TSTP Solution File: SWC116+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC116+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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 20:49:44 EDT 2023
% Result : Theorem 22.94s 3.85s
% Output : Proof 31.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC116+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 16:24:08 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.77/1.57 Prover 4: Preprocessing ...
% 5.77/1.57 Prover 1: Preprocessing ...
% 5.77/1.58 Prover 2: Preprocessing ...
% 5.77/1.58 Prover 0: Preprocessing ...
% 5.77/1.58 Prover 6: Preprocessing ...
% 5.77/1.58 Prover 3: Preprocessing ...
% 5.77/1.58 Prover 5: Preprocessing ...
% 16.51/3.01 Prover 2: Proving ...
% 16.51/3.02 Prover 5: Constructing countermodel ...
% 16.96/3.06 Prover 1: Constructing countermodel ...
% 16.96/3.07 Prover 6: Proving ...
% 16.96/3.08 Prover 3: Constructing countermodel ...
% 22.94/3.85 Prover 3: proved (3209ms)
% 22.94/3.85
% 22.94/3.85 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.94/3.85
% 22.94/3.86 Prover 5: stopped
% 22.94/3.86 Prover 2: stopped
% 22.94/3.86 Prover 6: stopped
% 22.94/3.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.94/3.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.94/3.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 22.94/3.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 23.16/3.89 Prover 4: Constructing countermodel ...
% 24.40/4.05 Prover 0: Proving ...
% 24.70/4.07 Prover 0: stopped
% 24.70/4.08 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.70/4.11 Prover 7: Preprocessing ...
% 24.70/4.17 Prover 8: Preprocessing ...
% 24.70/4.18 Prover 11: Preprocessing ...
% 24.70/4.19 Prover 10: Preprocessing ...
% 26.05/4.27 Prover 13: Preprocessing ...
% 26.89/4.38 Prover 7: Constructing countermodel ...
% 26.89/4.39 Prover 10: Constructing countermodel ...
% 27.85/4.53 Prover 13: Constructing countermodel ...
% 28.81/4.63 Prover 8: Warning: ignoring some quantifiers
% 28.81/4.64 Prover 1: Found proof (size 50)
% 28.81/4.64 Prover 1: proved (3998ms)
% 28.81/4.64 Prover 7: stopped
% 28.81/4.64 Prover 10: stopped
% 28.81/4.64 Prover 4: stopped
% 28.81/4.64 Prover 13: stopped
% 28.81/4.64 Prover 8: Constructing countermodel ...
% 28.81/4.65 Prover 8: stopped
% 30.55/5.07 Prover 11: Constructing countermodel ...
% 30.55/5.09 Prover 11: stopped
% 30.55/5.09
% 30.55/5.09 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 30.55/5.09
% 30.91/5.10 % SZS output start Proof for theBenchmark
% 30.91/5.11 Assumptions after simplification:
% 30.91/5.11 ---------------------------------
% 30.91/5.11
% 30.91/5.11 (ax15)
% 30.91/5.16 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 30.91/5.16 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 30.91/5.16 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 30.91/5.16
% 30.91/5.16 (ax17)
% 30.91/5.16 ssList(nil) = 0 & $i(nil)
% 30.91/5.16
% 30.91/5.16 (co1)
% 30.91/5.16 $i(nil) & ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 30.91/5.16 $i(v0) & ? [v2: $i] : ? [v3: any] : (segmentP(v2, v0) = v3 & ssList(v2) =
% 30.91/5.16 0 & $i(v2) & ? [v4: $i] : ? [v5: any] : (ssList(v4) = 0 & neq(v4, nil) =
% 30.91/5.16 v5 & $i(v4) & ? [v6: any] : (v4 = v0 & neq(v2, nil) = v6 & ( ~ (v6 = 0)
% 30.91/5.16 | (v5 = 0 & v3 = 0)) & ( ~ (v3 = 0) | ~ (v1 = 0)) & ( ~ (v2 = nil)
% 30.91/5.16 | ~ (v0 = nil)) & ( ~ (v2 = nil) | v0 = nil)))))
% 30.91/5.16
% 30.91/5.16 (function-axioms)
% 30.91/5.17 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 30.91/5.17 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 30.91/5.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 30.91/5.17 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 30.91/5.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 30.91/5.17 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 30.91/5.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 30.91/5.17 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 30.91/5.17 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 30.91/5.17 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 30.91/5.17 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 30.91/5.17 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 30.91/5.17 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 30.91/5.17 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 30.91/5.17 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 30.91/5.17 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 30.91/5.18 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 30.91/5.18 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 30.91/5.18 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 30.91/5.18 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 30.91/5.18 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 30.91/5.18 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 30.91/5.18 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 30.91/5.18 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 30.91/5.18 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 30.91/5.18 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 30.91/5.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 30.91/5.18 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 30.91/5.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 30.91/5.18 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 30.91/5.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 30.91/5.18 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 30.91/5.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 30.91/5.18 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 30.91/5.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 30.91/5.18 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 30.91/5.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 30.91/5.18 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 30.91/5.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 30.91/5.18 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 30.91/5.18 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 30.91/5.18 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 30.91/5.18 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 30.91/5.18
% 30.91/5.18 Further assumptions not needed in the proof:
% 30.91/5.18 --------------------------------------------
% 30.91/5.18 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 30.91/5.18 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34,
% 30.91/5.18 ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46,
% 30.91/5.18 ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58,
% 30.91/5.18 ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7,
% 30.91/5.18 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 30.91/5.18 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 30.91/5.18 ax94, ax95
% 30.91/5.18
% 30.91/5.18 Those formulas are unsatisfiable:
% 30.91/5.18 ---------------------------------
% 30.91/5.18
% 30.91/5.18 Begin of proof
% 30.91/5.18 |
% 30.91/5.18 | ALPHA: (ax17) implies:
% 30.91/5.18 | (1) ssList(nil) = 0
% 30.91/5.18 |
% 30.91/5.18 | ALPHA: (co1) implies:
% 30.91/5.18 | (2) $i(nil)
% 31.30/5.18 | (3) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 31.30/5.18 | $i(v0) & ? [v2: $i] : ? [v3: any] : (segmentP(v2, v0) = v3 &
% 31.30/5.18 | ssList(v2) = 0 & $i(v2) & ? [v4: $i] : ? [v5: any] : (ssList(v4)
% 31.30/5.18 | = 0 & neq(v4, nil) = v5 & $i(v4) & ? [v6: any] : (v4 = v0 &
% 31.30/5.18 | neq(v2, nil) = v6 & ( ~ (v6 = 0) | (v5 = 0 & v3 = 0)) & ( ~ (v3
% 31.30/5.18 | = 0) | ~ (v1 = 0)) & ( ~ (v2 = nil) | ~ (v0 = nil)) & ( ~
% 31.30/5.18 | (v2 = nil) | v0 = nil)))))
% 31.30/5.18 |
% 31.30/5.18 | ALPHA: (function-axioms) implies:
% 31.30/5.18 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 31.30/5.18 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 31.30/5.18 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 31.30/5.18 | ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0))
% 31.30/5.18 |
% 31.30/5.18 | DELTA: instantiating (3) with fresh symbols all_93_0, all_93_1 gives:
% 31.30/5.18 | (6) ssList(all_93_1) = 0 & neq(all_93_1, nil) = all_93_0 & $i(all_93_1) &
% 31.30/5.18 | ? [v0: $i] : ? [v1: any] : (segmentP(v0, all_93_1) = v1 & ssList(v0) =
% 31.30/5.19 | 0 & $i(v0) & ? [v2: $i] : ? [v3: any] : (ssList(v2) = 0 & neq(v2,
% 31.30/5.19 | nil) = v3 & $i(v2) & ? [v4: any] : (v2 = all_93_1 & neq(v0, nil)
% 31.30/5.19 | = v4 & ( ~ (v4 = 0) | (v3 = 0 & v1 = 0)) & ( ~ (v1 = 0) | ~
% 31.30/5.19 | (all_93_0 = 0)) & ( ~ (v0 = nil) | ~ (all_93_1 = nil)) & ( ~
% 31.30/5.19 | (v0 = nil) | all_93_1 = nil))))
% 31.30/5.19 |
% 31.30/5.19 | ALPHA: (6) implies:
% 31.30/5.19 | (7) neq(all_93_1, nil) = all_93_0
% 31.30/5.19 | (8) ? [v0: $i] : ? [v1: any] : (segmentP(v0, all_93_1) = v1 & ssList(v0)
% 31.30/5.19 | = 0 & $i(v0) & ? [v2: $i] : ? [v3: any] : (ssList(v2) = 0 & neq(v2,
% 31.30/5.19 | nil) = v3 & $i(v2) & ? [v4: any] : (v2 = all_93_1 & neq(v0, nil)
% 31.30/5.19 | = v4 & ( ~ (v4 = 0) | (v3 = 0 & v1 = 0)) & ( ~ (v1 = 0) | ~
% 31.30/5.19 | (all_93_0 = 0)) & ( ~ (v0 = nil) | ~ (all_93_1 = nil)) & ( ~
% 31.30/5.19 | (v0 = nil) | all_93_1 = nil))))
% 31.30/5.19 |
% 31.30/5.19 | DELTA: instantiating (8) with fresh symbols all_97_0, all_97_1 gives:
% 31.30/5.19 | (9) segmentP(all_97_1, all_93_1) = all_97_0 & ssList(all_97_1) = 0 &
% 31.30/5.19 | $i(all_97_1) & ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0,
% 31.30/5.19 | nil) = v1 & $i(v0) & ? [v2: any] : (v0 = all_93_1 & neq(all_97_1,
% 31.30/5.19 | nil) = v2 & ( ~ (v2 = 0) | (v1 = 0 & all_97_0 = 0)) & ( ~
% 31.30/5.19 | (all_97_0 = 0) | ~ (all_93_0 = 0)) & ( ~ (all_97_1 = nil) | ~
% 31.30/5.19 | (all_93_1 = nil)) & ( ~ (all_97_1 = nil) | all_93_1 = nil)))
% 31.30/5.19 |
% 31.30/5.19 | ALPHA: (9) implies:
% 31.30/5.19 | (10) $i(all_97_1)
% 31.30/5.19 | (11) ssList(all_97_1) = 0
% 31.30/5.19 | (12) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 31.30/5.19 | $i(v0) & ? [v2: any] : (v0 = all_93_1 & neq(all_97_1, nil) = v2 & (
% 31.30/5.19 | ~ (v2 = 0) | (v1 = 0 & all_97_0 = 0)) & ( ~ (all_97_0 = 0) | ~
% 31.30/5.19 | (all_93_0 = 0)) & ( ~ (all_97_1 = nil) | ~ (all_93_1 = nil)) &
% 31.30/5.19 | ( ~ (all_97_1 = nil) | all_93_1 = nil)))
% 31.30/5.19 |
% 31.30/5.19 | DELTA: instantiating (12) with fresh symbols all_99_0, all_99_1 gives:
% 31.30/5.19 | (13) ssList(all_99_1) = 0 & neq(all_99_1, nil) = all_99_0 & $i(all_99_1) &
% 31.30/5.19 | ? [v0: any] : (all_99_1 = all_93_1 & neq(all_97_1, nil) = v0 & ( ~ (v0
% 31.30/5.19 | = 0) | (all_99_0 = 0 & all_97_0 = 0)) & ( ~ (all_97_0 = 0) | ~
% 31.30/5.19 | (all_93_0 = 0)) & ( ~ (all_97_1 = nil) | ~ (all_93_1 = nil)) & (
% 31.30/5.19 | ~ (all_97_1 = nil) | all_93_1 = nil))
% 31.30/5.19 |
% 31.30/5.19 | ALPHA: (13) implies:
% 31.30/5.19 | (14) neq(all_99_1, nil) = all_99_0
% 31.30/5.19 | (15) ? [v0: any] : (all_99_1 = all_93_1 & neq(all_97_1, nil) = v0 & ( ~
% 31.30/5.19 | (v0 = 0) | (all_99_0 = 0 & all_97_0 = 0)) & ( ~ (all_97_0 = 0) |
% 31.30/5.19 | ~ (all_93_0 = 0)) & ( ~ (all_97_1 = nil) | ~ (all_93_1 = nil)) &
% 31.30/5.19 | ( ~ (all_97_1 = nil) | all_93_1 = nil))
% 31.30/5.19 |
% 31.30/5.19 | DELTA: instantiating (15) with fresh symbol all_101_0 gives:
% 31.30/5.19 | (16) all_99_1 = all_93_1 & neq(all_97_1, nil) = all_101_0 & ( ~ (all_101_0
% 31.30/5.19 | = 0) | (all_99_0 = 0 & all_97_0 = 0)) & ( ~ (all_97_0 = 0) | ~
% 31.30/5.19 | (all_93_0 = 0)) & ( ~ (all_97_1 = nil) | ~ (all_93_1 = nil)) & ( ~
% 31.30/5.19 | (all_97_1 = nil) | all_93_1 = nil)
% 31.30/5.19 |
% 31.30/5.19 | ALPHA: (16) implies:
% 31.30/5.19 | (17) all_99_1 = all_93_1
% 31.30/5.19 | (18) neq(all_97_1, nil) = all_101_0
% 31.30/5.19 | (19) ~ (all_97_1 = nil) | all_93_1 = nil
% 31.30/5.19 | (20) ~ (all_97_1 = nil) | ~ (all_93_1 = nil)
% 31.30/5.19 | (21) ~ (all_97_0 = 0) | ~ (all_93_0 = 0)
% 31.30/5.19 | (22) ~ (all_101_0 = 0) | (all_99_0 = 0 & all_97_0 = 0)
% 31.30/5.19 |
% 31.30/5.19 | REDUCE: (14), (17) imply:
% 31.30/5.19 | (23) neq(all_93_1, nil) = all_99_0
% 31.30/5.19 |
% 31.30/5.20 | GROUND_INST: instantiating (5) with all_93_0, all_99_0, nil, all_93_1,
% 31.30/5.20 | simplifying with (7), (23) gives:
% 31.30/5.20 | (24) all_99_0 = all_93_0
% 31.30/5.20 |
% 31.30/5.20 | GROUND_INST: instantiating (ax15) with all_97_1, simplifying with (10), (11)
% 31.30/5.20 | gives:
% 31.30/5.20 | (25) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_1, v0) = v1) | ~ $i(v0)
% 31.30/5.20 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 31.30/5.20 | ~ (v0 = all_97_1)) & (v1 = 0 | v0 = all_97_1)))
% 31.30/5.20 |
% 31.30/5.20 | GROUND_INST: instantiating (25) with nil, all_101_0, simplifying with (2),
% 31.30/5.20 | (18) gives:
% 31.30/5.20 | (26) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_101_0 = 0)
% 31.30/5.20 | | ~ (all_97_1 = nil)) & (all_101_0 = 0 | all_97_1 = nil))
% 31.30/5.20 |
% 31.30/5.20 | BETA: splitting (19) gives:
% 31.30/5.20 |
% 31.30/5.20 | Case 1:
% 31.30/5.20 | |
% 31.30/5.20 | | (27) ~ (all_97_1 = nil)
% 31.30/5.20 | |
% 31.30/5.20 | | BETA: splitting (26) gives:
% 31.30/5.20 | |
% 31.30/5.20 | | Case 1:
% 31.30/5.20 | | |
% 31.30/5.20 | | | (28) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 31.30/5.20 | | |
% 31.30/5.20 | | | DELTA: instantiating (28) with fresh symbol all_284_0 gives:
% 31.30/5.20 | | | (29) ~ (all_284_0 = 0) & ssList(nil) = all_284_0
% 31.30/5.20 | | |
% 31.30/5.20 | | | ALPHA: (29) implies:
% 31.30/5.20 | | | (30) ~ (all_284_0 = 0)
% 31.30/5.20 | | | (31) ssList(nil) = all_284_0
% 31.30/5.20 | | |
% 31.30/5.20 | | | DELTA: instantiating (28) with fresh symbol all_286_0 gives:
% 31.30/5.20 | | | (32) ~ (all_286_0 = 0) & ssList(nil) = all_286_0
% 31.30/5.20 | | |
% 31.30/5.20 | | | ALPHA: (32) implies:
% 31.30/5.20 | | | (33) ssList(nil) = all_286_0
% 31.30/5.20 | | |
% 31.30/5.20 | | | GROUND_INST: instantiating (4) with 0, all_286_0, nil, simplifying with
% 31.30/5.20 | | | (1), (33) gives:
% 31.30/5.20 | | | (34) all_286_0 = 0
% 31.30/5.20 | | |
% 31.30/5.20 | | | GROUND_INST: instantiating (4) with all_284_0, all_286_0, nil, simplifying
% 31.30/5.20 | | | with (31), (33) gives:
% 31.30/5.20 | | | (35) all_286_0 = all_284_0
% 31.30/5.20 | | |
% 31.30/5.20 | | | COMBINE_EQS: (34), (35) imply:
% 31.30/5.20 | | | (36) all_284_0 = 0
% 31.30/5.20 | | |
% 31.30/5.20 | | | SIMP: (36) implies:
% 31.30/5.20 | | | (37) all_284_0 = 0
% 31.30/5.20 | | |
% 31.30/5.20 | | | REDUCE: (30), (37) imply:
% 31.30/5.20 | | | (38) $false
% 31.30/5.20 | | |
% 31.30/5.20 | | | CLOSE: (38) is inconsistent.
% 31.30/5.20 | | |
% 31.30/5.20 | | Case 2:
% 31.30/5.20 | | |
% 31.30/5.20 | | | (39) ( ~ (all_101_0 = 0) | ~ (all_97_1 = nil)) & (all_101_0 = 0 |
% 31.30/5.20 | | | all_97_1 = nil)
% 31.30/5.20 | | |
% 31.30/5.20 | | | ALPHA: (39) implies:
% 31.30/5.20 | | | (40) all_101_0 = 0 | all_97_1 = nil
% 31.30/5.20 | | |
% 31.30/5.20 | | | BETA: splitting (40) gives:
% 31.30/5.20 | | |
% 31.30/5.20 | | | Case 1:
% 31.30/5.20 | | | |
% 31.30/5.20 | | | | (41) all_97_1 = nil
% 31.30/5.20 | | | |
% 31.30/5.20 | | | | REDUCE: (27), (41) imply:
% 31.30/5.20 | | | | (42) $false
% 31.30/5.20 | | | |
% 31.30/5.20 | | | | CLOSE: (42) is inconsistent.
% 31.30/5.20 | | | |
% 31.30/5.20 | | | Case 2:
% 31.30/5.20 | | | |
% 31.30/5.20 | | | | (43) all_101_0 = 0
% 31.30/5.20 | | | |
% 31.30/5.20 | | | | BETA: splitting (22) gives:
% 31.30/5.20 | | | |
% 31.30/5.20 | | | | Case 1:
% 31.30/5.20 | | | | |
% 31.30/5.20 | | | | | (44) ~ (all_101_0 = 0)
% 31.30/5.20 | | | | |
% 31.30/5.20 | | | | | REDUCE: (43), (44) imply:
% 31.30/5.20 | | | | | (45) $false
% 31.30/5.20 | | | | |
% 31.30/5.20 | | | | | CLOSE: (45) is inconsistent.
% 31.30/5.20 | | | | |
% 31.30/5.20 | | | | Case 2:
% 31.30/5.20 | | | | |
% 31.30/5.20 | | | | | (46) all_99_0 = 0 & all_97_0 = 0
% 31.30/5.20 | | | | |
% 31.30/5.20 | | | | | ALPHA: (46) implies:
% 31.30/5.20 | | | | | (47) all_97_0 = 0
% 31.30/5.20 | | | | | (48) all_99_0 = 0
% 31.30/5.20 | | | | |
% 31.30/5.20 | | | | | COMBINE_EQS: (24), (48) imply:
% 31.30/5.20 | | | | | (49) all_93_0 = 0
% 31.30/5.20 | | | | |
% 31.30/5.20 | | | | | SIMP: (49) implies:
% 31.30/5.20 | | | | | (50) all_93_0 = 0
% 31.30/5.20 | | | | |
% 31.30/5.20 | | | | | BETA: splitting (21) gives:
% 31.30/5.20 | | | | |
% 31.30/5.20 | | | | | Case 1:
% 31.30/5.20 | | | | | |
% 31.30/5.20 | | | | | | (51) ~ (all_97_0 = 0)
% 31.30/5.20 | | | | | |
% 31.30/5.20 | | | | | | REDUCE: (47), (51) imply:
% 31.30/5.20 | | | | | | (52) $false
% 31.30/5.20 | | | | | |
% 31.30/5.20 | | | | | | CLOSE: (52) is inconsistent.
% 31.30/5.20 | | | | | |
% 31.30/5.20 | | | | | Case 2:
% 31.30/5.20 | | | | | |
% 31.30/5.20 | | | | | | (53) ~ (all_93_0 = 0)
% 31.30/5.20 | | | | | |
% 31.30/5.20 | | | | | | REDUCE: (50), (53) imply:
% 31.30/5.20 | | | | | | (54) $false
% 31.30/5.20 | | | | | |
% 31.30/5.20 | | | | | | CLOSE: (54) is inconsistent.
% 31.30/5.20 | | | | | |
% 31.30/5.20 | | | | | End of split
% 31.30/5.20 | | | | |
% 31.30/5.20 | | | | End of split
% 31.30/5.20 | | | |
% 31.30/5.20 | | | End of split
% 31.30/5.20 | | |
% 31.30/5.20 | | End of split
% 31.30/5.20 | |
% 31.30/5.20 | Case 2:
% 31.30/5.20 | |
% 31.30/5.21 | | (55) all_93_1 = nil
% 31.30/5.21 | | (56) all_97_1 = nil
% 31.30/5.21 | |
% 31.30/5.21 | | BETA: splitting (20) gives:
% 31.30/5.21 | |
% 31.30/5.21 | | Case 1:
% 31.30/5.21 | | |
% 31.30/5.21 | | | (57) ~ (all_97_1 = nil)
% 31.30/5.21 | | |
% 31.30/5.21 | | | REDUCE: (56), (57) imply:
% 31.30/5.21 | | | (58) $false
% 31.30/5.21 | | |
% 31.30/5.21 | | | CLOSE: (58) is inconsistent.
% 31.30/5.21 | | |
% 31.30/5.21 | | Case 2:
% 31.30/5.21 | | |
% 31.30/5.21 | | | (59) ~ (all_93_1 = nil)
% 31.30/5.21 | | |
% 31.30/5.21 | | | REDUCE: (55), (59) imply:
% 31.30/5.21 | | | (60) $false
% 31.30/5.21 | | |
% 31.30/5.21 | | | CLOSE: (60) is inconsistent.
% 31.30/5.21 | | |
% 31.30/5.21 | | End of split
% 31.30/5.21 | |
% 31.30/5.21 | End of split
% 31.30/5.21 |
% 31.30/5.21 End of proof
% 31.30/5.21 % SZS output end Proof for theBenchmark
% 31.30/5.21
% 31.30/5.21 4592ms
%------------------------------------------------------------------------------