TSTP Solution File: SWC030+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC030+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 20:49:17 EDT 2023
% Result : Theorem 21.68s 3.78s
% Output : Proof 34.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC030+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 : n001.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 15:55:35 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.64 ________ _____
% 0.20/0.64 ___ __ \_________(_)________________________________
% 0.20/0.64 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.20/0.64 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.20/0.64 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.20/0.64
% 0.20/0.64 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.20/0.64 (2023-06-19)
% 0.20/0.64
% 0.20/0.64 (c) Philipp Rümmer, 2009-2023
% 0.20/0.64 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.20/0.64 Amanda Stjerna.
% 0.20/0.64 Free software under BSD-3-Clause.
% 0.20/0.64
% 0.20/0.64 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.20/0.64
% 0.20/0.64 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.20/0.66 Running up to 7 provers in parallel.
% 0.20/0.67 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.20/0.67 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.20/0.67 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.20/0.67 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.20/0.67 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.20/0.67 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 0.20/0.67 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 4.18/1.49 Prover 1: Preprocessing ...
% 4.18/1.49 Prover 4: Preprocessing ...
% 4.18/1.53 Prover 0: Preprocessing ...
% 4.18/1.53 Prover 3: Preprocessing ...
% 4.18/1.53 Prover 2: Preprocessing ...
% 4.18/1.53 Prover 6: Preprocessing ...
% 4.18/1.54 Prover 5: Preprocessing ...
% 14.63/2.80 Prover 2: Proving ...
% 15.62/2.87 Prover 5: Constructing countermodel ...
% 15.62/2.89 Prover 6: Proving ...
% 15.62/2.91 Prover 1: Constructing countermodel ...
% 16.24/2.98 Prover 3: Constructing countermodel ...
% 21.68/3.73 Prover 4: Constructing countermodel ...
% 21.68/3.78 Prover 0: Proving ...
% 21.68/3.78 Prover 3: proved (3112ms)
% 21.68/3.78
% 21.68/3.78 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 21.68/3.78
% 21.68/3.80 Prover 5: stopped
% 21.68/3.80 Prover 6: stopped
% 21.68/3.80 Prover 2: stopped
% 21.68/3.82 Prover 0: stopped
% 21.68/3.83 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 21.68/3.83 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 21.68/3.83 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 21.68/3.83 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 21.68/3.84 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.62/4.14 Prover 8: Preprocessing ...
% 24.62/4.15 Prover 13: Preprocessing ...
% 24.62/4.17 Prover 11: Preprocessing ...
% 25.22/4.20 Prover 10: Preprocessing ...
% 25.22/4.21 Prover 7: Preprocessing ...
% 27.13/4.43 Prover 7: Constructing countermodel ...
% 27.13/4.46 Prover 10: Constructing countermodel ...
% 27.74/4.55 Prover 13: Constructing countermodel ...
% 27.74/4.63 Prover 8: Warning: ignoring some quantifiers
% 27.74/4.64 Prover 8: Constructing countermodel ...
% 33.24/5.24 Prover 11: Constructing countermodel ...
% 33.97/5.33 Prover 1: Found proof (size 59)
% 33.97/5.33 Prover 1: proved (4657ms)
% 33.97/5.33 Prover 4: stopped
% 33.97/5.33 Prover 7: stopped
% 33.97/5.33 Prover 10: stopped
% 33.97/5.33 Prover 8: stopped
% 33.97/5.33 Prover 11: stopped
% 33.97/5.33 Prover 13: stopped
% 33.97/5.33
% 33.97/5.33 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.97/5.33
% 33.97/5.33 % SZS output start Proof for theBenchmark
% 33.97/5.34 Assumptions after simplification:
% 33.97/5.34 ---------------------------------
% 33.97/5.34
% 33.97/5.34 (ax83)
% 33.97/5.36 $i(nil) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : !
% 33.97/5.36 [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0)
% 33.97/5.36 & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = nil)) & ( ~ (v1
% 33.97/5.36 = nil) | ~ (v0 = nil) | v2 = nil))))
% 33.97/5.36
% 33.97/5.36 (co1)
% 33.97/5.36 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) =
% 33.97/5.36 0 & $i(v1) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] :
% 33.97/5.36 (ssList(v3) = 0 & app(v3, v2) = v0 & app(v2, v3) = v1 & $i(v3))) & ((v1
% 33.97/5.36 = nil & ~ (v0 = nil)) | (v0 = nil & ~ (v1 = nil)))))
% 33.97/5.36
% 33.97/5.37 (function-axioms)
% 33.97/5.38 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 33.97/5.38 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 33.97/5.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 33.97/5.38 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 33.97/5.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 33.97/5.38 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 33.97/5.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 33.97/5.38 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 33.97/5.38 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 33.97/5.38 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 33.97/5.38 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 33.97/5.38 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 33.97/5.38 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 33.97/5.38 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 33.97/5.38 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 33.97/5.38 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 33.97/5.38 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.97/5.38 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 33.97/5.38 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 33.97/5.38 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 33.97/5.38 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 33.97/5.38 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 33.97/5.38 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 33.97/5.38 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 33.97/5.38 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 33.97/5.38 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 33.97/5.38 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 33.97/5.38 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 33.97/5.38 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 33.97/5.38 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 33.97/5.38 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 33.97/5.38 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 33.97/5.38 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.97/5.38 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 33.97/5.38 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 33.97/5.38 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 33.97/5.38
% 33.97/5.38 Further assumptions not needed in the proof:
% 33.97/5.38 --------------------------------------------
% 33.97/5.38 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax2, ax20,
% 33.97/5.38 ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32,
% 33.97/5.38 ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44,
% 33.97/5.38 ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56,
% 33.97/5.38 ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68,
% 33.97/5.38 ax69, ax7, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8,
% 33.97/5.38 ax80, ax81, ax82, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92,
% 33.97/5.38 ax93, ax94, ax95
% 33.97/5.38
% 33.97/5.38 Those formulas are unsatisfiable:
% 33.97/5.38 ---------------------------------
% 33.97/5.38
% 33.97/5.38 Begin of proof
% 33.97/5.38 |
% 33.97/5.38 | ALPHA: (ax83) implies:
% 33.97/5.38 | (1) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2:
% 33.97/5.38 | $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 =
% 33.97/5.38 | 0) & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 =
% 33.97/5.38 | nil)) & ( ~ (v1 = nil) | ~ (v0 = nil) | v2 = nil))))
% 33.97/5.38 |
% 33.97/5.38 | ALPHA: (co1) implies:
% 33.97/5.38 | (2) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0
% 33.97/5.38 | & $i(v1) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: $i] :
% 33.97/5.38 | (ssList(v3) = 0 & app(v3, v2) = v0 & app(v2, v3) = v1 & $i(v3)))
% 33.97/5.38 | & ((v1 = nil & ~ (v0 = nil)) | (v0 = nil & ~ (v1 = nil)))))
% 33.97/5.38 |
% 33.97/5.38 | ALPHA: (function-axioms) implies:
% 33.97/5.39 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 33.97/5.39 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 33.97/5.39 | (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.97/5.39 | (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 33.97/5.39 |
% 33.97/5.39 | DELTA: instantiating (2) with fresh symbol all_93_0 gives:
% 33.97/5.39 | (5) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : (ssList(v0) = 0 &
% 33.97/5.39 | $i(v0) & ? [v1: $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] :
% 33.97/5.39 | (ssList(v2) = 0 & app(v2, v1) = all_93_0 & app(v1, v2) = v0 &
% 34.32/5.39 | $i(v2))) & ((v0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil &
% 34.32/5.39 | ~ (v0 = nil))))
% 34.32/5.39 |
% 34.32/5.39 | ALPHA: (5) implies:
% 34.32/5.39 | (6) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0
% 34.32/5.39 | & $i(v1) & ? [v2: $i] : (ssList(v2) = 0 & app(v2, v1) = all_93_0 &
% 34.32/5.39 | app(v1, v2) = v0 & $i(v2))) & ((v0 = nil & ~ (all_93_0 = nil)) |
% 34.32/5.39 | (all_93_0 = nil & ~ (v0 = nil))))
% 34.32/5.39 |
% 34.32/5.39 | DELTA: instantiating (6) with fresh symbol all_97_0 gives:
% 34.32/5.39 | (7) ssList(all_97_0) = 0 & $i(all_97_0) & ? [v0: $i] : (ssList(v0) = 0 &
% 34.32/5.39 | $i(v0) & ? [v1: $i] : (ssList(v1) = 0 & app(v1, v0) = all_93_0 &
% 34.32/5.39 | app(v0, v1) = all_97_0 & $i(v1))) & ((all_97_0 = nil & ~ (all_93_0
% 34.32/5.39 | = nil)) | (all_93_0 = nil & ~ (all_97_0 = nil)))
% 34.32/5.39 |
% 34.32/5.39 | ALPHA: (7) implies:
% 34.32/5.39 | (8) (all_97_0 = nil & ~ (all_93_0 = nil)) | (all_93_0 = nil & ~ (all_97_0
% 34.32/5.39 | = nil))
% 34.32/5.39 | (9) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0
% 34.32/5.39 | & app(v1, v0) = all_93_0 & app(v0, v1) = all_97_0 & $i(v1)))
% 34.32/5.39 |
% 34.32/5.39 | DELTA: instantiating (9) with fresh symbol all_99_0 gives:
% 34.32/5.39 | (10) ssList(all_99_0) = 0 & $i(all_99_0) & ? [v0: $i] : (ssList(v0) = 0 &
% 34.32/5.39 | app(v0, all_99_0) = all_93_0 & app(all_99_0, v0) = all_97_0 &
% 34.32/5.39 | $i(v0))
% 34.32/5.39 |
% 34.32/5.39 | ALPHA: (10) implies:
% 34.32/5.39 | (11) $i(all_99_0)
% 34.32/5.39 | (12) ssList(all_99_0) = 0
% 34.32/5.39 | (13) ? [v0: $i] : (ssList(v0) = 0 & app(v0, all_99_0) = all_93_0 &
% 34.32/5.39 | app(all_99_0, v0) = all_97_0 & $i(v0))
% 34.32/5.39 |
% 34.32/5.39 | DELTA: instantiating (13) with fresh symbol all_101_0 gives:
% 34.32/5.39 | (14) ssList(all_101_0) = 0 & app(all_101_0, all_99_0) = all_93_0 &
% 34.32/5.39 | app(all_99_0, all_101_0) = all_97_0 & $i(all_101_0)
% 34.32/5.39 |
% 34.32/5.39 | ALPHA: (14) implies:
% 34.32/5.39 | (15) $i(all_101_0)
% 34.32/5.39 | (16) app(all_99_0, all_101_0) = all_97_0
% 34.32/5.39 | (17) app(all_101_0, all_99_0) = all_93_0
% 34.32/5.39 | (18) ssList(all_101_0) = 0
% 34.32/5.39 |
% 34.32/5.39 | GROUND_INST: instantiating (1) with all_99_0, simplifying with (11), (12)
% 34.32/5.39 | gives:
% 34.32/5.39 | (19) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_99_0, v0) = v1) | ~ $i(v0) |
% 34.32/5.39 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = nil) |
% 34.32/5.39 | (v0 = nil & all_99_0 = nil)) & ( ~ (v0 = nil) | ~ (all_99_0 =
% 34.32/5.39 | nil) | v1 = nil)))
% 34.32/5.40 |
% 34.32/5.40 | GROUND_INST: instantiating (1) with all_101_0, simplifying with (15), (18)
% 34.32/5.40 | gives:
% 34.32/5.40 | (20) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_101_0, v0) = v1) | ~ $i(v0)
% 34.32/5.40 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = nil) |
% 34.32/5.40 | (v0 = nil & all_101_0 = nil)) & ( ~ (v0 = nil) | ~ (all_101_0 =
% 34.32/5.40 | nil) | v1 = nil)))
% 34.32/5.40 |
% 34.32/5.40 | GROUND_INST: instantiating (20) with all_99_0, all_93_0, simplifying with
% 34.32/5.40 | (11), (17) gives:
% 34.32/5.40 | (21) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_99_0) = v0) | (( ~ (all_101_0
% 34.32/5.40 | = nil) | ~ (all_99_0 = nil) | all_93_0 = nil) & ( ~ (all_93_0 =
% 34.32/5.40 | nil) | (all_101_0 = nil & all_99_0 = nil)))
% 34.32/5.40 |
% 34.32/5.40 | GROUND_INST: instantiating (19) with all_101_0, all_97_0, simplifying with
% 34.32/5.40 | (15), (16) gives:
% 34.32/5.40 | (22) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) = v0) | (( ~
% 34.32/5.40 | (all_101_0 = nil) | ~ (all_99_0 = nil) | all_97_0 = nil) & ( ~
% 34.32/5.40 | (all_97_0 = nil) | (all_101_0 = nil & all_99_0 = nil)))
% 34.32/5.40 |
% 34.32/5.40 | BETA: splitting (8) gives:
% 34.32/5.40 |
% 34.32/5.40 | Case 1:
% 34.32/5.40 | |
% 34.32/5.40 | | (23) all_97_0 = nil & ~ (all_93_0 = nil)
% 34.32/5.40 | |
% 34.32/5.40 | | ALPHA: (23) implies:
% 34.32/5.40 | | (24) all_97_0 = nil
% 34.32/5.40 | | (25) ~ (all_93_0 = nil)
% 34.32/5.40 | |
% 34.32/5.40 | | REDUCE: (16), (24) imply:
% 34.32/5.40 | | (26) app(all_99_0, all_101_0) = nil
% 34.32/5.40 | |
% 34.32/5.40 | | BETA: splitting (22) gives:
% 34.32/5.40 | |
% 34.32/5.40 | | Case 1:
% 34.32/5.40 | | |
% 34.32/5.40 | | | (27) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) = v0)
% 34.32/5.40 | | |
% 34.32/5.40 | | | DELTA: instantiating (27) with fresh symbol all_396_0 gives:
% 34.32/5.40 | | | (28) ~ (all_396_0 = 0) & ssList(all_101_0) = all_396_0
% 34.32/5.40 | | |
% 34.32/5.40 | | | ALPHA: (28) implies:
% 34.32/5.40 | | | (29) ~ (all_396_0 = 0)
% 34.32/5.40 | | | (30) ssList(all_101_0) = all_396_0
% 34.32/5.40 | | |
% 34.32/5.40 | | | GROUND_INST: instantiating (3) with 0, all_396_0, all_101_0, simplifying
% 34.32/5.40 | | | with (18), (30) gives:
% 34.32/5.40 | | | (31) all_396_0 = 0
% 34.32/5.40 | | |
% 34.32/5.40 | | | REDUCE: (29), (31) imply:
% 34.32/5.40 | | | (32) $false
% 34.32/5.40 | | |
% 34.32/5.40 | | | CLOSE: (32) is inconsistent.
% 34.32/5.40 | | |
% 34.32/5.40 | | Case 2:
% 34.32/5.40 | | |
% 34.32/5.40 | | | (33) ( ~ (all_101_0 = nil) | ~ (all_99_0 = nil) | all_97_0 = nil) & (
% 34.32/5.40 | | | ~ (all_97_0 = nil) | (all_101_0 = nil & all_99_0 = nil))
% 34.32/5.40 | | |
% 34.32/5.40 | | | ALPHA: (33) implies:
% 34.32/5.40 | | | (34) ~ (all_97_0 = nil) | (all_101_0 = nil & all_99_0 = nil)
% 34.32/5.40 | | |
% 34.32/5.40 | | | BETA: splitting (34) gives:
% 34.32/5.40 | | |
% 34.32/5.40 | | | Case 1:
% 34.32/5.40 | | | |
% 34.32/5.40 | | | | (35) ~ (all_97_0 = nil)
% 34.32/5.40 | | | |
% 34.32/5.40 | | | | REDUCE: (24), (35) imply:
% 34.32/5.40 | | | | (36) $false
% 34.32/5.40 | | | |
% 34.32/5.40 | | | | CLOSE: (36) is inconsistent.
% 34.32/5.40 | | | |
% 34.32/5.40 | | | Case 2:
% 34.32/5.40 | | | |
% 34.32/5.40 | | | | (37) all_101_0 = nil & all_99_0 = nil
% 34.32/5.40 | | | |
% 34.32/5.40 | | | | ALPHA: (37) implies:
% 34.32/5.40 | | | | (38) all_99_0 = nil
% 34.32/5.40 | | | | (39) all_101_0 = nil
% 34.32/5.40 | | | |
% 34.32/5.40 | | | | REDUCE: (17), (38), (39) imply:
% 34.32/5.40 | | | | (40) app(nil, nil) = all_93_0
% 34.32/5.40 | | | |
% 34.32/5.40 | | | | REDUCE: (26), (38), (39) imply:
% 34.32/5.40 | | | | (41) app(nil, nil) = nil
% 34.32/5.40 | | | |
% 34.32/5.40 | | | | GROUND_INST: instantiating (4) with nil, all_93_0, nil, nil, simplifying
% 34.32/5.40 | | | | with (40), (41) gives:
% 34.32/5.40 | | | | (42) all_93_0 = nil
% 34.32/5.40 | | | |
% 34.32/5.40 | | | | REDUCE: (25), (42) imply:
% 34.32/5.40 | | | | (43) $false
% 34.32/5.40 | | | |
% 34.32/5.40 | | | | CLOSE: (43) is inconsistent.
% 34.32/5.40 | | | |
% 34.32/5.40 | | | End of split
% 34.32/5.40 | | |
% 34.32/5.40 | | End of split
% 34.32/5.40 | |
% 34.32/5.40 | Case 2:
% 34.32/5.40 | |
% 34.32/5.40 | | (44) all_93_0 = nil & ~ (all_97_0 = nil)
% 34.32/5.40 | |
% 34.32/5.40 | | ALPHA: (44) implies:
% 34.32/5.40 | | (45) all_93_0 = nil
% 34.32/5.40 | | (46) ~ (all_97_0 = nil)
% 34.32/5.40 | |
% 34.32/5.41 | | REDUCE: (17), (45) imply:
% 34.32/5.41 | | (47) app(all_101_0, all_99_0) = nil
% 34.32/5.41 | |
% 34.32/5.41 | | BETA: splitting (21) gives:
% 34.32/5.41 | |
% 34.32/5.41 | | Case 1:
% 34.32/5.41 | | |
% 34.32/5.41 | | | (48) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_99_0) = v0)
% 34.32/5.41 | | |
% 34.32/5.41 | | | DELTA: instantiating (48) with fresh symbol all_396_0 gives:
% 34.32/5.41 | | | (49) ~ (all_396_0 = 0) & ssList(all_99_0) = all_396_0
% 34.32/5.41 | | |
% 34.32/5.41 | | | ALPHA: (49) implies:
% 34.32/5.41 | | | (50) ~ (all_396_0 = 0)
% 34.32/5.41 | | | (51) ssList(all_99_0) = all_396_0
% 34.32/5.41 | | |
% 34.32/5.41 | | | GROUND_INST: instantiating (3) with 0, all_396_0, all_99_0, simplifying
% 34.32/5.41 | | | with (12), (51) gives:
% 34.32/5.41 | | | (52) all_396_0 = 0
% 34.32/5.41 | | |
% 34.32/5.41 | | | REDUCE: (50), (52) imply:
% 34.32/5.41 | | | (53) $false
% 34.32/5.41 | | |
% 34.32/5.41 | | | CLOSE: (53) is inconsistent.
% 34.32/5.41 | | |
% 34.32/5.41 | | Case 2:
% 34.32/5.41 | | |
% 34.32/5.41 | | | (54) ( ~ (all_101_0 = nil) | ~ (all_99_0 = nil) | all_93_0 = nil) & (
% 34.32/5.41 | | | ~ (all_93_0 = nil) | (all_101_0 = nil & all_99_0 = nil))
% 34.32/5.41 | | |
% 34.32/5.41 | | | ALPHA: (54) implies:
% 34.32/5.41 | | | (55) ~ (all_93_0 = nil) | (all_101_0 = nil & all_99_0 = nil)
% 34.32/5.41 | | |
% 34.32/5.41 | | | BETA: splitting (55) gives:
% 34.32/5.41 | | |
% 34.32/5.41 | | | Case 1:
% 34.32/5.41 | | | |
% 34.32/5.41 | | | | (56) ~ (all_93_0 = nil)
% 34.32/5.41 | | | |
% 34.32/5.41 | | | | REDUCE: (45), (56) imply:
% 34.32/5.41 | | | | (57) $false
% 34.32/5.41 | | | |
% 34.32/5.41 | | | | CLOSE: (57) is inconsistent.
% 34.32/5.41 | | | |
% 34.32/5.41 | | | Case 2:
% 34.32/5.41 | | | |
% 34.32/5.41 | | | | (58) all_101_0 = nil & all_99_0 = nil
% 34.32/5.41 | | | |
% 34.32/5.41 | | | | ALPHA: (58) implies:
% 34.32/5.41 | | | | (59) all_99_0 = nil
% 34.32/5.41 | | | | (60) all_101_0 = nil
% 34.32/5.41 | | | |
% 34.32/5.41 | | | | REDUCE: (47), (59), (60) imply:
% 34.32/5.41 | | | | (61) app(nil, nil) = nil
% 34.32/5.41 | | | |
% 34.32/5.41 | | | | REDUCE: (16), (59), (60) imply:
% 34.32/5.41 | | | | (62) app(nil, nil) = all_97_0
% 34.32/5.41 | | | |
% 34.32/5.41 | | | | GROUND_INST: instantiating (4) with nil, all_97_0, nil, nil, simplifying
% 34.32/5.41 | | | | with (61), (62) gives:
% 34.32/5.41 | | | | (63) all_97_0 = nil
% 34.32/5.41 | | | |
% 34.32/5.41 | | | | REDUCE: (46), (63) imply:
% 34.32/5.41 | | | | (64) $false
% 34.32/5.41 | | | |
% 34.32/5.41 | | | | CLOSE: (64) is inconsistent.
% 34.32/5.41 | | | |
% 34.32/5.41 | | | End of split
% 34.32/5.41 | | |
% 34.32/5.41 | | End of split
% 34.32/5.41 | |
% 34.32/5.41 | End of split
% 34.32/5.41 |
% 34.32/5.41 End of proof
% 34.32/5.41 % SZS output end Proof for theBenchmark
% 34.32/5.41
% 34.32/5.41 4770ms
%------------------------------------------------------------------------------