TSTP Solution File: SWC207+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC207+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 : n022.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 20:50:14 EDT 2023
% Result : Theorem 23.87s 3.98s
% Output : Proof 38.93s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC207+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n022.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 14:59:39 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.59 ________ _____
% 0.19/0.59 ___ __ \_________(_)________________________________
% 0.19/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.59
% 0.19/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.59 (2023-06-19)
% 0.19/0.59
% 0.19/0.59 (c) Philipp Rümmer, 2009-2023
% 0.19/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.59 Amanda Stjerna.
% 0.19/0.59 Free software under BSD-3-Clause.
% 0.19/0.59
% 0.19/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.59
% 0.19/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.60 Running up to 7 provers in parallel.
% 0.19/0.62 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.62 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.62 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.62 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.62 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.62 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.62 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.63/1.53 Prover 4: Preprocessing ...
% 5.63/1.53 Prover 1: Preprocessing ...
% 5.63/1.56 Prover 2: Preprocessing ...
% 5.63/1.56 Prover 0: Preprocessing ...
% 5.63/1.56 Prover 3: Preprocessing ...
% 6.19/1.57 Prover 6: Preprocessing ...
% 6.19/1.57 Prover 5: Preprocessing ...
% 15.21/2.81 Prover 2: Proving ...
% 15.84/2.88 Prover 5: Constructing countermodel ...
% 16.16/2.94 Prover 1: Constructing countermodel ...
% 16.71/2.99 Prover 3: Constructing countermodel ...
% 17.12/3.04 Prover 6: Proving ...
% 23.87/3.93 Prover 4: Constructing countermodel ...
% 23.87/3.96 Prover 0: Proving ...
% 23.87/3.98 Prover 3: proved (3362ms)
% 23.87/3.98
% 23.87/3.98 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 23.87/3.98
% 23.87/3.98 Prover 5: stopped
% 23.87/3.98 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 23.87/3.98 Prover 6: stopped
% 23.87/3.99 Prover 2: stopped
% 23.87/3.99 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 23.87/3.99 Prover 0: stopped
% 24.63/4.00 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 24.63/4.00 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 24.63/4.00 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 26.14/4.21 Prover 8: Preprocessing ...
% 26.14/4.26 Prover 13: Preprocessing ...
% 26.14/4.29 Prover 7: Preprocessing ...
% 26.92/4.34 Prover 10: Preprocessing ...
% 26.92/4.35 Prover 11: Preprocessing ...
% 27.68/4.51 Prover 10: Constructing countermodel ...
% 28.72/4.56 Prover 13: Constructing countermodel ...
% 28.72/4.57 Prover 7: Constructing countermodel ...
% 29.67/4.68 Prover 8: Warning: ignoring some quantifiers
% 29.67/4.70 Prover 8: Constructing countermodel ...
% 35.84/5.50 Prover 11: Constructing countermodel ...
% 37.90/5.81 Prover 1: Found proof (size 66)
% 37.90/5.81 Prover 1: proved (5201ms)
% 37.90/5.81 Prover 11: stopped
% 37.90/5.81 Prover 10: stopped
% 37.90/5.81 Prover 7: stopped
% 37.90/5.81 Prover 8: stopped
% 37.90/5.81 Prover 4: stopped
% 37.90/5.81 Prover 13: stopped
% 37.90/5.81
% 37.90/5.81 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 37.90/5.81
% 37.90/5.82 % SZS output start Proof for theBenchmark
% 37.90/5.83 Assumptions after simplification:
% 37.90/5.83 ---------------------------------
% 37.90/5.83
% 37.90/5.83 (ax15)
% 38.43/5.85 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 38.43/5.85 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 38.43/5.85 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 38.43/5.85
% 38.43/5.86 (ax17)
% 38.43/5.86 ssList(nil) = 0 & $i(nil)
% 38.43/5.86
% 38.43/5.86 (ax18)
% 38.43/5.86 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (cons(v1,
% 38.43/5.86 v0) = v0) | ~ $i(v1) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v1) =
% 38.43/5.86 v2)))
% 38.43/5.86
% 38.43/5.86 (ax20)
% 38.43/5.86 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1:
% 38.43/5.86 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 38.43/5.86 ssItem(v2) = 0 & $i(v2))))
% 38.43/5.86
% 38.43/5.86 (ax23)
% 38.43/5.86 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : (
% 38.43/5.86 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (hd(v2) =
% 38.43/5.86 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v1))))
% 38.43/5.86
% 38.43/5.86 (ax25)
% 38.43/5.86 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: $i] : (
% 38.43/5.86 ~ (cons(v1, v0) = v2) | ~ $i(v1) | ? [v3: any] : ? [v4: $i] : (tl(v2) =
% 38.43/5.86 v4 & ssItem(v1) = v3 & $i(v4) & ( ~ (v3 = 0) | v4 = v0))))
% 38.43/5.86
% 38.43/5.86 (co1)
% 38.43/5.87 $i(nil) & ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 38.43/5.87 $i(v0) & ? [v2: $i] : ( ~ (v1 = 0) & ssList(v2) = 0 & neq(v2, nil) = 0 &
% 38.43/5.87 $i(v2) & ( ? [v3: $i] : (memberP(v2, v3) = 0 & cons(v3, nil) = v0 &
% 38.43/5.87 ssItem(v3) = 0 & $i(v3) & ! [v4: $i] : (v4 = v3 | ~ (memberP(v2, v4)
% 38.43/5.87 = 0) | ~ $i(v4) | ? [v5: any] : ? [v6: any] : (leq(v3, v4) = v6
% 38.43/5.87 & ssItem(v4) = v5 & ( ~ (v6 = 0) | ~ (v5 = 0))))) | (v2 = nil &
% 38.43/5.87 v0 = nil))))
% 38.43/5.87
% 38.43/5.87 (function-axioms)
% 38.43/5.87 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 38.43/5.87 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 38.43/5.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 38.43/5.87 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 38.43/5.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 38.43/5.87 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 38.43/5.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 38.43/5.87 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 38.43/5.87 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 38.43/5.87 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 38.43/5.87 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 38.43/5.87 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 38.43/5.87 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 38.43/5.87 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 38.43/5.87 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 38.43/5.87 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 38.43/5.87 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 38.43/5.87 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 38.43/5.87 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 38.43/5.87 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 38.43/5.87 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 38.43/5.87 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 38.43/5.87 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 38.43/5.87 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 38.43/5.87 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 38.43/5.87 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 38.43/5.87 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 38.43/5.87 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 38.43/5.87 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 38.43/5.87 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 38.43/5.87 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 38.43/5.87 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 38.43/5.87 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 38.43/5.87 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 38.43/5.87 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 38.43/5.87 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 38.43/5.87
% 38.43/5.87 Further assumptions not needed in the proof:
% 38.43/5.87 --------------------------------------------
% 38.43/5.88 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax19, ax2, ax21, ax22, ax24, ax26,
% 38.43/5.88 ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36, ax37, ax38,
% 38.43/5.88 ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47, ax48, ax49, ax5,
% 38.43/5.88 ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59, ax6, ax60, ax61,
% 38.43/5.88 ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71, ax72, ax73,
% 38.43/5.88 ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, ax84, ax85,
% 38.43/5.88 ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 38.43/5.88
% 38.43/5.88 Those formulas are unsatisfiable:
% 38.43/5.88 ---------------------------------
% 38.43/5.88
% 38.43/5.88 Begin of proof
% 38.43/5.88 |
% 38.43/5.88 | ALPHA: (ax17) implies:
% 38.43/5.88 | (1) ssList(nil) = 0
% 38.43/5.88 |
% 38.43/5.88 | ALPHA: (ax20) implies:
% 38.43/5.88 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 38.43/5.88 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 38.43/5.88 | ssItem(v2) = 0 & $i(v2))))
% 38.43/5.88 |
% 38.43/5.88 | ALPHA: (co1) implies:
% 38.43/5.88 | (3) $i(nil)
% 38.43/5.88 | (4) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 38.43/5.88 | $i(v0) & ? [v2: $i] : ( ~ (v1 = 0) & ssList(v2) = 0 & neq(v2, nil) =
% 38.43/5.88 | 0 & $i(v2) & ( ? [v3: $i] : (memberP(v2, v3) = 0 & cons(v3, nil) =
% 38.43/5.88 | v0 & ssItem(v3) = 0 & $i(v3) & ! [v4: $i] : (v4 = v3 | ~
% 38.43/5.88 | (memberP(v2, v4) = 0) | ~ $i(v4) | ? [v5: any] : ? [v6:
% 38.43/5.88 | any] : (leq(v3, v4) = v6 & ssItem(v4) = v5 & ( ~ (v6 = 0) |
% 38.43/5.88 | ~ (v5 = 0))))) | (v2 = nil & v0 = nil))))
% 38.43/5.88 |
% 38.43/5.88 | ALPHA: (function-axioms) implies:
% 38.43/5.88 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 38.43/5.88 | (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 38.43/5.88 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 38.43/5.88 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 38.43/5.88 | (7) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 38.43/5.88 | ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0))
% 38.43/5.88 |
% 38.43/5.88 | DELTA: instantiating (4) with fresh symbols all_93_0, all_93_1 gives:
% 38.43/5.89 | (8) ssList(all_93_1) = 0 & neq(all_93_1, nil) = all_93_0 & $i(all_93_1) &
% 38.43/5.89 | ? [v0: $i] : ( ~ (all_93_0 = 0) & ssList(v0) = 0 & neq(v0, nil) = 0 &
% 38.43/5.89 | $i(v0) & ( ? [v1: $i] : (memberP(v0, v1) = 0 & cons(v1, nil) =
% 38.43/5.89 | all_93_1 & ssItem(v1) = 0 & $i(v1) & ! [v2: $i] : (v2 = v1 | ~
% 38.43/5.89 | (memberP(v0, v2) = 0) | ~ $i(v2) | ? [v3: any] : ? [v4: any]
% 38.43/5.89 | : (leq(v1, v2) = v4 & ssItem(v2) = v3 & ( ~ (v4 = 0) | ~ (v3 =
% 38.43/5.89 | 0))))) | (v0 = nil & all_93_1 = nil)))
% 38.43/5.89 |
% 38.43/5.89 | ALPHA: (8) implies:
% 38.43/5.89 | (9) $i(all_93_1)
% 38.43/5.89 | (10) neq(all_93_1, nil) = all_93_0
% 38.43/5.89 | (11) ssList(all_93_1) = 0
% 38.43/5.89 | (12) ? [v0: $i] : ( ~ (all_93_0 = 0) & ssList(v0) = 0 & neq(v0, nil) = 0 &
% 38.43/5.89 | $i(v0) & ( ? [v1: $i] : (memberP(v0, v1) = 0 & cons(v1, nil) =
% 38.43/5.89 | all_93_1 & ssItem(v1) = 0 & $i(v1) & ! [v2: $i] : (v2 = v1 | ~
% 38.43/5.89 | (memberP(v0, v2) = 0) | ~ $i(v2) | ? [v3: any] : ? [v4:
% 38.43/5.89 | any] : (leq(v1, v2) = v4 & ssItem(v2) = v3 & ( ~ (v4 = 0) |
% 38.43/5.89 | ~ (v3 = 0))))) | (v0 = nil & all_93_1 = nil)))
% 38.43/5.89 |
% 38.43/5.89 | DELTA: instantiating (12) with fresh symbol all_97_0 gives:
% 38.43/5.89 | (13) ~ (all_93_0 = 0) & ssList(all_97_0) = 0 & neq(all_97_0, nil) = 0 &
% 38.43/5.89 | $i(all_97_0) & ( ? [v0: $i] : (memberP(all_97_0, v0) = 0 & cons(v0,
% 38.43/5.89 | nil) = all_93_1 & ssItem(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 =
% 38.43/5.89 | v0 | ~ (memberP(all_97_0, v1) = 0) | ~ $i(v1) | ? [v2: any] :
% 38.43/5.89 | ? [v3: any] : (leq(v0, v1) = v3 & ssItem(v1) = v2 & ( ~ (v3 =
% 38.43/5.89 | 0) | ~ (v2 = 0))))) | (all_97_0 = nil & all_93_1 = nil))
% 38.43/5.89 |
% 38.43/5.89 | ALPHA: (13) implies:
% 38.43/5.89 | (14) ~ (all_93_0 = 0)
% 38.43/5.89 | (15) $i(all_97_0)
% 38.43/5.89 | (16) neq(all_97_0, nil) = 0
% 38.43/5.89 | (17) ssList(all_97_0) = 0
% 38.43/5.89 | (18) ? [v0: $i] : (memberP(all_97_0, v0) = 0 & cons(v0, nil) = all_93_1 &
% 38.43/5.89 | ssItem(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 = v0 | ~
% 38.43/5.89 | (memberP(all_97_0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3:
% 38.43/5.89 | any] : (leq(v0, v1) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~
% 38.43/5.89 | (v2 = 0))))) | (all_97_0 = nil & all_93_1 = nil)
% 38.43/5.89 |
% 38.43/5.89 | GROUND_INST: instantiating (ax25) with nil, simplifying with (1), (3) gives:
% 38.43/5.89 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 38.43/5.89 | [v2: any] : ? [v3: $i] : (tl(v1) = v3 & ssItem(v0) = v2 & $i(v3) &
% 38.43/5.89 | ( ~ (v2 = 0) | v3 = nil)))
% 38.43/5.89 |
% 38.43/5.89 | GROUND_INST: instantiating (ax23) with nil, simplifying with (1), (3) gives:
% 38.81/5.89 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1) | ~ $i(v0) | ?
% 38.81/5.89 | [v2: any] : ? [v3: $i] : (hd(v1) = v3 & ssItem(v0) = v2 & $i(v3) &
% 38.81/5.89 | ( ~ (v2 = 0) | v3 = v0)))
% 38.81/5.89 |
% 38.81/5.89 | GROUND_INST: instantiating (ax18) with nil, simplifying with (1), (3) gives:
% 38.81/5.90 | (21) ! [v0: $i] : ( ~ (cons(v0, nil) = nil) | ~ $i(v0) | ? [v1: int] : (
% 38.81/5.90 | ~ (v1 = 0) & ssItem(v0) = v1))
% 38.81/5.90 |
% 38.81/5.90 | GROUND_INST: instantiating (ax15) with all_93_1, simplifying with (9), (11)
% 38.81/5.90 | gives:
% 38.81/5.90 | (22) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_93_1, v0) = v1) | ~ $i(v0)
% 38.81/5.90 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 38.81/5.90 | ~ (v0 = all_93_1)) & (v1 = 0 | v0 = all_93_1)))
% 38.81/5.90 |
% 38.81/5.90 | GROUND_INST: instantiating (2) with all_97_0, simplifying with (15), (17)
% 38.81/5.90 | gives:
% 38.81/5.90 | (23) all_97_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i]
% 38.81/5.90 | : (cons(v1, v0) = all_97_0 & ssItem(v1) = 0 & $i(v1)))
% 38.81/5.90 |
% 38.81/5.90 | GROUND_INST: instantiating (22) with nil, all_93_0, simplifying with (3), (10)
% 38.81/5.90 | gives:
% 38.81/5.90 | (24) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_93_0 = 0)
% 38.81/5.90 | | ~ (all_93_1 = nil)) & (all_93_0 = 0 | all_93_1 = nil))
% 38.81/5.90 |
% 38.81/5.90 | BETA: splitting (24) gives:
% 38.81/5.90 |
% 38.81/5.90 | Case 1:
% 38.81/5.90 | |
% 38.81/5.90 | | (25) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 38.81/5.90 | |
% 38.81/5.90 | | DELTA: instantiating (25) with fresh symbol all_274_0 gives:
% 38.81/5.90 | | (26) ~ (all_274_0 = 0) & ssList(nil) = all_274_0
% 38.81/5.90 | |
% 38.81/5.90 | | ALPHA: (26) implies:
% 38.81/5.90 | | (27) ~ (all_274_0 = 0)
% 38.81/5.90 | | (28) ssList(nil) = all_274_0
% 38.81/5.90 | |
% 38.81/5.90 | | DELTA: instantiating (25) with fresh symbol all_276_0 gives:
% 38.81/5.90 | | (29) ~ (all_276_0 = 0) & ssList(nil) = all_276_0
% 38.81/5.90 | |
% 38.81/5.90 | | ALPHA: (29) implies:
% 38.81/5.90 | | (30) ssList(nil) = all_276_0
% 38.81/5.90 | |
% 38.81/5.90 | | GROUND_INST: instantiating (6) with 0, all_276_0, nil, simplifying with (1),
% 38.81/5.90 | | (30) gives:
% 38.81/5.90 | | (31) all_276_0 = 0
% 38.81/5.90 | |
% 38.81/5.90 | | GROUND_INST: instantiating (6) with all_274_0, all_276_0, nil, simplifying
% 38.81/5.90 | | with (28), (30) gives:
% 38.81/5.90 | | (32) all_276_0 = all_274_0
% 38.81/5.90 | |
% 38.81/5.90 | | COMBINE_EQS: (31), (32) imply:
% 38.81/5.90 | | (33) all_274_0 = 0
% 38.81/5.90 | |
% 38.81/5.90 | | REDUCE: (27), (33) imply:
% 38.81/5.90 | | (34) $false
% 38.81/5.90 | |
% 38.81/5.90 | | CLOSE: (34) is inconsistent.
% 38.81/5.90 | |
% 38.81/5.90 | Case 2:
% 38.81/5.90 | |
% 38.81/5.90 | | (35) ( ~ (all_93_0 = 0) | ~ (all_93_1 = nil)) & (all_93_0 = 0 | all_93_1
% 38.81/5.90 | | = nil)
% 38.81/5.90 | |
% 38.81/5.90 | | ALPHA: (35) implies:
% 38.81/5.90 | | (36) all_93_0 = 0 | all_93_1 = nil
% 38.81/5.90 | |
% 38.81/5.90 | | BETA: splitting (36) gives:
% 38.81/5.90 | |
% 38.81/5.90 | | Case 1:
% 38.81/5.90 | | |
% 38.81/5.90 | | | (37) all_93_1 = nil
% 38.81/5.90 | | |
% 38.81/5.90 | | | REDUCE: (10), (37) imply:
% 38.81/5.90 | | | (38) neq(nil, nil) = all_93_0
% 38.81/5.90 | | |
% 38.81/5.90 | | | BETA: splitting (18) gives:
% 38.81/5.90 | | |
% 38.81/5.90 | | | Case 1:
% 38.81/5.90 | | | |
% 38.81/5.91 | | | | (39) ? [v0: $i] : (memberP(all_97_0, v0) = 0 & cons(v0, nil) =
% 38.81/5.91 | | | | all_93_1 & ssItem(v0) = 0 & $i(v0) & ! [v1: $i] : (v1 = v0 |
% 38.81/5.91 | | | | ~ (memberP(all_97_0, v1) = 0) | ~ $i(v1) | ? [v2: any] :
% 38.81/5.91 | | | | ? [v3: any] : (leq(v0, v1) = v3 & ssItem(v1) = v2 & ( ~ (v3
% 38.81/5.91 | | | | = 0) | ~ (v2 = 0)))))
% 38.81/5.91 | | | |
% 38.81/5.91 | | | | DELTA: instantiating (39) with fresh symbol all_299_0 gives:
% 38.81/5.91 | | | | (40) memberP(all_97_0, all_299_0) = 0 & cons(all_299_0, nil) =
% 38.81/5.91 | | | | all_93_1 & ssItem(all_299_0) = 0 & $i(all_299_0) & ! [v0: any]
% 38.81/5.91 | | | | : (v0 = all_299_0 | ~ (memberP(all_97_0, v0) = 0) | ~ $i(v0) |
% 38.81/5.91 | | | | ? [v1: any] : ? [v2: any] : (leq(all_299_0, v0) = v2 &
% 38.81/5.91 | | | | ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0))))
% 38.81/5.91 | | | |
% 38.81/5.91 | | | | ALPHA: (40) implies:
% 38.81/5.91 | | | | (41) $i(all_299_0)
% 38.81/5.91 | | | | (42) ssItem(all_299_0) = 0
% 38.81/5.91 | | | | (43) cons(all_299_0, nil) = all_93_1
% 38.81/5.91 | | | |
% 38.81/5.91 | | | | REDUCE: (37), (43) imply:
% 38.81/5.91 | | | | (44) cons(all_299_0, nil) = nil
% 38.81/5.91 | | | |
% 38.81/5.91 | | | | BETA: splitting (23) gives:
% 38.81/5.91 | | | |
% 38.81/5.91 | | | | Case 1:
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | (45) all_97_0 = nil
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | REDUCE: (16), (45) imply:
% 38.81/5.91 | | | | | (46) neq(nil, nil) = 0
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | GROUND_INST: instantiating (7) with all_93_0, 0, nil, nil, simplifying
% 38.81/5.91 | | | | | with (38), (46) gives:
% 38.81/5.91 | | | | | (47) all_93_0 = 0
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | REDUCE: (14), (47) imply:
% 38.81/5.91 | | | | | (48) $false
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | CLOSE: (48) is inconsistent.
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | Case 2:
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | GROUND_INST: instantiating (21) with all_299_0, simplifying with (41),
% 38.81/5.91 | | | | | (44) gives:
% 38.81/5.91 | | | | | (49) ? [v0: int] : ( ~ (v0 = 0) & ssItem(all_299_0) = v0)
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | GROUND_INST: instantiating (19) with all_299_0, nil, simplifying with
% 38.81/5.91 | | | | | (41), (44) gives:
% 38.81/5.91 | | | | | (50) ? [v0: any] : ? [v1: $i] : (tl(nil) = v1 & ssItem(all_299_0)
% 38.81/5.91 | | | | | = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = nil))
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | GROUND_INST: instantiating (20) with all_299_0, nil, simplifying with
% 38.81/5.91 | | | | | (41), (44) gives:
% 38.81/5.91 | | | | | (51) ? [v0: any] : ? [v1: $i] : (hd(nil) = v1 & ssItem(all_299_0)
% 38.81/5.91 | | | | | = v0 & $i(v1) & ( ~ (v0 = 0) | v1 = all_299_0))
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | DELTA: instantiating (49) with fresh symbol all_518_0 gives:
% 38.81/5.91 | | | | | (52) ~ (all_518_0 = 0) & ssItem(all_299_0) = all_518_0
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | ALPHA: (52) implies:
% 38.81/5.91 | | | | | (53) ~ (all_518_0 = 0)
% 38.81/5.91 | | | | | (54) ssItem(all_299_0) = all_518_0
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | DELTA: instantiating (50) with fresh symbols all_520_0, all_520_1
% 38.81/5.91 | | | | | gives:
% 38.81/5.91 | | | | | (55) tl(nil) = all_520_0 & ssItem(all_299_0) = all_520_1 &
% 38.81/5.91 | | | | | $i(all_520_0) & ( ~ (all_520_1 = 0) | all_520_0 = nil)
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | ALPHA: (55) implies:
% 38.81/5.91 | | | | | (56) ssItem(all_299_0) = all_520_1
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | DELTA: instantiating (51) with fresh symbols all_522_0, all_522_1
% 38.81/5.91 | | | | | gives:
% 38.81/5.91 | | | | | (57) hd(nil) = all_522_0 & ssItem(all_299_0) = all_522_1 &
% 38.81/5.91 | | | | | $i(all_522_0) & ( ~ (all_522_1 = 0) | all_522_0 = all_299_0)
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | ALPHA: (57) implies:
% 38.81/5.91 | | | | | (58) ssItem(all_299_0) = all_522_1
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | GROUND_INST: instantiating (5) with all_518_0, all_520_1, all_299_0,
% 38.81/5.91 | | | | | simplifying with (54), (56) gives:
% 38.81/5.91 | | | | | (59) all_520_1 = all_518_0
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | GROUND_INST: instantiating (5) with 0, all_522_1, all_299_0,
% 38.81/5.91 | | | | | simplifying with (42), (58) gives:
% 38.81/5.91 | | | | | (60) all_522_1 = 0
% 38.81/5.91 | | | | |
% 38.81/5.91 | | | | | GROUND_INST: instantiating (5) with all_520_1, all_522_1, all_299_0,
% 38.81/5.91 | | | | | simplifying with (56), (58) gives:
% 38.81/5.91 | | | | | (61) all_522_1 = all_520_1
% 38.81/5.91 | | | | |
% 38.81/5.92 | | | | | COMBINE_EQS: (60), (61) imply:
% 38.81/5.92 | | | | | (62) all_520_1 = 0
% 38.81/5.92 | | | | |
% 38.81/5.92 | | | | | SIMP: (62) implies:
% 38.81/5.92 | | | | | (63) all_520_1 = 0
% 38.81/5.92 | | | | |
% 38.81/5.92 | | | | | COMBINE_EQS: (59), (63) imply:
% 38.81/5.92 | | | | | (64) all_518_0 = 0
% 38.81/5.92 | | | | |
% 38.81/5.92 | | | | | SIMP: (64) implies:
% 38.81/5.92 | | | | | (65) all_518_0 = 0
% 38.81/5.92 | | | | |
% 38.81/5.92 | | | | | REDUCE: (53), (65) imply:
% 38.81/5.92 | | | | | (66) $false
% 38.81/5.92 | | | | |
% 38.81/5.92 | | | | | CLOSE: (66) is inconsistent.
% 38.81/5.92 | | | | |
% 38.81/5.92 | | | | End of split
% 38.81/5.92 | | | |
% 38.81/5.92 | | | Case 2:
% 38.81/5.92 | | | |
% 38.81/5.92 | | | | (67) all_97_0 = nil & all_93_1 = nil
% 38.81/5.92 | | | |
% 38.81/5.92 | | | | ALPHA: (67) implies:
% 38.81/5.92 | | | | (68) all_97_0 = nil
% 38.81/5.92 | | | |
% 38.81/5.92 | | | | REDUCE: (16), (68) imply:
% 38.81/5.92 | | | | (69) neq(nil, nil) = 0
% 38.81/5.92 | | | |
% 38.81/5.92 | | | | GROUND_INST: instantiating (7) with all_93_0, 0, nil, nil, simplifying
% 38.81/5.92 | | | | with (38), (69) gives:
% 38.81/5.92 | | | | (70) all_93_0 = 0
% 38.81/5.92 | | | |
% 38.93/5.92 | | | | REDUCE: (14), (70) imply:
% 38.93/5.92 | | | | (71) $false
% 38.93/5.92 | | | |
% 38.93/5.92 | | | | CLOSE: (71) is inconsistent.
% 38.93/5.92 | | | |
% 38.93/5.92 | | | End of split
% 38.93/5.92 | | |
% 38.93/5.92 | | Case 2:
% 38.93/5.92 | | |
% 38.93/5.92 | | | (72) all_93_0 = 0
% 38.93/5.92 | | |
% 38.93/5.92 | | | REDUCE: (14), (72) imply:
% 38.93/5.92 | | | (73) $false
% 38.93/5.92 | | |
% 38.93/5.92 | | | CLOSE: (73) is inconsistent.
% 38.93/5.92 | | |
% 38.93/5.92 | | End of split
% 38.93/5.92 | |
% 38.93/5.92 | End of split
% 38.93/5.92 |
% 38.93/5.92 End of proof
% 38.93/5.92 % SZS output end Proof for theBenchmark
% 38.93/5.92
% 38.93/5.92 5326ms
%------------------------------------------------------------------------------