TSTP Solution File: SWC001+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC001+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 : n024.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 20:49:06 EDT 2023
% Result : Theorem 27.79s 4.32s
% Output : Proof 39.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC001+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n024.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 16:33:08 EDT 2023
% 0.13/0.35 % 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 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 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 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 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 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 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 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.92/1.51 Prover 4: Preprocessing ...
% 5.92/1.51 Prover 1: Preprocessing ...
% 6.45/1.54 Prover 0: Preprocessing ...
% 6.45/1.54 Prover 3: Preprocessing ...
% 6.45/1.54 Prover 2: Preprocessing ...
% 6.45/1.54 Prover 5: Preprocessing ...
% 6.45/1.54 Prover 6: Preprocessing ...
% 16.03/2.81 Prover 2: Proving ...
% 16.71/2.88 Prover 1: Constructing countermodel ...
% 16.97/2.92 Prover 5: Constructing countermodel ...
% 17.70/3.06 Prover 3: Constructing countermodel ...
% 18.35/3.11 Prover 6: Proving ...
% 23.09/3.80 Prover 4: Constructing countermodel ...
% 25.61/4.11 Prover 0: Proving ...
% 27.79/4.32 Prover 0: proved (3689ms)
% 27.79/4.32
% 27.79/4.32 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.79/4.32
% 27.79/4.32 Prover 5: stopped
% 27.95/4.33 Prover 3: stopped
% 27.95/4.34 Prover 6: stopped
% 27.95/4.34 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 27.95/4.34 Prover 2: stopped
% 27.95/4.35 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 27.95/4.35 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 27.95/4.35 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 27.95/4.36 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 29.85/4.61 Prover 11: Preprocessing ...
% 29.85/4.64 Prover 7: Preprocessing ...
% 29.85/4.65 Prover 8: Preprocessing ...
% 29.85/4.65 Prover 13: Preprocessing ...
% 29.85/4.66 Prover 10: Preprocessing ...
% 32.18/4.89 Prover 10: Constructing countermodel ...
% 32.18/4.89 Prover 7: Constructing countermodel ...
% 32.92/4.99 Prover 13: Constructing countermodel ...
% 33.59/5.15 Prover 8: Warning: ignoring some quantifiers
% 33.59/5.18 Prover 8: Constructing countermodel ...
% 37.56/5.63 Prover 1: Found proof (size 39)
% 37.56/5.63 Prover 1: proved (4995ms)
% 37.56/5.63 Prover 4: stopped
% 37.56/5.63 Prover 13: stopped
% 37.56/5.63 Prover 8: stopped
% 37.56/5.63 Prover 10: stopped
% 37.56/5.63 Prover 7: stopped
% 38.69/5.82 Prover 11: Constructing countermodel ...
% 38.69/5.84 Prover 11: stopped
% 38.69/5.84
% 38.69/5.84 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.69/5.84
% 38.69/5.85 % SZS output start Proof for theBenchmark
% 38.69/5.85 Assumptions after simplification:
% 38.69/5.85 ---------------------------------
% 38.69/5.85
% 38.69/5.85 (co1)
% 39.02/5.88 ? [v0: $i] : ? [v1: any] : (duplicatefreeP(v0) = v1 & ssList(v0) = 0 &
% 39.02/5.88 $i(v0) & ? [v2: $i] : (v1 = 0 & ssList(v2) = 0 & $i(v2) & ! [v3: $i] : !
% 39.02/5.88 [v4: any] : ( ~ (memberP(v0, v3) = v4) | ~ $i(v3) | ? [v5: any] : ?
% 39.02/5.88 [v6: any] : (memberP(v2, v3) = v6 & ssItem(v3) = v5 & ( ~ (v5 = 0) | ((
% 39.02/5.88 ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 = 0))))) & ? [v3: $i]
% 39.02/5.88 : ? [v4: any] : ? [v5: any] : (memberP(v2, v3) = v4 & memberP(v0, v3) =
% 39.02/5.88 v5 & ssItem(v3) = 0 & $i(v3) & ( ~ (v5 = 0) | ~ (v4 = 0)) & (v5 = 0 |
% 39.02/5.88 v4 = 0))))
% 39.02/5.88
% 39.02/5.88 (function-axioms)
% 39.02/5.89 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 39.02/5.89 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 39.02/5.89 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 39.02/5.89 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 39.02/5.90 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 39.02/5.90 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 39.02/5.90 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 39.02/5.90 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 39.02/5.90 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 39.02/5.90 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 39.02/5.90 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 39.02/5.90 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 39.02/5.90 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 39.02/5.90 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 39.02/5.90 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 39.02/5.90 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 39.02/5.90 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 39.02/5.90 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 39.02/5.90 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 39.02/5.90 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 39.02/5.90 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 39.02/5.90 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 39.02/5.90 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 39.02/5.90 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 39.02/5.90 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 39.02/5.90 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 39.02/5.90 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 39.02/5.90 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 39.02/5.90 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 39.02/5.90 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 39.02/5.90 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 39.02/5.90 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 39.02/5.90 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 39.02/5.90 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 39.02/5.90 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 39.02/5.90 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 39.02/5.90 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 39.02/5.90 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 39.02/5.90 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 39.02/5.90 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 39.02/5.90 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 39.02/5.90 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 39.02/5.90 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 39.02/5.90
% 39.02/5.90 Further assumptions not needed in the proof:
% 39.02/5.90 --------------------------------------------
% 39.02/5.90 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax2, ax20,
% 39.02/5.90 ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32,
% 39.02/5.90 ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44,
% 39.02/5.90 ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56,
% 39.02/5.90 ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68,
% 39.02/5.90 ax69, ax7, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8,
% 39.02/5.90 ax80, ax81, ax82, ax83, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91,
% 39.02/5.90 ax92, ax93, ax94, ax95
% 39.02/5.90
% 39.02/5.90 Those formulas are unsatisfiable:
% 39.02/5.90 ---------------------------------
% 39.02/5.90
% 39.02/5.90 Begin of proof
% 39.02/5.90 |
% 39.16/5.90 | ALPHA: (function-axioms) implies:
% 39.16/5.90 | (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 39.16/5.90 | (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 39.16/5.90 | (2) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 39.16/5.90 | ! [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3,
% 39.16/5.90 | v2) = v0))
% 39.16/5.90 |
% 39.16/5.90 | DELTA: instantiating (co1) with fresh symbols all_93_0, all_93_1 gives:
% 39.16/5.91 | (3) duplicatefreeP(all_93_1) = all_93_0 & ssList(all_93_1) = 0 &
% 39.16/5.91 | $i(all_93_1) & ? [v0: $i] : (all_93_0 = 0 & ssList(v0) = 0 & $i(v0) &
% 39.16/5.91 | ! [v1: $i] : ! [v2: any] : ( ~ (memberP(all_93_1, v1) = v2) | ~
% 39.16/5.91 | $i(v1) | ? [v3: any] : ? [v4: any] : (memberP(v0, v1) = v4 &
% 39.16/5.91 | ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~
% 39.16/5.91 | (v2 = 0) | v4 = 0))))) & ? [v1: $i] : ? [v2: any] : ?
% 39.16/5.91 | [v3: any] : (memberP(v0, v1) = v2 & memberP(all_93_1, v1) = v3 &
% 39.16/5.91 | ssItem(v1) = 0 & $i(v1) & ( ~ (v3 = 0) | ~ (v2 = 0)) & (v3 = 0 |
% 39.16/5.91 | v2 = 0)))
% 39.16/5.91 |
% 39.16/5.91 | ALPHA: (3) implies:
% 39.16/5.91 | (4) ? [v0: $i] : (all_93_0 = 0 & ssList(v0) = 0 & $i(v0) & ! [v1: $i] :
% 39.16/5.91 | ! [v2: any] : ( ~ (memberP(all_93_1, v1) = v2) | ~ $i(v1) | ? [v3:
% 39.16/5.91 | any] : ? [v4: any] : (memberP(v0, v1) = v4 & ssItem(v1) = v3 & (
% 39.16/5.91 | ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 =
% 39.16/5.91 | 0))))) & ? [v1: $i] : ? [v2: any] : ? [v3: any] :
% 39.16/5.91 | (memberP(v0, v1) = v2 & memberP(all_93_1, v1) = v3 & ssItem(v1) = 0 &
% 39.16/5.91 | $i(v1) & ( ~ (v3 = 0) | ~ (v2 = 0)) & (v3 = 0 | v2 = 0)))
% 39.16/5.91 |
% 39.16/5.91 | DELTA: instantiating (4) with fresh symbol all_97_0 gives:
% 39.16/5.91 | (5) all_93_0 = 0 & ssList(all_97_0) = 0 & $i(all_97_0) & ! [v0: $i] : !
% 39.16/5.91 | [v1: any] : ( ~ (memberP(all_93_1, v0) = v1) | ~ $i(v0) | ? [v2: any]
% 39.16/5.91 | : ? [v3: any] : (memberP(all_97_0, v0) = v3 & ssItem(v0) = v2 & ( ~
% 39.16/5.91 | (v2 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1 = 0) | v3 = 0))))) &
% 39.16/5.91 | ? [v0: $i] : ? [v1: any] : ? [v2: any] : (memberP(all_97_0, v0) = v1
% 39.16/5.91 | & memberP(all_93_1, v0) = v2 & ssItem(v0) = 0 & $i(v0) & ( ~ (v2 = 0)
% 39.16/5.91 | | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 39.16/5.91 |
% 39.16/5.91 | ALPHA: (5) implies:
% 39.16/5.91 | (6) ! [v0: $i] : ! [v1: any] : ( ~ (memberP(all_93_1, v0) = v1) | ~
% 39.16/5.91 | $i(v0) | ? [v2: any] : ? [v3: any] : (memberP(all_97_0, v0) = v3 &
% 39.16/5.91 | ssItem(v0) = v2 & ( ~ (v2 = 0) | (( ~ (v3 = 0) | v1 = 0) & ( ~ (v1
% 39.16/5.91 | = 0) | v3 = 0)))))
% 39.16/5.91 | (7) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (memberP(all_97_0, v0) = v1
% 39.16/5.91 | & memberP(all_93_1, v0) = v2 & ssItem(v0) = 0 & $i(v0) & ( ~ (v2 = 0)
% 39.16/5.91 | | ~ (v1 = 0)) & (v2 = 0 | v1 = 0))
% 39.16/5.91 |
% 39.16/5.91 | DELTA: instantiating (7) with fresh symbols all_100_0, all_100_1, all_100_2
% 39.16/5.91 | gives:
% 39.16/5.91 | (8) memberP(all_97_0, all_100_2) = all_100_1 & memberP(all_93_1, all_100_2)
% 39.16/5.91 | = all_100_0 & ssItem(all_100_2) = 0 & $i(all_100_2) & ( ~ (all_100_0 =
% 39.16/5.91 | 0) | ~ (all_100_1 = 0)) & (all_100_0 = 0 | all_100_1 = 0)
% 39.16/5.91 |
% 39.16/5.91 | ALPHA: (8) implies:
% 39.16/5.91 | (9) $i(all_100_2)
% 39.16/5.91 | (10) ssItem(all_100_2) = 0
% 39.16/5.91 | (11) memberP(all_93_1, all_100_2) = all_100_0
% 39.16/5.91 | (12) memberP(all_97_0, all_100_2) = all_100_1
% 39.16/5.92 | (13) all_100_0 = 0 | all_100_1 = 0
% 39.16/5.92 | (14) ~ (all_100_0 = 0) | ~ (all_100_1 = 0)
% 39.16/5.92 |
% 39.16/5.92 | GROUND_INST: instantiating (6) with all_100_2, all_100_0, simplifying with
% 39.16/5.92 | (9), (11) gives:
% 39.16/5.92 | (15) ? [v0: any] : ? [v1: any] : (memberP(all_97_0, all_100_2) = v1 &
% 39.16/5.92 | ssItem(all_100_2) = v0 & ( ~ (v0 = 0) | (( ~ (v1 = 0) | all_100_0 =
% 39.16/5.92 | 0) & ( ~ (all_100_0 = 0) | v1 = 0))))
% 39.16/5.92 |
% 39.16/5.92 | DELTA: instantiating (15) with fresh symbols all_271_0, all_271_1 gives:
% 39.16/5.92 | (16) memberP(all_97_0, all_100_2) = all_271_0 & ssItem(all_100_2) =
% 39.16/5.92 | all_271_1 & ( ~ (all_271_1 = 0) | (( ~ (all_271_0 = 0) | all_100_0 =
% 39.16/5.92 | 0) & ( ~ (all_100_0 = 0) | all_271_0 = 0)))
% 39.16/5.92 |
% 39.16/5.92 | ALPHA: (16) implies:
% 39.16/5.92 | (17) ssItem(all_100_2) = all_271_1
% 39.16/5.92 | (18) memberP(all_97_0, all_100_2) = all_271_0
% 39.16/5.92 | (19) ~ (all_271_1 = 0) | (( ~ (all_271_0 = 0) | all_100_0 = 0) & ( ~
% 39.16/5.92 | (all_100_0 = 0) | all_271_0 = 0))
% 39.16/5.92 |
% 39.16/5.92 | GROUND_INST: instantiating (1) with 0, all_271_1, all_100_2, simplifying with
% 39.16/5.92 | (10), (17) gives:
% 39.16/5.92 | (20) all_271_1 = 0
% 39.16/5.92 |
% 39.16/5.92 | GROUND_INST: instantiating (2) with all_100_1, all_271_0, all_100_2, all_97_0,
% 39.16/5.92 | simplifying with (12), (18) gives:
% 39.16/5.92 | (21) all_271_0 = all_100_1
% 39.16/5.92 |
% 39.16/5.92 | BETA: splitting (14) gives:
% 39.16/5.92 |
% 39.16/5.92 | Case 1:
% 39.16/5.92 | |
% 39.16/5.92 | | (22) ~ (all_100_0 = 0)
% 39.16/5.92 | |
% 39.16/5.92 | | BETA: splitting (13) gives:
% 39.16/5.92 | |
% 39.16/5.92 | | Case 1:
% 39.16/5.92 | | |
% 39.16/5.92 | | | (23) all_100_0 = 0
% 39.16/5.92 | | |
% 39.16/5.92 | | | REDUCE: (22), (23) imply:
% 39.16/5.92 | | | (24) $false
% 39.16/5.92 | | |
% 39.16/5.92 | | | CLOSE: (24) is inconsistent.
% 39.16/5.92 | | |
% 39.16/5.92 | | Case 2:
% 39.16/5.92 | | |
% 39.16/5.92 | | | (25) all_100_1 = 0
% 39.16/5.92 | | |
% 39.16/5.92 | | | COMBINE_EQS: (21), (25) imply:
% 39.16/5.92 | | | (26) all_271_0 = 0
% 39.16/5.92 | | |
% 39.16/5.92 | | | BETA: splitting (19) gives:
% 39.16/5.92 | | |
% 39.16/5.92 | | | Case 1:
% 39.16/5.92 | | | |
% 39.16/5.92 | | | | (27) ~ (all_271_1 = 0)
% 39.16/5.92 | | | |
% 39.16/5.92 | | | | REDUCE: (20), (27) imply:
% 39.16/5.92 | | | | (28) $false
% 39.16/5.92 | | | |
% 39.16/5.92 | | | | CLOSE: (28) is inconsistent.
% 39.16/5.92 | | | |
% 39.16/5.92 | | | Case 2:
% 39.16/5.92 | | | |
% 39.16/5.92 | | | | (29) ( ~ (all_271_0 = 0) | all_100_0 = 0) & ( ~ (all_100_0 = 0) |
% 39.16/5.92 | | | | all_271_0 = 0)
% 39.16/5.92 | | | |
% 39.16/5.92 | | | | ALPHA: (29) implies:
% 39.16/5.92 | | | | (30) ~ (all_271_0 = 0) | all_100_0 = 0
% 39.16/5.92 | | | |
% 39.16/5.92 | | | | BETA: splitting (30) gives:
% 39.16/5.92 | | | |
% 39.16/5.92 | | | | Case 1:
% 39.16/5.92 | | | | |
% 39.16/5.92 | | | | | (31) ~ (all_271_0 = 0)
% 39.16/5.92 | | | | |
% 39.16/5.92 | | | | | REDUCE: (26), (31) imply:
% 39.16/5.92 | | | | | (32) $false
% 39.16/5.92 | | | | |
% 39.16/5.92 | | | | | CLOSE: (32) is inconsistent.
% 39.16/5.92 | | | | |
% 39.16/5.92 | | | | Case 2:
% 39.16/5.92 | | | | |
% 39.16/5.92 | | | | | (33) all_100_0 = 0
% 39.16/5.92 | | | | |
% 39.16/5.92 | | | | | REDUCE: (22), (33) imply:
% 39.16/5.92 | | | | | (34) $false
% 39.16/5.92 | | | | |
% 39.16/5.92 | | | | | CLOSE: (34) is inconsistent.
% 39.16/5.92 | | | | |
% 39.16/5.92 | | | | End of split
% 39.16/5.92 | | | |
% 39.16/5.92 | | | End of split
% 39.16/5.92 | | |
% 39.16/5.92 | | End of split
% 39.16/5.92 | |
% 39.16/5.92 | Case 2:
% 39.16/5.92 | |
% 39.16/5.92 | | (35) all_100_0 = 0
% 39.16/5.92 | | (36) ~ (all_100_1 = 0)
% 39.16/5.92 | |
% 39.16/5.92 | | BETA: splitting (19) gives:
% 39.16/5.92 | |
% 39.16/5.92 | | Case 1:
% 39.16/5.92 | | |
% 39.16/5.92 | | | (37) ~ (all_271_1 = 0)
% 39.16/5.92 | | |
% 39.16/5.92 | | | REDUCE: (20), (37) imply:
% 39.16/5.92 | | | (38) $false
% 39.16/5.92 | | |
% 39.16/5.92 | | | CLOSE: (38) is inconsistent.
% 39.16/5.92 | | |
% 39.16/5.92 | | Case 2:
% 39.16/5.92 | | |
% 39.16/5.92 | | | (39) ( ~ (all_271_0 = 0) | all_100_0 = 0) & ( ~ (all_100_0 = 0) |
% 39.16/5.92 | | | all_271_0 = 0)
% 39.16/5.92 | | |
% 39.16/5.92 | | | ALPHA: (39) implies:
% 39.16/5.92 | | | (40) ~ (all_100_0 = 0) | all_271_0 = 0
% 39.16/5.92 | | |
% 39.16/5.92 | | | BETA: splitting (40) gives:
% 39.16/5.92 | | |
% 39.16/5.92 | | | Case 1:
% 39.16/5.92 | | | |
% 39.16/5.92 | | | | (41) ~ (all_100_0 = 0)
% 39.16/5.92 | | | |
% 39.16/5.92 | | | | REDUCE: (35), (41) imply:
% 39.16/5.92 | | | | (42) $false
% 39.16/5.92 | | | |
% 39.16/5.92 | | | | CLOSE: (42) is inconsistent.
% 39.16/5.92 | | | |
% 39.16/5.92 | | | Case 2:
% 39.16/5.92 | | | |
% 39.16/5.92 | | | | (43) all_271_0 = 0
% 39.16/5.92 | | | |
% 39.16/5.92 | | | | COMBINE_EQS: (21), (43) imply:
% 39.16/5.92 | | | | (44) all_100_1 = 0
% 39.16/5.92 | | | |
% 39.28/5.93 | | | | REDUCE: (36), (44) imply:
% 39.28/5.93 | | | | (45) $false
% 39.28/5.93 | | | |
% 39.28/5.93 | | | | CLOSE: (45) is inconsistent.
% 39.28/5.93 | | | |
% 39.28/5.93 | | | End of split
% 39.28/5.93 | | |
% 39.28/5.93 | | End of split
% 39.28/5.93 | |
% 39.28/5.93 | End of split
% 39.28/5.93 |
% 39.28/5.93 End of proof
% 39.28/5.93 % SZS output end Proof for theBenchmark
% 39.28/5.93
% 39.28/5.93 5312ms
%------------------------------------------------------------------------------