TSTP Solution File: SWC415+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC415+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 : n027.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 20:51:20 EDT 2023
% Result : Theorem 24.26s 3.97s
% Output : Proof 33.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC415+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n027.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 16:25:37 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.60 ________ _____
% 0.20/0.60 ___ __ \_________(_)________________________________
% 0.20/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.60
% 0.20/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.60 (2023-06-19)
% 0.20/0.60
% 0.20/0.61 (c) Philipp Rümmer, 2009-2023
% 0.20/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.61 Amanda Stjerna.
% 0.20/0.61 Free software under BSD-3-Clause.
% 0.20/0.61
% 0.20/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.61
% 0.20/0.61 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.62 Running up to 7 provers in parallel.
% 0.20/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.20/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.76/1.46 Prover 4: Preprocessing ...
% 4.76/1.46 Prover 1: Preprocessing ...
% 5.53/1.52 Prover 0: Preprocessing ...
% 5.53/1.52 Prover 2: Preprocessing ...
% 5.53/1.52 Prover 3: Preprocessing ...
% 5.53/1.52 Prover 6: Preprocessing ...
% 5.53/1.52 Prover 5: Preprocessing ...
% 16.20/2.97 Prover 2: Proving ...
% 17.05/3.03 Prover 5: Constructing countermodel ...
% 17.05/3.09 Prover 1: Constructing countermodel ...
% 17.05/3.10 Prover 6: Proving ...
% 17.78/3.12 Prover 3: Constructing countermodel ...
% 23.14/3.82 Prover 0: Proving ...
% 23.14/3.82 Prover 4: Constructing countermodel ...
% 24.26/3.96 Prover 3: proved (3335ms)
% 24.26/3.97
% 24.26/3.97 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.26/3.97
% 24.26/3.97 Prover 2: stopped
% 24.26/3.97 Prover 6: stopped
% 24.59/4.00 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 24.59/4.00 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 24.59/4.00 Prover 5: stopped
% 24.59/4.01 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 24.59/4.01 Prover 0: stopped
% 24.59/4.03 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.59/4.03 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 25.59/4.20 Prover 13: Preprocessing ...
% 25.59/4.21 Prover 11: Preprocessing ...
% 26.38/4.26 Prover 7: Preprocessing ...
% 26.38/4.27 Prover 8: Preprocessing ...
% 26.82/4.31 Prover 10: Preprocessing ...
% 28.76/4.56 Prover 7: Constructing countermodel ...
% 28.76/4.57 Prover 10: Constructing countermodel ...
% 28.76/4.60 Prover 13: Constructing countermodel ...
% 30.29/4.77 Prover 8: Warning: ignoring some quantifiers
% 30.29/4.79 Prover 8: Constructing countermodel ...
% 31.08/5.00 Prover 1: Found proof (size 68)
% 31.08/5.00 Prover 1: proved (4368ms)
% 31.08/5.00 Prover 7: stopped
% 31.08/5.00 Prover 10: stopped
% 31.08/5.00 Prover 8: stopped
% 31.08/5.00 Prover 13: stopped
% 31.08/5.00 Prover 4: stopped
% 33.10/5.29 Prover 11: Constructing countermodel ...
% 33.10/5.31 Prover 11: stopped
% 33.10/5.31
% 33.10/5.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.10/5.31
% 33.10/5.32 % SZS output start Proof for theBenchmark
% 33.10/5.33 Assumptions after simplification:
% 33.10/5.33 ---------------------------------
% 33.10/5.33
% 33.10/5.33 (ax15)
% 33.57/5.38 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 33.57/5.38 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 33.57/5.38 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 33.57/5.38
% 33.57/5.38 (ax17)
% 33.57/5.38 ssList(nil) = 0 & $i(nil)
% 33.57/5.38
% 33.57/5.38 (ax24)
% 33.57/5.38 $i(nil) & ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (tl(v0) = v1) | ~ $i(v0)
% 33.57/5.38 | ? [v2: any] : ? [v3: any] : (ssList(v1) = v3 & ssList(v0) = v2 & ( ~ (v2
% 33.57/5.38 = 0) | v3 = 0)))
% 33.57/5.38
% 33.57/5.38 (co1)
% 33.57/5.39 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] :
% 33.57/5.39 ? [v3: any] : (tl(v1) = v2 & ssList(v1) = 0 & neq(v1, nil) = 0 & neq(nil,
% 33.57/5.39 v1) = v3 & $i(v2) & $i(v1) & ( ~ (v3 = 0) | ~ (v2 = v0)) & ( ~ (v3 = 0)
% 33.57/5.39 | v2 = v0 | ~ (ssList(v2) = 0))))
% 33.57/5.39
% 33.57/5.39 (function-axioms)
% 33.57/5.40 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 33.57/5.40 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 33.57/5.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 33.57/5.40 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 33.57/5.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 33.57/5.40 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 33.57/5.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 33.57/5.40 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 33.57/5.40 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 33.57/5.40 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 33.57/5.40 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 33.57/5.40 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 33.82/5.40 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 33.82/5.40 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 33.82/5.40 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 33.82/5.40 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 33.82/5.40 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.82/5.40 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 33.82/5.40 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 33.82/5.40 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 33.82/5.40 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 33.82/5.40 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 33.82/5.40 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 33.82/5.40 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 33.82/5.40 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 33.82/5.40 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.82/5.40 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 33.82/5.40 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.82/5.40 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 33.82/5.40 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.82/5.40 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 33.82/5.40 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.82/5.40 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 33.82/5.40 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.82/5.40 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 33.82/5.40 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.82/5.40 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 33.82/5.40 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.82/5.40 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 33.82/5.40 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.82/5.40 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 33.82/5.40 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 33.82/5.40 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 33.82/5.40
% 33.82/5.40 Further assumptions not needed in the proof:
% 33.82/5.40 --------------------------------------------
% 33.82/5.40 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 33.82/5.40 ax23, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35,
% 33.82/5.40 ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46, ax47,
% 33.82/5.40 ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59,
% 33.82/5.40 ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70,
% 33.82/5.40 ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82,
% 33.82/5.40 ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94,
% 33.82/5.40 ax95
% 33.82/5.40
% 33.82/5.40 Those formulas are unsatisfiable:
% 33.82/5.40 ---------------------------------
% 33.82/5.40
% 33.82/5.40 Begin of proof
% 33.82/5.40 |
% 33.82/5.40 | ALPHA: (ax17) implies:
% 33.82/5.40 | (1) ssList(nil) = 0
% 33.82/5.40 |
% 33.82/5.40 | ALPHA: (ax24) implies:
% 33.82/5.40 | (2) ! [v0: $i] : ! [v1: $i] : (v0 = nil | ~ (tl(v0) = v1) | ~ $i(v0) |
% 33.82/5.40 | ? [v2: any] : ? [v3: any] : (ssList(v1) = v3 & ssList(v0) = v2 & ( ~
% 33.82/5.40 | (v2 = 0) | v3 = 0)))
% 33.82/5.40 |
% 33.82/5.40 | ALPHA: (co1) implies:
% 33.82/5.40 | (3) $i(nil)
% 33.82/5.40 | (4) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: $i] : ?
% 33.82/5.40 | [v3: any] : (tl(v1) = v2 & ssList(v1) = 0 & neq(v1, nil) = 0 &
% 33.82/5.40 | neq(nil, v1) = v3 & $i(v2) & $i(v1) & ( ~ (v3 = 0) | ~ (v2 = v0))
% 33.82/5.40 | & ( ~ (v3 = 0) | v2 = v0 | ~ (ssList(v2) = 0))))
% 33.82/5.40 |
% 33.82/5.40 | ALPHA: (function-axioms) implies:
% 33.82/5.40 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 33.82/5.40 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 33.82/5.40 |
% 33.82/5.40 | DELTA: instantiating (4) with fresh symbol all_93_0 gives:
% 33.82/5.41 | (6) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : ? [v1: $i] : ?
% 33.82/5.41 | [v2: any] : (tl(v0) = v1 & ssList(v0) = 0 & neq(v0, nil) = 0 & neq(nil,
% 33.82/5.41 | v0) = v2 & $i(v1) & $i(v0) & ( ~ (v2 = 0) | ~ (v1 = all_93_0)) & (
% 33.82/5.41 | ~ (v2 = 0) | v1 = all_93_0 | ~ (ssList(v1) = 0)))
% 33.82/5.41 |
% 33.82/5.41 | ALPHA: (6) implies:
% 33.82/5.41 | (7) ? [v0: $i] : ? [v1: $i] : ? [v2: any] : (tl(v0) = v1 & ssList(v0) =
% 33.82/5.41 | 0 & neq(v0, nil) = 0 & neq(nil, v0) = v2 & $i(v1) & $i(v0) & ( ~ (v2
% 33.82/5.41 | = 0) | ~ (v1 = all_93_0)) & ( ~ (v2 = 0) | v1 = all_93_0 | ~
% 33.82/5.41 | (ssList(v1) = 0)))
% 33.82/5.41 |
% 33.82/5.41 | DELTA: instantiating (7) with fresh symbols all_97_0, all_97_1, all_97_2
% 33.82/5.41 | gives:
% 33.82/5.41 | (8) tl(all_97_2) = all_97_1 & ssList(all_97_2) = 0 & neq(all_97_2, nil) = 0
% 33.82/5.41 | & neq(nil, all_97_2) = all_97_0 & $i(all_97_1) & $i(all_97_2) & ( ~
% 33.82/5.41 | (all_97_0 = 0) | ~ (all_97_1 = all_93_0)) & ( ~ (all_97_0 = 0) |
% 33.82/5.41 | all_97_1 = all_93_0 | ~ (ssList(all_97_1) = 0))
% 33.82/5.41 |
% 33.82/5.41 | ALPHA: (8) implies:
% 33.82/5.41 | (9) $i(all_97_2)
% 33.82/5.41 | (10) neq(nil, all_97_2) = all_97_0
% 33.82/5.41 | (11) neq(all_97_2, nil) = 0
% 33.82/5.41 | (12) ssList(all_97_2) = 0
% 33.82/5.41 | (13) tl(all_97_2) = all_97_1
% 33.82/5.41 | (14) ~ (all_97_0 = 0) | all_97_1 = all_93_0 | ~ (ssList(all_97_1) = 0)
% 33.82/5.41 | (15) ~ (all_97_0 = 0) | ~ (all_97_1 = all_93_0)
% 33.82/5.41 |
% 33.82/5.41 | GROUND_INST: instantiating (ax15) with nil, simplifying with (1), (3) gives:
% 33.82/5.41 | (16) ! [v0: $i] : ! [v1: any] : ( ~ (neq(nil, v0) = v1) | ~ $i(v0) | ?
% 33.82/5.41 | [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) | ~ (v0
% 33.82/5.41 | = nil)) & (v1 = 0 | v0 = nil)))
% 33.82/5.41 |
% 33.82/5.41 | GROUND_INST: instantiating (ax15) with all_97_2, simplifying with (9), (12)
% 33.82/5.41 | gives:
% 33.82/5.41 | (17) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_2, v0) = v1) | ~ $i(v0)
% 33.82/5.41 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 33.82/5.41 | ~ (v0 = all_97_2)) & (v1 = 0 | v0 = all_97_2)))
% 33.82/5.41 |
% 33.82/5.41 | GROUND_INST: instantiating (2) with all_97_2, all_97_1, simplifying with (9),
% 33.82/5.41 | (13) gives:
% 33.82/5.41 | (18) all_97_2 = nil | ? [v0: any] : ? [v1: any] : (ssList(all_97_1) = v1
% 33.82/5.41 | & ssList(all_97_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 33.82/5.41 |
% 33.82/5.41 | GROUND_INST: instantiating (17) with nil, 0, simplifying with (3) gives:
% 33.82/5.41 | (19) ~ (all_97_2 = nil) | ~ (neq(nil, nil) = 0) | ? [v0: int] : ( ~ (v0
% 33.82/5.41 | = 0) & ssList(nil) = v0)
% 33.82/5.41 |
% 33.82/5.41 | GROUND_INST: instantiating (16) with all_97_2, all_97_0, simplifying with (9),
% 33.82/5.41 | (10) gives:
% 33.82/5.41 | (20) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_97_2) = v0) | (( ~ (all_97_0
% 33.82/5.41 | = 0) | ~ (all_97_2 = nil)) & (all_97_0 = 0 | all_97_2 = nil))
% 33.82/5.41 |
% 33.82/5.41 | BETA: splitting (18) gives:
% 33.82/5.41 |
% 33.82/5.42 | Case 1:
% 33.82/5.42 | |
% 33.82/5.42 | | (21) all_97_2 = nil
% 33.82/5.42 | |
% 33.82/5.42 | | REDUCE: (11), (21) imply:
% 33.82/5.42 | | (22) neq(nil, nil) = 0
% 33.82/5.42 | |
% 33.82/5.42 | | BETA: splitting (19) gives:
% 33.82/5.42 | |
% 33.82/5.42 | | Case 1:
% 33.82/5.42 | | |
% 33.82/5.42 | | | (23) ~ (neq(nil, nil) = 0)
% 33.82/5.42 | | |
% 33.82/5.42 | | | PRED_UNIFY: (22), (23) imply:
% 33.82/5.42 | | | (24) $false
% 33.82/5.42 | | |
% 33.82/5.42 | | | CLOSE: (24) is inconsistent.
% 33.82/5.42 | | |
% 33.82/5.42 | | Case 2:
% 33.82/5.42 | | |
% 33.82/5.42 | | | (25) ~ (all_97_2 = nil) | ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) =
% 33.82/5.42 | | | v0)
% 33.82/5.42 | | |
% 33.82/5.42 | | | BETA: splitting (25) gives:
% 33.82/5.42 | | |
% 33.82/5.42 | | | Case 1:
% 33.82/5.42 | | | |
% 33.82/5.42 | | | | (26) ~ (all_97_2 = nil)
% 33.82/5.42 | | | |
% 33.82/5.42 | | | | REDUCE: (21), (26) imply:
% 33.82/5.42 | | | | (27) $false
% 33.82/5.42 | | | |
% 33.82/5.42 | | | | CLOSE: (27) is inconsistent.
% 33.82/5.42 | | | |
% 33.82/5.42 | | | Case 2:
% 33.82/5.42 | | | |
% 33.82/5.42 | | | | (28) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 33.82/5.42 | | | |
% 33.82/5.42 | | | | DELTA: instantiating (28) with fresh symbol all_285_0 gives:
% 33.82/5.42 | | | | (29) ~ (all_285_0 = 0) & ssList(nil) = all_285_0
% 33.82/5.42 | | | |
% 33.82/5.42 | | | | ALPHA: (29) implies:
% 33.82/5.42 | | | | (30) ~ (all_285_0 = 0)
% 33.82/5.42 | | | | (31) ssList(nil) = all_285_0
% 33.82/5.42 | | | |
% 33.82/5.42 | | | | DELTA: instantiating (28) with fresh symbol all_287_0 gives:
% 33.82/5.42 | | | | (32) ~ (all_287_0 = 0) & ssList(nil) = all_287_0
% 33.82/5.42 | | | |
% 33.82/5.42 | | | | ALPHA: (32) implies:
% 33.82/5.42 | | | | (33) ssList(nil) = all_287_0
% 33.82/5.42 | | | |
% 33.82/5.42 | | | | GROUND_INST: instantiating (5) with 0, all_287_0, nil, simplifying with
% 33.82/5.42 | | | | (1), (33) gives:
% 33.82/5.42 | | | | (34) all_287_0 = 0
% 33.82/5.42 | | | |
% 33.82/5.42 | | | | GROUND_INST: instantiating (5) with all_285_0, all_287_0, nil,
% 33.82/5.42 | | | | simplifying with (31), (33) gives:
% 33.82/5.42 | | | | (35) all_287_0 = all_285_0
% 33.82/5.42 | | | |
% 33.82/5.42 | | | | COMBINE_EQS: (34), (35) imply:
% 33.82/5.42 | | | | (36) all_285_0 = 0
% 33.82/5.42 | | | |
% 33.82/5.42 | | | | REDUCE: (30), (36) imply:
% 33.82/5.42 | | | | (37) $false
% 33.82/5.42 | | | |
% 33.82/5.42 | | | | CLOSE: (37) is inconsistent.
% 33.82/5.42 | | | |
% 33.82/5.42 | | | End of split
% 33.82/5.42 | | |
% 33.82/5.42 | | End of split
% 33.82/5.42 | |
% 33.82/5.42 | Case 2:
% 33.82/5.42 | |
% 33.82/5.42 | | (38) ~ (all_97_2 = nil)
% 33.82/5.42 | | (39) ? [v0: any] : ? [v1: any] : (ssList(all_97_1) = v1 &
% 33.82/5.42 | | ssList(all_97_2) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 33.82/5.42 | |
% 33.82/5.42 | | DELTA: instantiating (39) with fresh symbols all_309_0, all_309_1 gives:
% 33.82/5.42 | | (40) ssList(all_97_1) = all_309_0 & ssList(all_97_2) = all_309_1 & ( ~
% 33.82/5.42 | | (all_309_1 = 0) | all_309_0 = 0)
% 33.82/5.42 | |
% 33.82/5.42 | | ALPHA: (40) implies:
% 33.82/5.42 | | (41) ssList(all_97_2) = all_309_1
% 33.82/5.42 | | (42) ssList(all_97_1) = all_309_0
% 33.82/5.42 | | (43) ~ (all_309_1 = 0) | all_309_0 = 0
% 33.82/5.42 | |
% 33.82/5.42 | | BETA: splitting (20) gives:
% 33.82/5.42 | |
% 33.82/5.42 | | Case 1:
% 33.82/5.42 | | |
% 33.82/5.42 | | | (44) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_97_2) = v0)
% 33.82/5.42 | | |
% 33.82/5.42 | | | DELTA: instantiating (44) with fresh symbol all_318_0 gives:
% 33.82/5.42 | | | (45) ~ (all_318_0 = 0) & ssList(all_97_2) = all_318_0
% 33.82/5.42 | | |
% 33.82/5.42 | | | ALPHA: (45) implies:
% 33.82/5.42 | | | (46) ~ (all_318_0 = 0)
% 33.82/5.42 | | | (47) ssList(all_97_2) = all_318_0
% 33.82/5.42 | | |
% 33.82/5.42 | | | GROUND_INST: instantiating (5) with 0, all_318_0, all_97_2, simplifying
% 33.82/5.42 | | | with (12), (47) gives:
% 33.82/5.42 | | | (48) all_318_0 = 0
% 33.82/5.42 | | |
% 33.82/5.42 | | | GROUND_INST: instantiating (5) with all_309_1, all_318_0, all_97_2,
% 33.82/5.42 | | | simplifying with (41), (47) gives:
% 33.82/5.43 | | | (49) all_318_0 = all_309_1
% 33.82/5.43 | | |
% 33.82/5.43 | | | COMBINE_EQS: (48), (49) imply:
% 33.82/5.43 | | | (50) all_309_1 = 0
% 33.82/5.43 | | |
% 33.82/5.43 | | | REDUCE: (46), (48) imply:
% 33.82/5.43 | | | (51) $false
% 33.82/5.43 | | |
% 33.82/5.43 | | | CLOSE: (51) is inconsistent.
% 33.82/5.43 | | |
% 33.82/5.43 | | Case 2:
% 33.82/5.43 | | |
% 33.82/5.43 | | | (52) ( ~ (all_97_0 = 0) | ~ (all_97_2 = nil)) & (all_97_0 = 0 |
% 33.82/5.43 | | | all_97_2 = nil)
% 33.82/5.43 | | |
% 33.82/5.43 | | | ALPHA: (52) implies:
% 33.82/5.43 | | | (53) all_97_0 = 0 | all_97_2 = nil
% 33.82/5.43 | | |
% 33.82/5.43 | | | BETA: splitting (53) gives:
% 33.82/5.43 | | |
% 33.82/5.43 | | | Case 1:
% 33.82/5.43 | | | |
% 33.82/5.43 | | | | (54) all_97_2 = nil
% 33.82/5.43 | | | |
% 33.82/5.43 | | | | REDUCE: (38), (54) imply:
% 33.82/5.43 | | | | (55) $false
% 33.82/5.43 | | | |
% 33.82/5.43 | | | | CLOSE: (55) is inconsistent.
% 33.82/5.43 | | | |
% 33.82/5.43 | | | Case 2:
% 33.82/5.43 | | | |
% 33.82/5.43 | | | | (56) all_97_0 = 0
% 33.82/5.43 | | | |
% 33.82/5.43 | | | | BETA: splitting (15) gives:
% 33.82/5.43 | | | |
% 33.82/5.43 | | | | Case 1:
% 33.82/5.43 | | | | |
% 33.82/5.43 | | | | | (57) ~ (all_97_0 = 0)
% 33.82/5.43 | | | | |
% 33.82/5.43 | | | | | REDUCE: (56), (57) imply:
% 33.82/5.43 | | | | | (58) $false
% 33.82/5.43 | | | | |
% 33.82/5.43 | | | | | CLOSE: (58) is inconsistent.
% 33.82/5.43 | | | | |
% 33.82/5.43 | | | | Case 2:
% 33.82/5.43 | | | | |
% 33.82/5.43 | | | | | (59) ~ (all_97_1 = all_93_0)
% 33.82/5.43 | | | | |
% 33.82/5.43 | | | | | BETA: splitting (14) gives:
% 33.82/5.43 | | | | |
% 33.82/5.43 | | | | | Case 1:
% 33.82/5.43 | | | | | |
% 33.82/5.43 | | | | | | (60) ~ (ssList(all_97_1) = 0)
% 33.82/5.43 | | | | | |
% 33.82/5.43 | | | | | | GROUND_INST: instantiating (5) with 0, all_309_1, all_97_2,
% 33.82/5.43 | | | | | | simplifying with (12), (41) gives:
% 33.82/5.43 | | | | | | (61) all_309_1 = 0
% 33.82/5.43 | | | | | |
% 33.82/5.43 | | | | | | BETA: splitting (43) gives:
% 33.82/5.43 | | | | | |
% 33.82/5.43 | | | | | | Case 1:
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | | (62) ~ (all_309_1 = 0)
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | | REDUCE: (61), (62) imply:
% 33.82/5.43 | | | | | | | (63) $false
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | | CLOSE: (63) is inconsistent.
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | Case 2:
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | | (64) all_309_0 = 0
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | | REDUCE: (42), (64) imply:
% 33.82/5.43 | | | | | | | (65) ssList(all_97_1) = 0
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | | PRED_UNIFY: (60), (65) imply:
% 33.82/5.43 | | | | | | | (66) $false
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | | CLOSE: (66) is inconsistent.
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | End of split
% 33.82/5.43 | | | | | |
% 33.82/5.43 | | | | | Case 2:
% 33.82/5.43 | | | | | |
% 33.82/5.43 | | | | | | (67) ~ (all_97_0 = 0) | all_97_1 = all_93_0
% 33.82/5.43 | | | | | |
% 33.82/5.43 | | | | | | BETA: splitting (67) gives:
% 33.82/5.43 | | | | | |
% 33.82/5.43 | | | | | | Case 1:
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | | (68) ~ (all_97_0 = 0)
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | | REDUCE: (56), (68) imply:
% 33.82/5.43 | | | | | | | (69) $false
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | | CLOSE: (69) is inconsistent.
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | Case 2:
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | | (70) all_97_1 = all_93_0
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | | REDUCE: (59), (70) imply:
% 33.82/5.43 | | | | | | | (71) $false
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | | CLOSE: (71) is inconsistent.
% 33.82/5.43 | | | | | | |
% 33.82/5.43 | | | | | | End of split
% 33.82/5.43 | | | | | |
% 33.82/5.43 | | | | | End of split
% 33.82/5.43 | | | | |
% 33.82/5.43 | | | | End of split
% 33.82/5.43 | | | |
% 33.82/5.43 | | | End of split
% 33.82/5.43 | | |
% 33.82/5.43 | | End of split
% 33.82/5.43 | |
% 33.82/5.43 | End of split
% 33.82/5.43 |
% 33.82/5.43 End of proof
% 33.82/5.43 % SZS output end Proof for theBenchmark
% 33.82/5.43
% 33.82/5.43 4824ms
%------------------------------------------------------------------------------