] : (v5 = v0 & ssList(v8) = 0 & app(v7, v8) = v2 &
% 109.23/15.20 | $i(v8) & ! [v9: $i] : ( ~ (memberP(v8, v9) = 0) | ~
% 109.23/15.20 | $i(v9) | ? [v10: any] : ? [v11: any] : (lt(v9, v4) =
% 109.23/15.20 | v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 =
% 109.23/15.20 | 0)))) & ! [v9: $i] : ( ~ (memberP(v6, v9) = 0) |
% 109.23/15.20 | ~ $i(v9) | ? [v10: any] : ? [v11: any] : (lt(v4, v9) =
% 109.23/15.20 | v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 =
% 109.23/15.20 | 0))))))) | (v2 = nil & v0 = nil))))
% 109.23/15.20 |
% 109.23/15.20 | ALPHA: (function-axioms) implies:
% 109.23/15.20 | (13) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 109.23/15.20 | : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 109.23/15.20 | (14) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i]
% 109.23/15.20 | : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 109.23/15.20 |
% 109.23/15.20 | DELTA: instantiating (12) with fresh symbols all_93_0, all_93_1 gives:
% 109.23/15.20 | (15) singletonP(all_93_1) = all_93_0 & ssList(all_93_1) = 0 & $i(all_93_1)
% 109.23/15.20 | & ? [v0: $i] : ? [v1: any] : (segmentP(v0, all_93_1) = v1 &
% 109.23/15.20 | ssList(v0) = 0 & neq(v0, nil) = 0 & $i(v0) & ( ~ (v1 = 0) | ~
% 109.23/15.20 | (all_93_0 = 0)) & ( ? [v2: $i] : ? [v3: $i] : (cons(v2, nil) = v3
% 109.23/15.20 | & ssItem(v2) = 0 & $i(v3) & $i(v2) & ? [v4: $i] : ? [v5: $i] :
% 109.23/15.20 | (ssList(v4) = 0 & app(v4, all_93_1) = v5 & $i(v5) & $i(v4) & ?
% 109.23/15.20 | [v6: $i] : (v3 = all_93_1 & ssList(v6) = 0 & app(v5, v6) = v0
% 109.23/15.20 | & $i(v6) & ! [v7: $i] : ( ~ (memberP(v6, v7) = 0) | ~
% 109.23/15.20 | $i(v7) | ? [v8: any] : ? [v9: any] : (lt(v7, v2) = v9 &
% 109.23/15.20 | ssItem(v7) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & !
% 109.23/15.20 | [v7: $i] : ( ~ (memberP(v4, v7) = 0) | ~ $i(v7) | ? [v8:
% 109.23/15.20 | any] : ? [v9: any] : (lt(v2, v7) = v9 & ssItem(v7) = v8
% 109.23/15.20 | & ( ~ (v9 = 0) | ~ (v8 = 0))))))) | (v0 = nil &
% 109.23/15.20 | all_93_1 = nil)))
% 109.23/15.20 |
% 109.23/15.20 | ALPHA: (15) implies:
% 109.23/15.20 | (16) $i(all_93_1)
% 109.23/15.20 | (17) ssList(all_93_1) = 0
% 109.23/15.20 | (18) singletonP(all_93_1) = all_93_0
% 109.23/15.21 | (19) ? [v0: $i] : ? [v1: any] : (segmentP(v0, all_93_1) = v1 & ssList(v0)
% 109.23/15.21 | = 0 & neq(v0, nil) = 0 & $i(v0) & ( ~ (v1 = 0) | ~ (all_93_0 = 0))
% 109.23/15.21 | & ( ? [v2: $i] : ? [v3: $i] : (cons(v2, nil) = v3 & ssItem(v2) = 0
% 109.23/15.21 | & $i(v3) & $i(v2) & ? [v4: $i] : ? [v5: $i] : (ssList(v4) = 0
% 109.23/15.21 | & app(v4, all_93_1) = v5 & $i(v5) & $i(v4) & ? [v6: $i] : (v3
% 109.23/15.21 | = all_93_1 & ssList(v6) = 0 & app(v5, v6) = v0 & $i(v6) & !
% 109.23/15.21 | [v7: $i] : ( ~ (memberP(v6, v7) = 0) | ~ $i(v7) | ? [v8:
% 109.23/15.21 | any] : ? [v9: any] : (lt(v7, v2) = v9 & ssItem(v7) = v8
% 109.23/15.21 | & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v7: $i] : ( ~
% 109.23/15.21 | (memberP(v4, v7) = 0) | ~ $i(v7) | ? [v8: any] : ? [v9:
% 109.23/15.21 | any] : (lt(v2, v7) = v9 & ssItem(v7) = v8 & ( ~ (v9 = 0)
% 109.23/15.21 | | ~ (v8 = 0))))))) | (v0 = nil & all_93_1 = nil)))
% 109.23/15.21 |
% 109.23/15.21 | DELTA: instantiating (19) with fresh symbols all_97_0, all_97_1 gives:
% 109.23/15.21 | (20) segmentP(all_97_1, all_93_1) = all_97_0 & ssList(all_97_1) = 0 &
% 109.23/15.21 | neq(all_97_1, nil) = 0 & $i(all_97_1) & ( ~ (all_97_0 = 0) | ~
% 109.23/15.21 | (all_93_0 = 0)) & ( ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 &
% 109.23/15.21 | ssItem(v0) = 0 & $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] :
% 109.23/15.21 | (ssList(v2) = 0 & app(v2, all_93_1) = v3 & $i(v3) & $i(v2) & ?
% 109.23/15.21 | [v4: $i] : (v1 = all_93_1 & ssList(v4) = 0 & app(v3, v4) =
% 109.23/15.21 | all_97_1 & $i(v4) & ! [v5: $i] : ( ~ (memberP(v4, v5) = 0) |
% 109.23/15.21 | ~ $i(v5) | ? [v6: any] : ? [v7: any] : (lt(v5, v0) = v7 &
% 109.23/15.21 | ssItem(v5) = v6 & ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v5:
% 109.23/15.21 | $i] : ( ~ (memberP(v2, v5) = 0) | ~ $i(v5) | ? [v6: any] :
% 109.23/15.21 | ? [v7: any] : (lt(v0, v5) = v7 & ssItem(v5) = v6 & ( ~ (v7
% 109.23/15.21 | = 0) | ~ (v6 = 0))))))) | (all_97_1 = nil & all_93_1
% 109.23/15.21 | = nil))
% 109.23/15.21 |
% 109.23/15.21 | ALPHA: (20) implies:
% 109.23/15.21 | (21) $i(all_97_1)
% 109.23/15.21 | (22) neq(all_97_1, nil) = 0
% 109.23/15.21 | (23) ssList(all_97_1) = 0
% 109.23/15.21 | (24) segmentP(all_97_1, all_93_1) = all_97_0
% 109.23/15.21 | (25) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = 0 &
% 109.23/15.21 | $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 &
% 109.23/15.21 | app(v2, all_93_1) = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (v1 =
% 109.23/15.21 | all_93_1 & ssList(v4) = 0 & app(v3, v4) = all_97_1 & $i(v4) & !
% 109.23/15.21 | [v5: $i] : ( ~ (memberP(v4, v5) = 0) | ~ $i(v5) | ? [v6: any]
% 109.23/15.21 | : ? [v7: any] : (lt(v5, v0) = v7 & ssItem(v5) = v6 & ( ~ (v7
% 109.23/15.21 | = 0) | ~ (v6 = 0)))) & ! [v5: $i] : ( ~ (memberP(v2,
% 109.23/15.21 | v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7: any] :
% 109.23/15.21 | (lt(v0, v5) = v7 & ssItem(v5) = v6 & ( ~ (v7 = 0) | ~ (v6 =
% 109.23/15.21 | 0))))))) | (all_97_1 = nil & all_93_1 = nil)
% 109.23/15.21 | (26) ~ (all_97_0 = 0) | ~ (all_93_0 = 0)
% 109.23/15.21 |
% 109.23/15.21 | GROUND_INST: instantiating (ax25) with nil, simplifying with (2), (11) gives:
% 109.23/15.22 | (27) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 109.23/15.22 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) &
% 109.23/15.22 | ( ~ (v2 = 0) | v3 = nil)))
% 109.23/15.22 |
% 109.23/15.22 | GROUND_INST: instantiating (ax23) with nil, simplifying with (2), (11) gives:
% 109.23/15.22 | (28) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 109.23/15.22 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) &
% 109.23/15.22 | ( ~ (v2 = 0) | v3 = v0)))
% 109.23/15.22 |
% 109.23/15.22 | GROUND_INST: instantiating (3) with all_97_1, simplifying with (21), (23)
% 109.23/15.22 | gives:
% 109.23/15.22 | (29) all_97_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i]
% 109.23/15.22 | : (cons(v1, v0) = all_97_1 & ssItem(v1) = 0 & $i(v1)))
% 109.23/15.22 |
% 109.23/15.22 | GROUND_INST: instantiating (ax7) with all_97_1, simplifying with (21), (23)
% 109.23/15.22 | gives:
% 109.23/15.22 | (30) ! [v0: $i] : ! [v1: any] : ( ~ (segmentP(all_97_1, v0) = v1) | ~
% 109.23/15.22 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 =
% 109.23/15.22 | 0) | ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 & app(v2, v0)
% 109.23/15.22 | = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (ssList(v4) = 0 &
% 109.23/15.22 | app(v3, v4) = all_97_1 & $i(v4)))) & (v1 = 0 | ! [v2: $i] :
% 109.23/15.22 | ! [v3: $i] : ( ~ (app(v2, v0) = v3) | ~ $i(v2) | ? [v4: int]
% 109.23/15.22 | : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i] : ( ~ (app(v3,
% 109.23/15.22 | v4) = all_97_1) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 =
% 109.23/15.22 | 0) & ssList(v4) = v5))))))
% 109.23/15.22 |
% 109.23/15.22 | GROUND_INST: instantiating (ax15) with all_97_1, simplifying with (21), (23)
% 109.23/15.22 | gives:
% 109.23/15.22 | (31) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_1, v0) = v1) | ~ $i(v0)
% 109.23/15.22 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 109.23/15.22 | ~ (v0 = all_97_1)) & (v1 = 0 | v0 = all_97_1)))
% 109.23/15.22 |
% 109.23/15.22 | GROUND_INST: instantiating (1) with all_93_1, all_93_0, simplifying with (16),
% 109.23/15.22 | (18) gives:
% 109.23/15.22 | (32) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ (all_93_0
% 109.23/15.22 | = 0) | ? [v0: $i] : (cons(v0, nil) = all_93_1 & ssItem(v0) = 0
% 109.23/15.22 | & $i(v0))) & (all_93_0 = 0 | ! [v0: $i] : ( ~ (cons(v0, nil) =
% 109.23/15.22 | all_93_1) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 109.23/15.22 | ssItem(v0) = v1))))
% 109.23/15.22 |
% 109.23/15.22 | GROUND_INST: instantiating (31) with nil, 0, simplifying with (11) gives:
% 109.23/15.22 | (33) ~ (all_97_1 = nil) | ~ (neq(nil, nil) = 0) | ? [v0: int] : ( ~ (v0
% 109.23/15.22 | = 0) & ssList(nil) = v0)
% 109.23/15.22 |
% 109.23/15.22 | GROUND_INST: instantiating (30) with all_93_1, all_97_0, simplifying with
% 109.23/15.22 | (16), (24) gives:
% 109.23/15.23 | (34) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ (all_97_0
% 109.23/15.23 | = 0) | ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0,
% 109.23/15.23 | all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2: $i] : (ssList(v2) =
% 109.23/15.23 | 0 & app(v1, v2) = all_97_1 & $i(v2)))) & (all_97_0 = 0 | !
% 109.23/15.23 | [v0: $i] : ! [v1: $i] : ( ~ (app(v0, all_93_1) = v1) | ~ $i(v0)
% 109.23/15.23 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ! [v2: $i] :
% 109.23/15.23 | ( ~ (app(v1, v2) = all_97_1) | ~ $i(v2) | ? [v3: int] : ( ~
% 109.23/15.23 | (v3 = 0) & ssList(v2) = v3)))))
% 109.23/15.23 |
% 109.23/15.23 | BETA: splitting (25) gives:
% 109.23/15.23 |
% 109.23/15.23 | Case 1:
% 109.23/15.23 | |
% 109.23/15.23 | | (35) ? [v0: $i] : ? [v1: $i] : (cons(v0, nil) = v1 & ssItem(v0) = 0 &
% 109.23/15.23 | | $i(v1) & $i(v0) & ? [v2: $i] : ? [v3: $i] : (ssList(v2) = 0 &
% 109.23/15.23 | | app(v2, all_93_1) = v3 & $i(v3) & $i(v2) & ? [v4: $i] : (v1 =
% 109.23/15.23 | | all_93_1 & ssList(v4) = 0 & app(v3, v4) = all_97_1 & $i(v4) &
% 109.23/15.23 | | ! [v5: $i] : ( ~ (memberP(v4, v5) = 0) | ~ $i(v5) | ? [v6:
% 109.23/15.23 | | any] : ? [v7: any] : (lt(v5, v0) = v7 & ssItem(v5) = v6 &
% 109.23/15.23 | | ( ~ (v7 = 0) | ~ (v6 = 0)))) & ! [v5: $i] : ( ~
% 109.23/15.23 | | (memberP(v2, v5) = 0) | ~ $i(v5) | ? [v6: any] : ? [v7:
% 109.23/15.23 | | any] : (lt(v0, v5) = v7 & ssItem(v5) = v6 & ( ~ (v7 = 0) |
% 109.23/15.23 | | ~ (v6 = 0)))))))
% 109.23/15.23 | |
% 109.23/15.23 | | DELTA: instantiating (35) with fresh symbols all_298_0, all_298_1 gives:
% 109.23/15.23 | | (36) cons(all_298_1, nil) = all_298_0 & ssItem(all_298_1) = 0 &
% 109.23/15.23 | | $i(all_298_0) & $i(all_298_1) & ? [v0: $i] : ? [v1: $i] :
% 109.23/15.23 | | (ssList(v0) = 0 & app(v0, all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2:
% 109.23/15.23 | | $i] : (all_298_0 = all_93_1 & ssList(v2) = 0 & app(v1, v2) =
% 109.23/15.23 | | all_97_1 & $i(v2) & ! [v3: $i] : ( ~ (memberP(v2, v3) = 0) | ~
% 109.23/15.23 | | $i(v3) | ? [v4: any] : ? [v5: any] : (lt(v3, all_298_1) = v5
% 109.23/15.23 | | & ssItem(v3) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))) & ! [v3:
% 109.23/15.23 | | $i] : ( ~ (memberP(v0, v3) = 0) | ~ $i(v3) | ? [v4: any] :
% 109.23/15.23 | | ? [v5: any] : (lt(all_298_1, v3) = v5 & ssItem(v3) = v4 & ( ~
% 109.23/15.23 | | (v5 = 0) | ~ (v4 = 0))))))
% 109.23/15.23 | |
% 109.23/15.23 | | ALPHA: (36) implies:
% 109.23/15.23 | | (37) $i(all_298_1)
% 109.23/15.23 | | (38) ssItem(all_298_1) = 0
% 109.23/15.23 | | (39) cons(all_298_1, nil) = all_298_0
% 109.23/15.23 | | (40) ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0 & app(v0, all_93_1) = v1
% 109.23/15.23 | | & $i(v1) & $i(v0) & ? [v2: $i] : (all_298_0 = all_93_1 &
% 109.23/15.23 | | ssList(v2) = 0 & app(v1, v2) = all_97_1 & $i(v2) & ! [v3: $i] :
% 109.23/15.23 | | ( ~ (memberP(v2, v3) = 0) | ~ $i(v3) | ? [v4: any] : ? [v5:
% 109.23/15.23 | | any] : (lt(v3, all_298_1) = v5 & ssItem(v3) = v4 & ( ~ (v5 =
% 109.23/15.23 | | 0) | ~ (v4 = 0)))) & ! [v3: $i] : ( ~ (memberP(v0, v3)
% 109.23/15.23 | | = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] :
% 109.23/15.23 | | (lt(all_298_1, v3) = v5 & ssItem(v3) = v4 & ( ~ (v5 = 0) | ~
% 109.23/15.23 | | (v4 = 0))))))
% 109.23/15.23 | |
% 109.23/15.23 | | DELTA: instantiating (40) with fresh symbols all_300_0, all_300_1 gives:
% 109.23/15.24 | | (41) ssList(all_300_1) = 0 & app(all_300_1, all_93_1) = all_300_0 &
% 109.23/15.24 | | $i(all_300_0) & $i(all_300_1) & ? [v0: $i] : (all_298_0 = all_93_1
% 109.23/15.24 | | & ssList(v0) = 0 & app(all_300_0, v0) = all_97_1 & $i(v0) & !
% 109.23/15.24 | | [v1: $i] : ( ~ (memberP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] :
% 109.23/15.24 | | ? [v3: any] : (lt(v1, all_298_1) = v3 & ssItem(v1) = v2 & ( ~
% 109.23/15.24 | | (v3 = 0) | ~ (v2 = 0)))) & ! [v1: $i] : ( ~
% 109.23/15.24 | | (memberP(all_300_1, v1) = 0) | ~ $i(v1) | ? [v2: any] : ?
% 109.23/15.24 | | [v3: any] : (lt(all_298_1, v1) = v3 & ssItem(v1) = v2 & ( ~ (v3
% 109.23/15.24 | | = 0) | ~ (v2 = 0)))))
% 109.23/15.24 | |
% 109.23/15.24 | | ALPHA: (41) implies:
% 109.23/15.24 | | (42) $i(all_300_1)
% 109.23/15.24 | | (43) app(all_300_1, all_93_1) = all_300_0
% 109.23/15.24 | | (44) ssList(all_300_1) = 0
% 109.23/15.24 | | (45) ? [v0: $i] : (all_298_0 = all_93_1 & ssList(v0) = 0 &
% 109.23/15.24 | | app(all_300_0, v0) = all_97_1 & $i(v0) & ! [v1: $i] : ( ~
% 109.23/15.24 | | (memberP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any]
% 109.23/15.24 | | : (lt(v1, all_298_1) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~
% 109.23/15.24 | | (v2 = 0)))) & ! [v1: $i] : ( ~ (memberP(all_300_1, v1) = 0)
% 109.23/15.24 | | | ~ $i(v1) | ? [v2: any] : ? [v3: any] : (lt(all_298_1, v1) =
% 109.23/15.24 | | v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 109.23/15.24 | |
% 109.23/15.24 | | DELTA: instantiating (45) with fresh symbol all_302_0 gives:
% 109.23/15.24 | | (46) all_298_0 = all_93_1 & ssList(all_302_0) = 0 & app(all_300_0,
% 109.23/15.24 | | all_302_0) = all_97_1 & $i(all_302_0) & ! [v0: $i] : ( ~
% 109.23/15.24 | | (memberP(all_302_0, v0) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2:
% 109.23/15.24 | | any] : (lt(v0, all_298_1) = v2 & ssItem(v0) = v1 & ( ~ (v2 = 0)
% 109.23/15.24 | | | ~ (v1 = 0)))) & ! [v0: $i] : ( ~ (memberP(all_300_1, v0) =
% 109.23/15.24 | | 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : (lt(all_298_1,
% 109.23/15.24 | | v0) = v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0))))
% 109.23/15.24 | |
% 109.23/15.24 | | ALPHA: (46) implies:
% 109.23/15.24 | | (47) all_298_0 = all_93_1
% 109.23/15.24 | | (48) $i(all_302_0)
% 109.23/15.24 | | (49) app(all_300_0, all_302_0) = all_97_1
% 109.23/15.24 | | (50) ssList(all_302_0) = 0
% 109.23/15.24 | |
% 109.23/15.24 | | REDUCE: (39), (47) imply:
% 109.23/15.24 | | (51) cons(all_298_1, nil) = all_93_1
% 109.23/15.24 | |
% 109.23/15.24 | | BETA: splitting (26) gives:
% 109.23/15.24 | |
% 109.23/15.24 | | Case 1:
% 109.23/15.24 | | |
% 109.23/15.24 | | | (52) ~ (all_97_0 = 0)
% 109.23/15.24 | | |
% 109.23/15.24 | | | BETA: splitting (34) gives:
% 109.23/15.24 | | |
% 109.23/15.24 | | | Case 1:
% 109.23/15.24 | | | |
% 109.23/15.24 | | | | (53) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0)
% 109.23/15.24 | | | |
% 109.23/15.24 | | | | DELTA: instantiating (53) with fresh symbol all_314_0 gives:
% 109.23/15.24 | | | | (54) ~ (all_314_0 = 0) & ssList(all_93_1) = all_314_0
% 109.54/15.24 | | | |
% 109.54/15.25 | | | | REF_CLOSE: (14), (17), (54) are inconsistent by sub-proof #2.
% 109.54/15.25 | | | |
% 109.54/15.25 | | | Case 2:
% 109.54/15.25 | | | |
% 109.54/15.25 | | | | (55) ( ~ (all_97_0 = 0) | ? [v0: $i] : ? [v1: $i] : (ssList(v0) = 0
% 109.54/15.25 | | | | & app(v0, all_93_1) = v1 & $i(v1) & $i(v0) & ? [v2: $i] :
% 109.54/15.25 | | | | (ssList(v2) = 0 & app(v1, v2) = all_97_1 & $i(v2)))) &
% 109.54/15.25 | | | | (all_97_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0,
% 109.54/15.25 | | | | all_93_1) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 =
% 109.54/15.25 | | | | 0) & ssList(v0) = v2) | ! [v2: $i] : ( ~ (app(v1, v2) =
% 109.54/15.25 | | | | all_97_1) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 109.54/15.25 | | | | ssList(v2) = v3))))
% 109.54/15.25 | | | |
% 109.54/15.25 | | | | ALPHA: (55) implies:
% 109.54/15.25 | | | | (56) all_97_0 = 0 | ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0,
% 109.54/15.25 | | | | all_93_1) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0)
% 109.54/15.25 | | | | & ssList(v0) = v2) | ! [v2: $i] : ( ~ (app(v1, v2) =
% 109.54/15.25 | | | | all_97_1) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 109.54/15.25 | | | | ssList(v2) = v3)))
% 109.54/15.25 | | | |
% 109.54/15.25 | | | | BETA: splitting (56) gives:
% 109.54/15.25 | | | |
% 109.54/15.25 | | | | Case 1:
% 109.54/15.25 | | | | |
% 109.54/15.25 | | | | | (57) all_97_0 = 0
% 109.54/15.25 | | | | |
% 109.54/15.25 | | | | | REDUCE: (52), (57) imply:
% 109.54/15.25 | | | | | (58) $false
% 109.54/15.25 | | | | |
% 109.54/15.25 | | | | | CLOSE: (58) is inconsistent.
% 109.54/15.25 | | | | |
% 109.54/15.25 | | | | Case 2:
% 109.54/15.25 | | | | |
% 109.54/15.25 | | | | | (59) ! [v0: $i] : ! [v1: $i] : ( ~ (app(v0, all_93_1) = v1) | ~
% 109.54/15.25 | | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | !
% 109.54/15.25 | | | | | [v2: $i] : ( ~ (app(v1, v2) = all_97_1) | ~ $i(v2) | ?
% 109.54/15.25 | | | | | [v3: int] : ( ~ (v3 = 0) & ssList(v2) = v3)))
% 109.54/15.25 | | | | |
% 109.54/15.25 | | | | | GROUND_INST: instantiating (59) with all_300_1, all_300_0, simplifying
% 109.54/15.25 | | | | | with (42), (43) gives:
% 109.54/15.25 | | | | | (60) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_300_1) = v0) | !
% 109.54/15.25 | | | | | [v0: $i] : ( ~ (app(all_300_0, v0) = all_97_1) | ~ $i(v0) |
% 109.54/15.25 | | | | | ? [v1: int] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 109.54/15.25 | | | | |
% 109.54/15.25 | | | | | BETA: splitting (60) gives:
% 109.54/15.25 | | | | |
% 109.54/15.25 | | | | | Case 1:
% 109.54/15.25 | | | | | |
% 109.54/15.25 | | | | | | (61) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_300_1) = v0)
% 109.54/15.25 | | | | | |
% 109.54/15.25 | | | | | | DELTA: instantiating (61) with fresh symbol all_1019_0 gives:
% 109.54/15.25 | | | | | | (62) ~ (all_1019_0 = 0) & ssList(all_300_1) = all_1019_0
% 109.54/15.25 | | | | | |
% 109.54/15.25 | | | | | | ALPHA: (62) implies:
% 109.54/15.25 | | | | | | (63) ~ (all_1019_0 = 0)
% 109.54/15.25 | | | | | | (64) ssList(all_300_1) = all_1019_0
% 109.54/15.25 | | | | | |
% 109.54/15.25 | | | | | | GROUND_INST: instantiating (14) with 0, all_1019_0, all_300_1,
% 109.54/15.25 | | | | | | simplifying with (44), (64) gives:
% 109.54/15.25 | | | | | | (65) all_1019_0 = 0
% 109.54/15.25 | | | | | |
% 109.54/15.25 | | | | | | REDUCE: (63), (65) imply:
% 109.54/15.25 | | | | | | (66) $false
% 109.54/15.25 | | | | | |
% 109.54/15.25 | | | | | | CLOSE: (66) is inconsistent.
% 109.54/15.25 | | | | | |
% 109.54/15.25 | | | | | Case 2:
% 109.54/15.25 | | | | | |
% 109.54/15.25 | | | | | | (67) ! [v0: $i] : ( ~ (app(all_300_0, v0) = all_97_1) | ~
% 109.54/15.25 | | | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 109.54/15.25 | | | | | |
% 109.54/15.25 | | | | | | GROUND_INST: instantiating (67) with all_302_0, simplifying with
% 109.54/15.25 | | | | | | (48), (49) gives:
% 109.54/15.25 | | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_302_0) = v0)
% 109.54/15.25 | | | | | |
% 109.54/15.25 | | | | | | DELTA: instantiating (68) with fresh symbol all_1016_0 gives:
% 109.54/15.25 | | | | | | (69) ~ (all_1016_0 = 0) & ssList(all_302_0) = all_1016_0
% 109.54/15.25 | | | | | |
% 109.54/15.25 | | | | | | ALPHA: (69) implies:
% 109.54/15.25 | | | | | | (70) ~ (all_1016_0 = 0)
% 109.54/15.25 | | | | | | (71) ssList(all_302_0) = all_1016_0
% 109.54/15.25 | | | | | |
% 109.54/15.25 | | | | | | GROUND_INST: instantiating (14) with 0, all_1016_0, all_302_0,
% 109.54/15.25 | | | | | | simplifying with (50), (71) gives:
% 109.54/15.25 | | | | | | (72) all_1016_0 = 0
% 109.54/15.25 | | | | | |
% 109.54/15.25 | | | | | | REDUCE: (70), (72) imply:
% 109.54/15.25 | | | | | | (73) $false
% 109.54/15.25 | | | | | |
% 109.54/15.25 | | | | | | CLOSE: (73) is inconsistent.
% 109.54/15.25 | | | | | |
% 109.54/15.25 | | | | | End of split
% 109.54/15.25 | | | | |
% 109.54/15.25 | | | | End of split
% 109.54/15.25 | | | |
% 109.54/15.26 | | | End of split
% 109.54/15.26 | | |
% 109.54/15.26 | | Case 2:
% 109.54/15.26 | | |
% 109.54/15.26 | | | (74) ~ (all_93_0 = 0)
% 109.54/15.26 | | |
% 109.54/15.26 | | | BETA: splitting (32) gives:
% 109.54/15.26 | | |
% 109.54/15.26 | | | Case 1:
% 109.54/15.26 | | | |
% 109.54/15.26 | | | | (75) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0)
% 109.54/15.26 | | | |
% 109.54/15.26 | | | | DELTA: instantiating (75) with fresh symbol all_314_0 gives:
% 109.54/15.26 | | | | (76) ~ (all_314_0 = 0) & ssList(all_93_1) = all_314_0
% 109.54/15.26 | | | |
% 109.54/15.26 | | | | REF_CLOSE: (14), (17), (76) are inconsistent by sub-proof #2.
% 109.54/15.26 | | | |
% 109.54/15.26 | | | Case 2:
% 109.54/15.26 | | | |
% 109.54/15.26 | | | | (77) ( ~ (all_93_0 = 0) | ? [v0: $i] : (cons(v0, nil) = all_93_1 &
% 109.54/15.26 | | | | ssItem(v0) = 0 & $i(v0))) & (all_93_0 = 0 | ! [v0: $i] : (
% 109.54/15.26 | | | | ~ (cons(v0, nil) = all_93_1) | ~ $i(v0) | ? [v1: int] : (
% 109.54/15.26 | | | | ~ (v1 = 0) & ssItem(v0) = v1)))
% 109.54/15.26 | | | |
% 109.54/15.26 | | | | ALPHA: (77) implies:
% 109.54/15.26 | | | | (78) all_93_0 = 0 | ! [v0: $i] : ( ~ (cons(v0, nil) = all_93_1) | ~
% 109.54/15.26 | | | | $i(v0) | ? [v1: int] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 109.54/15.26 | | | |
% 109.54/15.26 | | | | BETA: splitting (78) gives:
% 109.54/15.26 | | | |
% 109.54/15.26 | | | | Case 1:
% 109.54/15.26 | | | | |
% 109.54/15.26 | | | | | (79) all_93_0 = 0
% 109.54/15.26 | | | | |
% 109.54/15.26 | | | | | REDUCE: (74), (79) imply:
% 109.54/15.26 | | | | | (80) $false
% 109.54/15.26 | | | | |
% 109.54/15.26 | | | | | CLOSE: (80) is inconsistent.
% 109.54/15.26 | | | | |
% 109.54/15.26 | | | | Case 2:
% 109.54/15.26 | | | | |
% 109.54/15.26 | | | | | (81) ! [v0: $i] : ( ~ (cons(v0, nil) = all_93_1) | ~ $i(v0) | ?
% 109.54/15.26 | | | | | [v1: int] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 109.54/15.26 | | | | |
% 109.54/15.26 | | | | | BETA: splitting (29) gives:
% 109.54/15.26 | | | | |
% 109.54/15.26 | | | | | Case 1:
% 109.54/15.26 | | | | | |
% 109.54/15.26 | | | | | | (82) all_97_1 = nil
% 109.54/15.26 | | | | | |
% 109.54/15.26 | | | | | | REDUCE: (22), (82) imply:
% 109.54/15.26 | | | | | | (83) neq(nil, nil) = 0
% 109.54/15.26 | | | | | |
% 109.54/15.26 | | | | | | REF_CLOSE: (2), (14), (33), (82), (83) are inconsistent by sub-proof
% 109.54/15.26 | | | | | | #1.
% 109.54/15.26 | | | | | |
% 109.54/15.26 | | | | | Case 2:
% 109.54/15.26 | | | | | |
% 109.54/15.26 | | | | | |
% 109.54/15.26 | | | | | | GROUND_INST: instantiating (81) with all_298_1, simplifying with
% 109.54/15.26 | | | | | | (37), (51) gives:
% 109.54/15.26 | | | | | | (84) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_298_1) = v0)
% 109.54/15.26 | | | | | |
% 109.54/15.26 | | | | | | GROUND_INST: instantiating (27) with all_298_1, all_93_1,
% 109.54/15.26 | | | | | | simplifying with (37), (51) gives:
% 109.54/15.26 | | | | | | (85) ? [v0: any] : ? [v1: $i] : (tl(all_93_1) = v1 &
% 109.54/15.26 | | | | | | ssItem(all_298_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 109.54/15.26 | | | | | | nil))
% 109.54/15.26 | | | | | |
% 109.54/15.26 | | | | | | GROUND_INST: instantiating (28) with all_298_1, all_93_1,
% 109.54/15.26 | | | | | | simplifying with (37), (51) gives:
% 109.54/15.26 | | | | | | (86) ? [v0: any] : ? [v1: $i] : (hd(all_93_1) = v1 &
% 109.54/15.26 | | | | | | ssItem(all_298_1) = v0 & $i(v1) & ( ~ (v0 = 0) | v1 =
% 109.54/15.26 | | | | | | all_298_1))
% 109.54/15.26 | | | | | |
% 109.54/15.26 | | | | | | GROUND_INST: instantiating (10) with all_298_1, all_93_1,
% 109.54/15.26 | | | | | | simplifying with (37), (51) gives:
% 109.54/15.26 | | | | | | (87) ? [v0: any] : ? [v1: any] : (equalelemsP(all_93_1) = v1 &
% 109.54/15.26 | | | | | | ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 109.54/15.26 | | | | | |
% 109.54/15.26 | | | | | | GROUND_INST: instantiating (9) with all_298_1, all_93_1, simplifying
% 109.54/15.26 | | | | | | with (37), (51) gives:
% 109.54/15.26 | | | | | | (88) ? [v0: any] : ? [v1: any] : (duplicatefreeP(all_93_1) = v1
% 109.54/15.26 | | | | | | & ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 109.54/15.26 | | | | | |
% 109.54/15.26 | | | | | | GROUND_INST: instantiating (8) with all_298_1, all_93_1, simplifying
% 109.54/15.26 | | | | | | with (37), (51) gives:
% 109.54/15.26 | | | | | | (89) ? [v0: any] : ? [v1: any] : (strictorderedP(all_93_1) = v1
% 109.54/15.26 | | | | | | & ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 109.54/15.26 | | | | | |
% 109.54/15.26 | | | | | | GROUND_INST: instantiating (7) with all_298_1, all_93_1, simplifying
% 109.54/15.26 | | | | | | with (37), (51) gives:
% 109.54/15.26 | | | | | | (90) ? [v0: any] : ? [v1: any] : (totalorderedP(all_93_1) = v1
% 109.54/15.26 | | | | | | & ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 109.54/15.26 | | | | | |
% 109.54/15.26 | | | | | | GROUND_INST: instantiating (6) with all_298_1, all_93_1, simplifying
% 109.54/15.26 | | | | | | with (37), (51) gives:
% 109.54/15.26 | | | | | | (91) ? [v0: any] : ? [v1: any] : (strictorderP(all_93_1) = v1 &
% 109.54/15.26 | | | | | | ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 109.54/15.26 | | | | | |
% 109.54/15.26 | | | | | | GROUND_INST: instantiating (5) with all_298_1, all_93_1, simplifying
% 109.54/15.26 | | | | | | with (37), (51) gives:
% 109.54/15.27 | | | | | | (92) ? [v0: any] : ? [v1: any] : (totalorderP(all_93_1) = v1 &
% 109.54/15.27 | | | | | | ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | GROUND_INST: instantiating (4) with all_298_1, all_93_1, simplifying
% 109.54/15.27 | | | | | | with (37), (51) gives:
% 109.54/15.27 | | | | | | (93) ? [v0: any] : ? [v1: any] : (cyclefreeP(all_93_1) = v1 &
% 109.54/15.27 | | | | | | ssItem(all_298_1) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | DELTA: instantiating (84) with fresh symbol all_1119_0 gives:
% 109.54/15.27 | | | | | | (94) ~ (all_1119_0 = 0) & ssItem(all_298_1) = all_1119_0
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | ALPHA: (94) implies:
% 109.54/15.27 | | | | | | (95) ~ (all_1119_0 = 0)
% 109.54/15.27 | | | | | | (96) ssItem(all_298_1) = all_1119_0
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | DELTA: instantiating (93) with fresh symbols all_1121_0, all_1121_1
% 109.54/15.27 | | | | | | gives:
% 109.54/15.27 | | | | | | (97) cyclefreeP(all_93_1) = all_1121_0 & ssItem(all_298_1) =
% 109.54/15.27 | | | | | | all_1121_1 & ( ~ (all_1121_1 = 0) | all_1121_0 = 0)
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | ALPHA: (97) implies:
% 109.54/15.27 | | | | | | (98) ssItem(all_298_1) = all_1121_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | DELTA: instantiating (91) with fresh symbols all_1123_0, all_1123_1
% 109.54/15.27 | | | | | | gives:
% 109.54/15.27 | | | | | | (99) strictorderP(all_93_1) = all_1123_0 & ssItem(all_298_1) =
% 109.54/15.27 | | | | | | all_1123_1 & ( ~ (all_1123_1 = 0) | all_1123_0 = 0)
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | ALPHA: (99) implies:
% 109.54/15.27 | | | | | | (100) ssItem(all_298_1) = all_1123_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | DELTA: instantiating (90) with fresh symbols all_1125_0, all_1125_1
% 109.54/15.27 | | | | | | gives:
% 109.54/15.27 | | | | | | (101) totalorderedP(all_93_1) = all_1125_0 & ssItem(all_298_1) =
% 109.54/15.27 | | | | | | all_1125_1 & ( ~ (all_1125_1 = 0) | all_1125_0 = 0)
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | ALPHA: (101) implies:
% 109.54/15.27 | | | | | | (102) ssItem(all_298_1) = all_1125_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | DELTA: instantiating (92) with fresh symbols all_1127_0, all_1127_1
% 109.54/15.27 | | | | | | gives:
% 109.54/15.27 | | | | | | (103) totalorderP(all_93_1) = all_1127_0 & ssItem(all_298_1) =
% 109.54/15.27 | | | | | | all_1127_1 & ( ~ (all_1127_1 = 0) | all_1127_0 = 0)
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | ALPHA: (103) implies:
% 109.54/15.27 | | | | | | (104) ssItem(all_298_1) = all_1127_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | DELTA: instantiating (89) with fresh symbols all_1129_0, all_1129_1
% 109.54/15.27 | | | | | | gives:
% 109.54/15.27 | | | | | | (105) strictorderedP(all_93_1) = all_1129_0 & ssItem(all_298_1) =
% 109.54/15.27 | | | | | | all_1129_1 & ( ~ (all_1129_1 = 0) | all_1129_0 = 0)
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | ALPHA: (105) implies:
% 109.54/15.27 | | | | | | (106) ssItem(all_298_1) = all_1129_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | DELTA: instantiating (87) with fresh symbols all_1131_0, all_1131_1
% 109.54/15.27 | | | | | | gives:
% 109.54/15.27 | | | | | | (107) equalelemsP(all_93_1) = all_1131_0 & ssItem(all_298_1) =
% 109.54/15.27 | | | | | | all_1131_1 & ( ~ (all_1131_1 = 0) | all_1131_0 = 0)
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | ALPHA: (107) implies:
% 109.54/15.27 | | | | | | (108) ssItem(all_298_1) = all_1131_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | DELTA: instantiating (88) with fresh symbols all_1133_0, all_1133_1
% 109.54/15.27 | | | | | | gives:
% 109.54/15.27 | | | | | | (109) duplicatefreeP(all_93_1) = all_1133_0 & ssItem(all_298_1) =
% 109.54/15.27 | | | | | | all_1133_1 & ( ~ (all_1133_1 = 0) | all_1133_0 = 0)
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | ALPHA: (109) implies:
% 109.54/15.27 | | | | | | (110) ssItem(all_298_1) = all_1133_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | DELTA: instantiating (86) with fresh symbols all_1135_0, all_1135_1
% 109.54/15.27 | | | | | | gives:
% 109.54/15.27 | | | | | | (111) hd(all_93_1) = all_1135_0 & ssItem(all_298_1) = all_1135_1
% 109.54/15.27 | | | | | | & $i(all_1135_0) & ( ~ (all_1135_1 = 0) | all_1135_0 =
% 109.54/15.27 | | | | | | all_298_1)
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | ALPHA: (111) implies:
% 109.54/15.27 | | | | | | (112) ssItem(all_298_1) = all_1135_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | DELTA: instantiating (85) with fresh symbols all_1137_0, all_1137_1
% 109.54/15.27 | | | | | | gives:
% 109.54/15.27 | | | | | | (113) tl(all_93_1) = all_1137_0 & ssItem(all_298_1) = all_1137_1
% 109.54/15.27 | | | | | | & $i(all_1137_0) & ( ~ (all_1137_1 = 0) | all_1137_0 = nil)
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | ALPHA: (113) implies:
% 109.54/15.27 | | | | | | (114) ssItem(all_298_1) = all_1137_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with 0, all_1125_1, all_298_1,
% 109.54/15.27 | | | | | | simplifying with (38), (102) gives:
% 109.54/15.27 | | | | | | (115) all_1125_1 = 0
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1125_1, all_1129_1,
% 109.54/15.27 | | | | | | all_298_1, simplifying with (102), (106) gives:
% 109.54/15.27 | | | | | | (116) all_1129_1 = all_1125_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1121_1, all_1129_1,
% 109.54/15.27 | | | | | | all_298_1, simplifying with (98), (106) gives:
% 109.54/15.27 | | | | | | (117) all_1129_1 = all_1121_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1131_1, all_1133_1,
% 109.54/15.27 | | | | | | all_298_1, simplifying with (108), (110) gives:
% 109.54/15.27 | | | | | | (118) all_1133_1 = all_1131_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1127_1, all_1133_1,
% 109.54/15.27 | | | | | | all_298_1, simplifying with (104), (110) gives:
% 109.54/15.27 | | | | | | (119) all_1133_1 = all_1127_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1129_1, all_1135_1,
% 109.54/15.27 | | | | | | all_298_1, simplifying with (106), (112) gives:
% 109.54/15.27 | | | | | | (120) all_1135_1 = all_1129_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1127_1, all_1135_1,
% 109.54/15.27 | | | | | | all_298_1, simplifying with (104), (112) gives:
% 109.54/15.27 | | | | | | (121) all_1135_1 = all_1127_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1123_1, all_1135_1,
% 109.54/15.27 | | | | | | all_298_1, simplifying with (100), (112) gives:
% 109.54/15.27 | | | | | | (122) all_1135_1 = all_1123_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1133_1, all_1137_1,
% 109.54/15.27 | | | | | | all_298_1, simplifying with (110), (114) gives:
% 109.54/15.27 | | | | | | (123) all_1137_1 = all_1133_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | GROUND_INST: instantiating (13) with all_1119_0, all_1137_1,
% 109.54/15.27 | | | | | | all_298_1, simplifying with (96), (114) gives:
% 109.54/15.27 | | | | | | (124) all_1137_1 = all_1119_0
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | COMBINE_EQS: (123), (124) imply:
% 109.54/15.27 | | | | | | (125) all_1133_1 = all_1119_0
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | SIMP: (125) implies:
% 109.54/15.27 | | | | | | (126) all_1133_1 = all_1119_0
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | COMBINE_EQS: (120), (122) imply:
% 109.54/15.27 | | | | | | (127) all_1129_1 = all_1123_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | SIMP: (127) implies:
% 109.54/15.27 | | | | | | (128) all_1129_1 = all_1123_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | COMBINE_EQS: (121), (122) imply:
% 109.54/15.27 | | | | | | (129) all_1127_1 = all_1123_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | SIMP: (129) implies:
% 109.54/15.27 | | | | | | (130) all_1127_1 = all_1123_1
% 109.54/15.27 | | | | | |
% 109.54/15.27 | | | | | | COMBINE_EQS: (118), (126) imply:
% 109.54/15.27 | | | | | | (131) all_1131_1 = all_1119_0
% 109.54/15.27 | | | | | |
% 109.54/15.28 | | | | | | COMBINE_EQS: (118), (119) imply:
% 109.54/15.28 | | | | | | (132) all_1131_1 = all_1127_1
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | | COMBINE_EQS: (131), (132) imply:
% 109.54/15.28 | | | | | | (133) all_1127_1 = all_1119_0
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | | SIMP: (133) implies:
% 109.54/15.28 | | | | | | (134) all_1127_1 = all_1119_0
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | | COMBINE_EQS: (116), (117) imply:
% 109.54/15.28 | | | | | | (135) all_1125_1 = all_1121_1
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | | SIMP: (135) implies:
% 109.54/15.28 | | | | | | (136) all_1125_1 = all_1121_1
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | | COMBINE_EQS: (117), (128) imply:
% 109.54/15.28 | | | | | | (137) all_1123_1 = all_1121_1
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | | SIMP: (137) implies:
% 109.54/15.28 | | | | | | (138) all_1123_1 = all_1121_1
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | | COMBINE_EQS: (130), (134) imply:
% 109.54/15.28 | | | | | | (139) all_1123_1 = all_1119_0
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | | SIMP: (139) implies:
% 109.54/15.28 | | | | | | (140) all_1123_1 = all_1119_0
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | | COMBINE_EQS: (115), (136) imply:
% 109.54/15.28 | | | | | | (141) all_1121_1 = 0
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | | SIMP: (141) implies:
% 109.54/15.28 | | | | | | (142) all_1121_1 = 0
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | | COMBINE_EQS: (138), (140) imply:
% 109.54/15.28 | | | | | | (143) all_1121_1 = all_1119_0
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | | SIMP: (143) implies:
% 109.54/15.28 | | | | | | (144) all_1121_1 = all_1119_0
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | | COMBINE_EQS: (142), (144) imply:
% 109.54/15.28 | | | | | | (145) all_1119_0 = 0
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | | REDUCE: (95), (145) imply:
% 109.54/15.28 | | | | | | (146) $false
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | | CLOSE: (146) is inconsistent.
% 109.54/15.28 | | | | | |
% 109.54/15.28 | | | | | End of split
% 109.54/15.28 | | | | |
% 109.54/15.28 | | | | End of split
% 109.54/15.28 | | | |
% 109.54/15.28 | | | End of split
% 109.54/15.28 | | |
% 109.54/15.28 | | End of split
% 109.54/15.28 | |
% 109.54/15.28 | Case 2:
% 109.54/15.28 | |
% 109.54/15.28 | | (147) all_97_1 = nil & all_93_1 = nil
% 109.54/15.28 | |
% 109.54/15.28 | | ALPHA: (147) implies:
% 109.54/15.28 | | (148) all_93_1 = nil
% 109.54/15.28 | | (149) all_97_1 = nil
% 109.54/15.28 | |
% 109.54/15.28 | | REDUCE: (22), (149) imply:
% 109.54/15.28 | | (150) neq(nil, nil) = 0
% 109.54/15.28 | |
% 109.54/15.28 | | REF_CLOSE: (2), (14), (33), (149), (150) are inconsistent by sub-proof #1.
% 109.54/15.28 | |
% 109.54/15.28 | End of split
% 109.54/15.28 |
% 109.54/15.28 End of proof
% 109.54/15.28
% 109.54/15.28 Sub-proof #1 shows that the following formulas are inconsistent:
% 109.54/15.28 ----------------------------------------------------------------
% 109.54/15.28 (1) neq(nil, nil) = 0
% 109.54/15.28 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 109.54/15.28 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 109.54/15.28 (3) ~ (all_97_1 = nil) | ~ (neq(nil, nil) = 0) | ? [v0: int] : ( ~ (v0 =
% 109.54/15.28 0) & ssList(nil) = v0)
% 109.54/15.28 (4) all_97_1 = nil
% 109.54/15.28 (5) ssList(nil) = 0
% 109.54/15.28
% 109.54/15.28 Begin of proof
% 109.54/15.28 |
% 109.54/15.28 | BETA: splitting (3) gives:
% 109.54/15.28 |
% 109.54/15.28 | Case 1:
% 109.54/15.28 | |
% 109.54/15.28 | | (6) ~ (neq(nil, nil) = 0)
% 109.54/15.28 | |
% 109.54/15.28 | | PRED_UNIFY: (1), (6) imply:
% 109.54/15.28 | | (7) $false
% 109.54/15.28 | |
% 109.54/15.28 | | CLOSE: (7) is inconsistent.
% 109.54/15.28 | |
% 109.54/15.28 | Case 2:
% 109.54/15.28 | |
% 109.54/15.28 | | (8) ~ (all_97_1 = nil) | ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 109.54/15.28 | |
% 109.54/15.28 | | BETA: splitting (8) gives:
% 109.54/15.28 | |
% 109.54/15.28 | | Case 1:
% 109.54/15.28 | | |
% 109.54/15.28 | | | (9) ~ (all_97_1 = nil)
% 109.54/15.28 | | |
% 109.54/15.28 | | | REDUCE: (4), (9) imply:
% 109.54/15.28 | | | (10) $false
% 109.54/15.28 | | |
% 109.54/15.28 | | | CLOSE: (10) is inconsistent.
% 109.54/15.28 | | |
% 109.54/15.28 | | Case 2:
% 109.54/15.28 | | |
% 109.54/15.28 | | | (11) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 109.54/15.28 | | |
% 109.54/15.28 | | | DELTA: instantiating (11) with fresh symbol all_286_0 gives:
% 109.54/15.28 | | | (12) ~ (all_286_0 = 0) & ssList(nil) = all_286_0
% 109.54/15.28 | | |
% 109.54/15.28 | | | ALPHA: (12) implies:
% 109.54/15.28 | | | (13) ~ (all_286_0 = 0)
% 109.54/15.28 | | | (14) ssList(nil) = all_286_0
% 109.54/15.28 | | |
% 109.54/15.28 | | | DELTA: instantiating (11) with fresh symbol all_288_0 gives:
% 109.54/15.28 | | | (15) ~ (all_288_0 = 0) & ssList(nil) = all_288_0
% 109.54/15.28 | | |
% 109.54/15.28 | | | ALPHA: (15) implies:
% 109.54/15.28 | | | (16) ssList(nil) = all_288_0
% 109.54/15.28 | | |
% 109.54/15.28 | | | GROUND_INST: instantiating (2) with 0, all_288_0, nil, simplifying with
% 109.54/15.28 | | | (5), (16) gives:
% 109.54/15.28 | | | (17) all_288_0 = 0
% 109.54/15.28 | | |
% 109.54/15.28 | | | GROUND_INST: instantiating (2) with all_286_0, all_288_0, nil, simplifying
% 109.54/15.28 | | | with (14), (16) gives:
% 109.54/15.28 | | | (18) all_288_0 = all_286_0
% 109.54/15.28 | | |
% 109.54/15.28 | | | COMBINE_EQS: (17), (18) imply:
% 109.54/15.28 | | | (19) all_286_0 = 0
% 109.54/15.28 | | |
% 109.54/15.28 | | | REDUCE: (13), (19) imply:
% 109.54/15.28 | | | (20) $false
% 109.54/15.28 | | |
% 109.54/15.28 | | | CLOSE: (20) is inconsistent.
% 109.54/15.28 | | |
% 109.54/15.28 | | End of split
% 109.54/15.28 | |
% 109.54/15.28 | End of split
% 109.54/15.28 |
% 109.54/15.28 End of proof
% 109.54/15.28
% 109.54/15.28 Sub-proof #2 shows that the following formulas are inconsistent:
% 109.54/15.28 ----------------------------------------------------------------
% 109.54/15.28 (1) ~ (all_314_0 = 0) & ssList(all_93_1) = all_314_0
% 109.54/15.28 (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 109.54/15.28 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 109.54/15.28 (3) ssList(all_93_1) = 0
% 109.54/15.28
% 109.54/15.28 Begin of proof
% 109.54/15.28 |
% 109.54/15.28 | ALPHA: (1) implies:
% 109.54/15.28 | (4) ~ (all_314_0 = 0)
% 109.54/15.28 | (5) ssList(all_93_1) = all_314_0
% 109.54/15.28 |
% 109.54/15.28 | GROUND_INST: instantiating (2) with 0, all_314_0, all_93_1, simplifying with
% 109.54/15.28 | (3), (5) gives:
% 109.54/15.29 | (6) all_314_0 = 0
% 109.54/15.29 |
% 109.54/15.29 | REDUCE: (4), (6) imply:
% 109.54/15.29 | (7) $false
% 109.54/15.29 |
% 109.54/15.29 | CLOSE: (7) is inconsistent.
% 109.54/15.29 |
% 109.54/15.29 End of proof
% 109.54/15.29 % SZS output end Proof for theBenchmark
% 109.54/15.29
% 109.54/15.29 14628ms
%------------------------------------------------------------------------------