TSTP Solution File: SWC205+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC205+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 : n001.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 20:50:13 EDT 2023
% Result : Theorem 21.67s 3.71s
% Output : Proof 27.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC205+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.33 % Computer : n001.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 19:05:50 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.19/0.60 ________ _____
% 0.19/0.60 ___ __ \_________(_)________________________________
% 0.19/0.60 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.60 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.60 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.60
% 0.19/0.60 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.60 (2023-06-19)
% 0.19/0.60
% 0.19/0.60 (c) Philipp Rümmer, 2009-2023
% 0.19/0.60 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.60 Amanda Stjerna.
% 0.19/0.60 Free software under BSD-3-Clause.
% 0.19/0.60
% 0.19/0.60 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.60
% 0.19/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.19/0.63 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 4.72/1.39 Prover 4: Preprocessing ...
% 4.72/1.42 Prover 1: Preprocessing ...
% 4.72/1.46 Prover 2: Preprocessing ...
% 4.72/1.46 Prover 3: Preprocessing ...
% 4.72/1.46 Prover 5: Preprocessing ...
% 4.72/1.46 Prover 6: Preprocessing ...
% 4.72/1.46 Prover 0: Preprocessing ...
% 14.39/2.84 Prover 2: Proving ...
% 14.39/2.84 Prover 1: Constructing countermodel ...
% 14.39/2.84 Prover 5: Constructing countermodel ...
% 15.65/2.87 Prover 6: Proving ...
% 16.07/2.94 Prover 3: Constructing countermodel ...
% 21.67/3.66 Prover 4: Constructing countermodel ...
% 21.67/3.71 Prover 3: proved (3081ms)
% 21.67/3.71
% 21.67/3.71 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.67/3.71
% 22.13/3.72 Prover 0: Proving ...
% 22.13/3.72 Prover 6: stopped
% 22.13/3.73 Prover 5: stopped
% 22.13/3.74 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 22.13/3.74 Prover 0: stopped
% 22.13/3.74 Prover 2: stopped
% 22.13/3.75 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.13/3.75 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.13/3.75 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 22.13/3.75 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 24.00/3.97 Prover 10: Preprocessing ...
% 24.41/4.04 Prover 13: Preprocessing ...
% 24.41/4.06 Prover 11: Preprocessing ...
% 24.73/4.06 Prover 7: Preprocessing ...
% 24.73/4.08 Prover 8: Preprocessing ...
% 25.65/4.29 Prover 1: Found proof (size 49)
% 25.65/4.29 Prover 1: proved (3666ms)
% 25.65/4.29 Prover 4: stopped
% 26.59/4.33 Prover 11: stopped
% 26.59/4.36 Prover 7: Constructing countermodel ...
% 27.03/4.37 Prover 10: Constructing countermodel ...
% 27.03/4.38 Prover 7: stopped
% 27.03/4.38 Prover 10: stopped
% 27.03/4.39 Prover 13: Constructing countermodel ...
% 27.03/4.41 Prover 13: stopped
% 27.03/4.45 Prover 8: Warning: ignoring some quantifiers
% 27.49/4.46 Prover 8: Constructing countermodel ...
% 27.49/4.47 Prover 8: stopped
% 27.49/4.47
% 27.49/4.47 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.49/4.47
% 27.49/4.48 % SZS output start Proof for theBenchmark
% 27.49/4.48 Assumptions after simplification:
% 27.49/4.48 ---------------------------------
% 27.49/4.48
% 27.49/4.48 (ax15)
% 27.60/4.50 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 27.60/4.50 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 27.60/4.50 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 27.60/4.50
% 27.60/4.51 (ax17)
% 27.60/4.51 ssList(nil) = 0 & $i(nil)
% 27.60/4.51
% 27.60/4.51 (co1)
% 27.60/4.51 $i(nil) & ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 27.60/4.51 $i(v0) & ? [v2: $i] : ( ~ (v1 = 0) & ssList(v2) = 0 & neq(v2, nil) = 0 &
% 27.60/4.51 $i(v2) & ( ~ (v2 = nil) | v0 = nil) & ( ~ (v0 = nil) | v2 = nil)))
% 27.60/4.51
% 27.60/4.51 (function-axioms)
% 27.60/4.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 27.60/4.52 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 27.60/4.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.60/4.52 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 27.60/4.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.60/4.52 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 27.60/4.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.60/4.52 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 27.60/4.52 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.60/4.52 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 27.60/4.52 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 27.60/4.52 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 27.60/4.52 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 27.60/4.52 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 27.60/4.52 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 27.60/4.52 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 27.60/4.52 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.60/4.52 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 27.60/4.52 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 27.60/4.52 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 27.60/4.52 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 27.60/4.52 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 27.60/4.52 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 27.60/4.52 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 27.60/4.52 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 27.60/4.52 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 27.60/4.52 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 27.60/4.52 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 27.60/4.52 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 27.60/4.52 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 27.60/4.52 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 27.60/4.52 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 27.60/4.52 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.60/4.52 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 27.60/4.52 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 27.60/4.52 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 27.60/4.52
% 27.60/4.52 Further assumptions not needed in the proof:
% 27.60/4.52 --------------------------------------------
% 27.60/4.52 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 27.60/4.52 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34,
% 27.60/4.52 ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46,
% 27.60/4.52 ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58,
% 27.60/4.52 ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7,
% 27.60/4.52 ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81,
% 27.60/4.52 ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93,
% 27.60/4.52 ax94, ax95
% 27.60/4.52
% 27.60/4.52 Those formulas are unsatisfiable:
% 27.60/4.52 ---------------------------------
% 27.60/4.52
% 27.60/4.52 Begin of proof
% 27.60/4.52 |
% 27.60/4.52 | ALPHA: (ax17) implies:
% 27.60/4.52 | (1) ssList(nil) = 0
% 27.60/4.52 |
% 27.60/4.52 | ALPHA: (co1) implies:
% 27.60/4.52 | (2) $i(nil)
% 27.60/4.52 | (3) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 27.60/4.52 | $i(v0) & ? [v2: $i] : ( ~ (v1 = 0) & ssList(v2) = 0 & neq(v2, nil) =
% 27.60/4.52 | 0 & $i(v2) & ( ~ (v2 = nil) | v0 = nil) & ( ~ (v0 = nil) | v2 =
% 27.60/4.52 | nil)))
% 27.60/4.52 |
% 27.60/4.52 | ALPHA: (function-axioms) implies:
% 27.60/4.52 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 27.60/4.52 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 27.60/4.52 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 27.60/4.52 | ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0))
% 27.60/4.52 |
% 27.60/4.52 | DELTA: instantiating (3) with fresh symbols all_93_0, all_93_1 gives:
% 27.60/4.52 | (6) ssList(all_93_1) = 0 & neq(all_93_1, nil) = all_93_0 & $i(all_93_1) &
% 27.60/4.52 | ? [v0: $i] : ( ~ (all_93_0 = 0) & ssList(v0) = 0 & neq(v0, nil) = 0 &
% 27.60/4.53 | $i(v0) & ( ~ (v0 = nil) | all_93_1 = nil) & ( ~ (all_93_1 = nil) | v0
% 27.60/4.53 | = nil))
% 27.60/4.53 |
% 27.60/4.53 | ALPHA: (6) implies:
% 27.79/4.53 | (7) $i(all_93_1)
% 27.79/4.53 | (8) neq(all_93_1, nil) = all_93_0
% 27.79/4.53 | (9) ssList(all_93_1) = 0
% 27.79/4.53 | (10) ? [v0: $i] : ( ~ (all_93_0 = 0) & ssList(v0) = 0 & neq(v0, nil) = 0 &
% 27.79/4.53 | $i(v0) & ( ~ (v0 = nil) | all_93_1 = nil) & ( ~ (all_93_1 = nil) |
% 27.79/4.53 | v0 = nil))
% 27.79/4.53 |
% 27.79/4.53 | DELTA: instantiating (10) with fresh symbol all_97_0 gives:
% 27.79/4.53 | (11) ~ (all_93_0 = 0) & ssList(all_97_0) = 0 & neq(all_97_0, nil) = 0 &
% 27.79/4.53 | $i(all_97_0) & ( ~ (all_97_0 = nil) | all_93_1 = nil) & ( ~ (all_93_1
% 27.79/4.53 | = nil) | all_97_0 = nil)
% 27.79/4.53 |
% 27.79/4.53 | ALPHA: (11) implies:
% 27.79/4.53 | (12) ~ (all_93_0 = 0)
% 27.79/4.53 | (13) neq(all_97_0, nil) = 0
% 27.79/4.53 | (14) ~ (all_93_1 = nil) | all_97_0 = nil
% 27.79/4.53 |
% 27.79/4.53 | GROUND_INST: instantiating (ax15) with all_93_1, simplifying with (7), (9)
% 27.79/4.53 | gives:
% 27.79/4.53 | (15) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_93_1, v0) = v1) | ~ $i(v0)
% 27.79/4.53 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 27.79/4.53 | ~ (v0 = all_93_1)) & (v1 = 0 | v0 = all_93_1)))
% 27.79/4.53 |
% 27.79/4.53 | GROUND_INST: instantiating (15) with nil, all_93_0, simplifying with (2), (8)
% 27.79/4.53 | gives:
% 27.79/4.53 | (16) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_93_0 = 0)
% 27.79/4.53 | | ~ (all_93_1 = nil)) & (all_93_0 = 0 | all_93_1 = nil))
% 27.79/4.53 |
% 27.79/4.53 | BETA: splitting (16) gives:
% 27.79/4.53 |
% 27.79/4.53 | Case 1:
% 27.79/4.53 | |
% 27.79/4.53 | | (17) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 27.79/4.53 | |
% 27.79/4.53 | | DELTA: instantiating (17) with fresh symbol all_258_0 gives:
% 27.79/4.53 | | (18) ~ (all_258_0 = 0) & ssList(nil) = all_258_0
% 27.79/4.53 | |
% 27.79/4.53 | | ALPHA: (18) implies:
% 27.79/4.53 | | (19) ~ (all_258_0 = 0)
% 27.79/4.53 | | (20) ssList(nil) = all_258_0
% 27.79/4.53 | |
% 27.79/4.53 | | DELTA: instantiating (17) with fresh symbol all_260_0 gives:
% 27.79/4.53 | | (21) ~ (all_260_0 = 0) & ssList(nil) = all_260_0
% 27.79/4.53 | |
% 27.79/4.53 | | ALPHA: (21) implies:
% 27.79/4.53 | | (22) ssList(nil) = all_260_0
% 27.79/4.53 | |
% 27.79/4.53 | | DELTA: instantiating (17) with fresh symbol all_262_0 gives:
% 27.79/4.53 | | (23) ~ (all_262_0 = 0) & ssList(nil) = all_262_0
% 27.79/4.53 | |
% 27.79/4.53 | | ALPHA: (23) implies:
% 27.79/4.53 | | (24) ssList(nil) = all_262_0
% 27.79/4.53 | |
% 27.79/4.53 | | DELTA: instantiating (17) with fresh symbol all_264_0 gives:
% 27.79/4.53 | | (25) ~ (all_264_0 = 0) & ssList(nil) = all_264_0
% 27.79/4.53 | |
% 27.79/4.53 | | ALPHA: (25) implies:
% 27.79/4.53 | | (26) ssList(nil) = all_264_0
% 27.79/4.53 | |
% 27.79/4.53 | | DELTA: instantiating (17) with fresh symbol all_266_0 gives:
% 27.79/4.53 | | (27) ~ (all_266_0 = 0) & ssList(nil) = all_266_0
% 27.79/4.53 | |
% 27.79/4.53 | | ALPHA: (27) implies:
% 27.79/4.53 | | (28) ssList(nil) = all_266_0
% 27.79/4.53 | |
% 27.79/4.53 | | GROUND_INST: instantiating (4) with all_260_0, all_262_0, nil, simplifying
% 27.79/4.53 | | with (22), (24) gives:
% 27.79/4.53 | | (29) all_262_0 = all_260_0
% 27.79/4.53 | |
% 27.79/4.53 | | GROUND_INST: instantiating (4) with 0, all_264_0, nil, simplifying with (1),
% 27.79/4.53 | | (26) gives:
% 27.79/4.53 | | (30) all_264_0 = 0
% 27.79/4.53 | |
% 27.79/4.53 | | GROUND_INST: instantiating (4) with all_260_0, all_264_0, nil, simplifying
% 27.79/4.53 | | with (22), (26) gives:
% 27.79/4.53 | | (31) all_264_0 = all_260_0
% 27.79/4.53 | |
% 27.79/4.53 | | GROUND_INST: instantiating (4) with all_262_0, all_266_0, nil, simplifying
% 27.79/4.53 | | with (24), (28) gives:
% 27.79/4.53 | | (32) all_266_0 = all_262_0
% 27.79/4.53 | |
% 27.79/4.53 | | GROUND_INST: instantiating (4) with all_258_0, all_266_0, nil, simplifying
% 27.79/4.53 | | with (20), (28) gives:
% 27.79/4.53 | | (33) all_266_0 = all_258_0
% 27.79/4.53 | |
% 27.79/4.53 | | COMBINE_EQS: (32), (33) imply:
% 27.79/4.54 | | (34) all_262_0 = all_258_0
% 27.79/4.54 | |
% 27.79/4.54 | | SIMP: (34) implies:
% 27.79/4.54 | | (35) all_262_0 = all_258_0
% 27.79/4.54 | |
% 27.79/4.54 | | COMBINE_EQS: (30), (31) imply:
% 27.79/4.54 | | (36) all_260_0 = 0
% 27.79/4.54 | |
% 27.79/4.54 | | SIMP: (36) implies:
% 27.79/4.54 | | (37) all_260_0 = 0
% 27.79/4.54 | |
% 27.79/4.54 | | COMBINE_EQS: (29), (35) imply:
% 27.79/4.54 | | (38) all_260_0 = all_258_0
% 27.79/4.54 | |
% 27.79/4.54 | | SIMP: (38) implies:
% 27.79/4.54 | | (39) all_260_0 = all_258_0
% 27.79/4.54 | |
% 27.79/4.54 | | COMBINE_EQS: (37), (39) imply:
% 27.79/4.54 | | (40) all_258_0 = 0
% 27.79/4.54 | |
% 27.79/4.54 | | REDUCE: (19), (40) imply:
% 27.79/4.54 | | (41) $false
% 27.79/4.54 | |
% 27.79/4.54 | | CLOSE: (41) is inconsistent.
% 27.79/4.54 | |
% 27.79/4.54 | Case 2:
% 27.79/4.54 | |
% 27.85/4.54 | | (42) ( ~ (all_93_0 = 0) | ~ (all_93_1 = nil)) & (all_93_0 = 0 | all_93_1
% 27.85/4.54 | | = nil)
% 27.85/4.54 | |
% 27.85/4.54 | | ALPHA: (42) implies:
% 27.85/4.54 | | (43) all_93_0 = 0 | all_93_1 = nil
% 27.85/4.54 | |
% 27.85/4.54 | | BETA: splitting (43) gives:
% 27.85/4.54 | |
% 27.85/4.54 | | Case 1:
% 27.85/4.54 | | |
% 27.85/4.54 | | | (44) all_93_1 = nil
% 27.85/4.54 | | |
% 27.85/4.54 | | | REDUCE: (8), (44) imply:
% 27.85/4.54 | | | (45) neq(nil, nil) = all_93_0
% 27.85/4.54 | | |
% 27.85/4.54 | | | BETA: splitting (14) gives:
% 27.85/4.54 | | |
% 27.85/4.54 | | | Case 1:
% 27.85/4.54 | | | |
% 27.85/4.54 | | | | (46) ~ (all_93_1 = nil)
% 27.85/4.54 | | | |
% 27.85/4.54 | | | | REDUCE: (44), (46) imply:
% 27.85/4.54 | | | | (47) $false
% 27.85/4.54 | | | |
% 27.85/4.54 | | | | CLOSE: (47) is inconsistent.
% 27.85/4.54 | | | |
% 27.85/4.54 | | | Case 2:
% 27.85/4.54 | | | |
% 27.85/4.54 | | | | (48) all_97_0 = nil
% 27.85/4.54 | | | |
% 27.85/4.54 | | | | REDUCE: (13), (48) imply:
% 27.85/4.54 | | | | (49) neq(nil, nil) = 0
% 27.85/4.54 | | | |
% 27.85/4.54 | | | | GROUND_INST: instantiating (5) with 0, all_93_0, nil, nil, simplifying
% 27.85/4.54 | | | | with (45), (49) gives:
% 27.85/4.54 | | | | (50) all_93_0 = 0
% 27.85/4.54 | | | |
% 27.85/4.54 | | | | REDUCE: (12), (50) imply:
% 27.85/4.54 | | | | (51) $false
% 27.85/4.54 | | | |
% 27.85/4.54 | | | | CLOSE: (51) is inconsistent.
% 27.85/4.54 | | | |
% 27.85/4.54 | | | End of split
% 27.85/4.54 | | |
% 27.85/4.54 | | Case 2:
% 27.85/4.54 | | |
% 27.85/4.54 | | | (52) all_93_0 = 0
% 27.85/4.54 | | |
% 27.85/4.54 | | | REDUCE: (12), (52) imply:
% 27.85/4.54 | | | (53) $false
% 27.85/4.54 | | |
% 27.85/4.54 | | | CLOSE: (53) is inconsistent.
% 27.85/4.54 | | |
% 27.85/4.54 | | End of split
% 27.85/4.54 | |
% 27.85/4.54 | End of split
% 27.85/4.54 |
% 27.85/4.54 End of proof
% 27.85/4.54 % SZS output end Proof for theBenchmark
% 27.85/4.54
% 27.85/4.54 3940ms
%------------------------------------------------------------------------------