TSTP Solution File: SWC129+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC129+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 20:49:48 EDT 2023
% Result : Theorem 21.79s 3.66s
% Output : Proof 28.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC129+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.12 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 16:36:08 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.20/0.59 ________ _____
% 0.20/0.59 ___ __ \_________(_)________________________________
% 0.20/0.59 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.59 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.59 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.59
% 0.20/0.59 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.59 (2023-06-19)
% 0.20/0.59
% 0.20/0.59 (c) Philipp Rümmer, 2009-2023
% 0.20/0.59 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.59 Amanda Stjerna.
% 0.20/0.59 Free software under BSD-3-Clause.
% 0.20/0.59
% 0.20/0.59 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.59
% 0.20/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.61 Running up to 7 provers in parallel.
% 0.20/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.21/1.48 Prover 1: Preprocessing ...
% 5.21/1.49 Prover 4: Preprocessing ...
% 5.85/1.54 Prover 2: Preprocessing ...
% 5.85/1.54 Prover 0: Preprocessing ...
% 5.85/1.54 Prover 6: Preprocessing ...
% 5.85/1.54 Prover 5: Preprocessing ...
% 5.85/1.54 Prover 3: Preprocessing ...
% 15.93/2.89 Prover 2: Proving ...
% 16.39/2.95 Prover 5: Constructing countermodel ...
% 17.18/3.03 Prover 3: Constructing countermodel ...
% 17.49/3.09 Prover 1: Constructing countermodel ...
% 17.49/3.11 Prover 6: Proving ...
% 21.79/3.65 Prover 3: proved (3036ms)
% 21.79/3.66
% 21.79/3.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.79/3.66
% 21.79/3.66 Prover 5: stopped
% 21.79/3.67 Prover 6: stopped
% 21.79/3.68 Prover 2: stopped
% 21.79/3.68 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 21.79/3.68 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 21.79/3.68 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 21.79/3.69 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 23.20/3.95 Prover 8: Preprocessing ...
% 24.38/3.98 Prover 4: Constructing countermodel ...
% 24.38/3.98 Prover 7: Preprocessing ...
% 24.38/3.99 Prover 10: Preprocessing ...
% 24.60/4.02 Prover 11: Preprocessing ...
% 25.43/4.14 Prover 0: Proving ...
% 25.43/4.16 Prover 0: stopped
% 25.43/4.17 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 26.74/4.30 Prover 13: Preprocessing ...
% 26.95/4.31 Prover 10: Constructing countermodel ...
% 27.07/4.32 Prover 7: Constructing countermodel ...
% 27.07/4.41 Prover 1: Found proof (size 30)
% 27.07/4.41 Prover 1: proved (3791ms)
% 27.07/4.41 Prover 4: stopped
% 27.07/4.41 Prover 11: stopped
% 27.07/4.41 Prover 7: stopped
% 27.77/4.41 Prover 13: stopped
% 27.77/4.41 Prover 10: stopped
% 27.77/4.45 Prover 8: Warning: ignoring some quantifiers
% 27.77/4.46 Prover 8: Constructing countermodel ...
% 27.77/4.48 Prover 8: stopped
% 27.77/4.48
% 27.77/4.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.77/4.48
% 27.77/4.48 % SZS output start Proof for theBenchmark
% 27.77/4.49 Assumptions after simplification:
% 27.77/4.49 ---------------------------------
% 27.77/4.49
% 27.77/4.49 (ax15)
% 27.77/4.51 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 27.77/4.51 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 27.77/4.51 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 27.77/4.51
% 27.77/4.51 (ax17)
% 27.77/4.51 ssList(nil) = 0 & $i(nil)
% 27.77/4.51
% 27.77/4.51 (ax60)
% 27.77/4.51 cyclefreeP(nil) = 0 & $i(nil)
% 27.77/4.51
% 27.77/4.51 (co1)
% 27.77/4.52 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any]
% 27.77/4.52 : (cyclefreeP(v1) = v2 & ssList(v1) = 0 & $i(v1) & ? [v3: $i] : (ssList(v3)
% 27.77/4.52 = 0 & $i(v3) & ? [v4: int] : (v3 = v0 & ~ (v4 = 0) & ~ (v2 = 0) &
% 27.77/4.52 neq(v1, nil) = v4))))
% 27.77/4.52
% 27.77/4.52 (function-axioms)
% 27.77/4.53 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 27.77/4.53 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 27.77/4.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.77/4.53 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 27.77/4.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.77/4.53 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 27.77/4.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.77/4.53 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 27.77/4.53 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.77/4.53 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 27.77/4.53 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 27.77/4.53 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 27.77/4.53 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 27.77/4.53 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 27.77/4.53 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 27.77/4.53 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 27.77/4.53 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.77/4.53 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 27.77/4.53 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 27.77/4.53 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 27.77/4.53 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 27.77/4.53 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 27.77/4.53 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 27.77/4.53 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 27.77/4.53 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 27.77/4.53 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.77/4.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 27.77/4.53 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.77/4.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 27.77/4.53 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.77/4.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 27.77/4.53 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.77/4.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 27.77/4.53 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.77/4.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 27.77/4.53 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.77/4.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 27.77/4.53 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.77/4.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 27.77/4.53 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.77/4.53 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 27.77/4.53 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 27.77/4.53 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 27.77/4.53
% 27.77/4.53 Further assumptions not needed in the proof:
% 27.77/4.53 --------------------------------------------
% 27.77/4.53 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 27.77/4.53 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34,
% 27.77/4.53 ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46,
% 27.77/4.53 ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58,
% 27.77/4.53 ax59, ax6, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70,
% 27.77/4.53 ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82,
% 27.77/4.53 ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94,
% 27.77/4.53 ax95
% 27.77/4.53
% 27.77/4.53 Those formulas are unsatisfiable:
% 27.77/4.53 ---------------------------------
% 27.77/4.53
% 27.77/4.53 Begin of proof
% 27.77/4.53 |
% 27.77/4.53 | ALPHA: (ax17) implies:
% 27.77/4.53 | (1) ssList(nil) = 0
% 27.77/4.53 |
% 27.77/4.53 | ALPHA: (ax60) implies:
% 27.77/4.53 | (2) cyclefreeP(nil) = 0
% 27.77/4.53 |
% 27.77/4.53 | ALPHA: (co1) implies:
% 27.77/4.53 | (3) $i(nil)
% 27.77/4.54 | (4) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] :
% 27.77/4.54 | (cyclefreeP(v1) = v2 & ssList(v1) = 0 & $i(v1) & ? [v3: $i] :
% 27.77/4.54 | (ssList(v3) = 0 & $i(v3) & ? [v4: int] : (v3 = v0 & ~ (v4 = 0) &
% 27.77/4.54 | ~ (v2 = 0) & neq(v1, nil) = v4))))
% 27.77/4.54 |
% 27.77/4.54 | ALPHA: (function-axioms) implies:
% 27.77/4.54 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 27.77/4.54 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 27.77/4.54 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 27.77/4.54 | (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ (cyclefreeP(v2) = v0))
% 27.77/4.54 |
% 27.77/4.54 | DELTA: instantiating (4) with fresh symbol all_93_0 gives:
% 27.77/4.54 | (7) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : ? [v1: any] :
% 27.77/4.54 | (cyclefreeP(v0) = v1 & ssList(v0) = 0 & $i(v0) & ? [v2: $i] :
% 27.77/4.54 | (ssList(v2) = 0 & $i(v2) & ? [v3: int] : (v2 = all_93_0 & ~ (v3 =
% 27.77/4.54 | 0) & ~ (v1 = 0) & neq(v0, nil) = v3)))
% 27.77/4.54 |
% 27.77/4.54 | ALPHA: (7) implies:
% 27.77/4.54 | (8) ? [v0: $i] : ? [v1: any] : (cyclefreeP(v0) = v1 & ssList(v0) = 0 &
% 27.77/4.54 | $i(v0) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: int] : (v2
% 27.77/4.54 | = all_93_0 & ~ (v3 = 0) & ~ (v1 = 0) & neq(v0, nil) = v3)))
% 27.77/4.54 |
% 27.77/4.54 | DELTA: instantiating (8) with fresh symbols all_97_0, all_97_1 gives:
% 27.77/4.54 | (9) cyclefreeP(all_97_1) = all_97_0 & ssList(all_97_1) = 0 & $i(all_97_1) &
% 27.77/4.54 | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: int] : (v0 = all_93_0
% 27.77/4.54 | & ~ (v1 = 0) & ~ (all_97_0 = 0) & neq(all_97_1, nil) = v1))
% 27.77/4.54 |
% 27.77/4.54 | ALPHA: (9) implies:
% 27.77/4.54 | (10) $i(all_97_1)
% 27.77/4.54 | (11) ssList(all_97_1) = 0
% 27.77/4.54 | (12) cyclefreeP(all_97_1) = all_97_0
% 27.77/4.54 | (13) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: int] : (v0 = all_93_0
% 27.77/4.54 | & ~ (v1 = 0) & ~ (all_97_0 = 0) & neq(all_97_1, nil) = v1))
% 27.77/4.54 |
% 27.77/4.54 | DELTA: instantiating (13) with fresh symbol all_99_0 gives:
% 27.77/4.54 | (14) ssList(all_99_0) = 0 & $i(all_99_0) & ? [v0: int] : (all_99_0 =
% 27.77/4.54 | all_93_0 & ~ (v0 = 0) & ~ (all_97_0 = 0) & neq(all_97_1, nil) =
% 27.77/4.54 | v0)
% 27.77/4.54 |
% 27.77/4.54 | ALPHA: (14) implies:
% 27.77/4.54 | (15) ? [v0: int] : (all_99_0 = all_93_0 & ~ (v0 = 0) & ~ (all_97_0 = 0)
% 27.77/4.54 | & neq(all_97_1, nil) = v0)
% 27.77/4.54 |
% 27.77/4.54 | DELTA: instantiating (15) with fresh symbol all_101_0 gives:
% 27.77/4.54 | (16) all_99_0 = all_93_0 & ~ (all_101_0 = 0) & ~ (all_97_0 = 0) &
% 27.77/4.54 | neq(all_97_1, nil) = all_101_0
% 27.77/4.54 |
% 27.77/4.54 | ALPHA: (16) implies:
% 27.77/4.54 | (17) ~ (all_97_0 = 0)
% 27.77/4.54 | (18) ~ (all_101_0 = 0)
% 27.77/4.54 | (19) neq(all_97_1, nil) = all_101_0
% 27.77/4.54 |
% 27.77/4.55 | GROUND_INST: instantiating (ax15) with all_97_1, simplifying with (10), (11)
% 27.77/4.55 | gives:
% 27.77/4.55 | (20) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_1, v0) = v1) | ~ $i(v0)
% 27.77/4.55 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 27.77/4.55 | ~ (v0 = all_97_1)) & (v1 = 0 | v0 = all_97_1)))
% 27.77/4.55 |
% 27.77/4.55 | GROUND_INST: instantiating (20) with nil, all_101_0, simplifying with (3),
% 27.77/4.55 | (19) gives:
% 27.77/4.55 | (21) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_101_0 = 0)
% 27.77/4.55 | | ~ (all_97_1 = nil)) & (all_101_0 = 0 | all_97_1 = nil))
% 27.77/4.55 |
% 27.77/4.55 | BETA: splitting (21) gives:
% 27.77/4.55 |
% 27.77/4.55 | Case 1:
% 27.77/4.55 | |
% 27.77/4.55 | | (22) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 27.77/4.55 | |
% 27.77/4.55 | | DELTA: instantiating (22) with fresh symbol all_261_0 gives:
% 27.77/4.55 | | (23) ~ (all_261_0 = 0) & ssList(nil) = all_261_0
% 27.77/4.55 | |
% 27.77/4.55 | | ALPHA: (23) implies:
% 27.77/4.55 | | (24) ~ (all_261_0 = 0)
% 27.77/4.55 | | (25) ssList(nil) = all_261_0
% 27.77/4.55 | |
% 27.77/4.55 | | GROUND_INST: instantiating (5) with 0, all_261_0, nil, simplifying with (1),
% 27.77/4.55 | | (25) gives:
% 27.77/4.55 | | (26) all_261_0 = 0
% 27.77/4.55 | |
% 27.77/4.55 | | REDUCE: (24), (26) imply:
% 27.77/4.55 | | (27) $false
% 27.77/4.55 | |
% 27.77/4.55 | | CLOSE: (27) is inconsistent.
% 27.77/4.55 | |
% 27.77/4.55 | Case 2:
% 27.77/4.55 | |
% 27.77/4.55 | | (28) ( ~ (all_101_0 = 0) | ~ (all_97_1 = nil)) & (all_101_0 = 0 |
% 27.77/4.55 | | all_97_1 = nil)
% 27.77/4.55 | |
% 27.77/4.55 | | ALPHA: (28) implies:
% 27.77/4.55 | | (29) all_101_0 = 0 | all_97_1 = nil
% 27.77/4.55 | |
% 27.77/4.55 | | BETA: splitting (29) gives:
% 27.77/4.55 | |
% 27.77/4.55 | | Case 1:
% 27.77/4.55 | | |
% 27.77/4.55 | | | (30) all_97_1 = nil
% 27.77/4.55 | | |
% 27.77/4.55 | | | REDUCE: (12), (30) imply:
% 27.77/4.55 | | | (31) cyclefreeP(nil) = all_97_0
% 27.77/4.55 | | |
% 28.22/4.55 | | | GROUND_INST: instantiating (6) with 0, all_97_0, nil, simplifying with
% 28.22/4.55 | | | (2), (31) gives:
% 28.22/4.55 | | | (32) all_97_0 = 0
% 28.22/4.55 | | |
% 28.22/4.55 | | | REDUCE: (17), (32) imply:
% 28.22/4.55 | | | (33) $false
% 28.22/4.55 | | |
% 28.22/4.55 | | | CLOSE: (33) is inconsistent.
% 28.22/4.55 | | |
% 28.22/4.55 | | Case 2:
% 28.22/4.55 | | |
% 28.22/4.55 | | | (34) all_101_0 = 0
% 28.22/4.55 | | |
% 28.22/4.55 | | | REDUCE: (18), (34) imply:
% 28.22/4.55 | | | (35) $false
% 28.22/4.55 | | |
% 28.22/4.55 | | | CLOSE: (35) is inconsistent.
% 28.22/4.55 | | |
% 28.22/4.55 | | End of split
% 28.22/4.55 | |
% 28.22/4.55 | End of split
% 28.22/4.55 |
% 28.22/4.55 End of proof
% 28.22/4.55 % SZS output end Proof for theBenchmark
% 28.22/4.55
% 28.22/4.55 3958ms
%------------------------------------------------------------------------------