TSTP Solution File: SWC105+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC105+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 : n010.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 20:49:41 EDT 2023
% Result : Theorem 26.86s 4.31s
% Output : Proof 40.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC105+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 : n010.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 16:29:34 EDT 2023
% 0.13/0.34 % 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 ...
% 0.19/0.62 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 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 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 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 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 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 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 4.95/1.42 Prover 1: Preprocessing ...
% 4.95/1.42 Prover 4: Preprocessing ...
% 4.95/1.45 Prover 0: Preprocessing ...
% 4.95/1.45 Prover 5: Preprocessing ...
% 4.95/1.45 Prover 3: Preprocessing ...
% 4.95/1.45 Prover 2: Preprocessing ...
% 4.95/1.46 Prover 6: Preprocessing ...
% 13.06/2.57 Prover 2: Proving ...
% 13.06/2.60 Prover 1: Constructing countermodel ...
% 13.23/2.62 Prover 5: Constructing countermodel ...
% 15.12/2.76 Prover 6: Proving ...
% 15.12/2.81 Prover 3: Constructing countermodel ...
% 22.51/3.73 Prover 4: Constructing countermodel ...
% 22.94/3.91 Prover 0: Proving ...
% 26.86/4.31 Prover 3: proved (3677ms)
% 26.86/4.31
% 26.86/4.31 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.86/4.31
% 26.86/4.31 Prover 5: stopped
% 26.86/4.31 Prover 6: stopped
% 26.86/4.31 Prover 0: stopped
% 26.86/4.32 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 26.86/4.32 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 26.86/4.32 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 26.86/4.32 Prover 2: stopped
% 26.86/4.33 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 26.86/4.34 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 27.78/4.56 Prover 7: Preprocessing ...
% 28.92/4.62 Prover 11: Preprocessing ...
% 28.92/4.62 Prover 8: Preprocessing ...
% 28.92/4.63 Prover 10: Preprocessing ...
% 29.70/4.69 Prover 13: Preprocessing ...
% 30.60/4.82 Prover 7: Constructing countermodel ...
% 30.60/4.83 Prover 10: Constructing countermodel ...
% 32.27/5.11 Prover 13: Constructing countermodel ...
% 32.45/5.19 Prover 8: Warning: ignoring some quantifiers
% 32.45/5.20 Prover 8: Constructing countermodel ...
% 40.01/6.02 Prover 11: Constructing countermodel ...
% 40.18/6.09 Prover 1: Found proof (size 102)
% 40.18/6.09 Prover 1: proved (5462ms)
% 40.18/6.09 Prover 8: stopped
% 40.18/6.09 Prover 13: stopped
% 40.18/6.09 Prover 11: stopped
% 40.18/6.09 Prover 7: stopped
% 40.18/6.09 Prover 4: stopped
% 40.18/6.09 Prover 10: stopped
% 40.18/6.09
% 40.18/6.10 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 40.18/6.10
% 40.18/6.10 % SZS output start Proof for theBenchmark
% 40.18/6.11 Assumptions after simplification:
% 40.18/6.11 ---------------------------------
% 40.18/6.11
% 40.18/6.11 (ax15)
% 40.71/6.14 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 40.71/6.14 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 40.71/6.14 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 40.71/6.14
% 40.71/6.14 (ax17)
% 40.71/6.14 ssList(nil) = 0 & $i(nil)
% 40.71/6.14
% 40.71/6.14 (ax48)
% 40.71/6.14 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : (v1 = v0 | ~
% 40.71/6.14 (rearsegP(v0, v1) = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] :
% 40.71/6.14 (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))))
% 40.71/6.14
% 40.71/6.14 (ax6)
% 40.71/6.14 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 40.71/6.14 ( ~ (rearsegP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 40.71/6.14 ssList(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : (ssList(v3) = 0 &
% 40.71/6.14 app(v3, v1) = v0 & $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (app(v3,
% 40.71/6.14 v1) = v0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v3)
% 40.71/6.14 = v4))))))
% 40.71/6.14
% 40.71/6.14 (ax83)
% 40.71/6.14 $i(nil) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : !
% 40.71/6.14 [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0)
% 40.71/6.14 & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = nil)) & ( ~ (v1
% 40.71/6.14 = nil) | ~ (v0 = nil) | v2 = nil))))
% 40.71/6.14
% 40.71/6.14 (co1)
% 40.71/6.14 $i(nil) & ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 40.71/6.14 $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] : (rearsegP(v2, v0) = v4
% 40.71/6.14 & ssList(v2) = 0 & neq(v2, nil) = v3 & $i(v2) & ((v4 = 0 & v1 = 0) | (v2 =
% 40.71/6.14 nil & v0 = nil)) & ((v3 = 0 & ( ~ (v4 = 0) | ~ (v1 = 0))) | (v2 = nil
% 40.71/6.14 & ~ (v0 = nil)))))
% 40.71/6.14
% 40.71/6.14 (function-axioms)
% 40.71/6.15 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 40.71/6.15 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 40.71/6.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 40.71/6.15 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 40.71/6.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 40.71/6.15 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 40.71/6.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 40.71/6.15 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 40.71/6.15 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 40.71/6.15 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 40.71/6.15 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 40.71/6.15 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 40.71/6.15 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 40.71/6.15 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 40.71/6.15 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 40.71/6.15 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 40.71/6.15 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 40.71/6.15 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 40.71/6.15 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 40.71/6.15 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 40.71/6.15 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 40.71/6.15 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 40.71/6.15 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 40.71/6.15 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 40.71/6.15 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 40.71/6.15 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 40.71/6.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 40.71/6.15 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 40.71/6.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 40.71/6.15 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 40.71/6.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 40.71/6.15 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 40.71/6.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 40.71/6.15 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 40.71/6.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 40.71/6.15 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 40.71/6.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 40.71/6.15 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 40.71/6.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 40.71/6.15 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 40.71/6.15 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 40.71/6.15 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 40.71/6.15 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 40.71/6.15
% 40.71/6.15 Further assumptions not needed in the proof:
% 40.71/6.15 --------------------------------------------
% 40.71/6.15 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 40.71/6.15 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34,
% 40.71/6.15 ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46,
% 40.71/6.15 ax47, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59,
% 40.71/6.15 ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71,
% 40.71/6.15 ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax84,
% 40.71/6.15 ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 40.71/6.15
% 40.71/6.15 Those formulas are unsatisfiable:
% 40.71/6.15 ---------------------------------
% 40.71/6.15
% 40.71/6.15 Begin of proof
% 40.71/6.15 |
% 40.71/6.15 | ALPHA: (ax17) implies:
% 40.71/6.15 | (1) ssList(nil) = 0
% 40.71/6.15 |
% 40.71/6.15 | ALPHA: (ax83) implies:
% 40.71/6.16 | (2) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2:
% 40.71/6.16 | $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 =
% 40.71/6.16 | 0) & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 =
% 40.71/6.16 | nil)) & ( ~ (v1 = nil) | ~ (v0 = nil) | v2 = nil))))
% 40.71/6.16 |
% 40.71/6.16 | ALPHA: (co1) implies:
% 40.71/6.16 | (3) $i(nil)
% 40.71/6.16 | (4) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 40.71/6.16 | $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] : (rearsegP(v2,
% 40.71/6.16 | v0) = v4 & ssList(v2) = 0 & neq(v2, nil) = v3 & $i(v2) & ((v4 = 0
% 40.71/6.16 | & v1 = 0) | (v2 = nil & v0 = nil)) & ((v3 = 0 & ( ~ (v4 = 0) |
% 40.71/6.16 | ~ (v1 = 0))) | (v2 = nil & ~ (v0 = nil)))))
% 40.71/6.16 |
% 40.71/6.16 | ALPHA: (function-axioms) implies:
% 40.71/6.16 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 40.71/6.16 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 40.71/6.16 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 40.71/6.16 | ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0))
% 40.71/6.16 |
% 40.71/6.16 | DELTA: instantiating (4) with fresh symbols all_93_0, all_93_1 gives:
% 40.71/6.16 | (7) ssList(all_93_1) = 0 & neq(all_93_1, nil) = all_93_0 & $i(all_93_1) &
% 40.71/6.16 | ? [v0: $i] : ? [v1: any] : ? [v2: any] : (rearsegP(v0, all_93_1) = v2
% 40.71/6.16 | & ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ((v2 = 0 & all_93_0 =
% 40.71/6.16 | 0) | (v0 = nil & all_93_1 = nil)) & ((v1 = 0 & ( ~ (v2 = 0) | ~
% 40.71/6.16 | (all_93_0 = 0))) | (v0 = nil & ~ (all_93_1 = nil))))
% 40.71/6.16 |
% 40.71/6.16 | ALPHA: (7) implies:
% 40.71/6.16 | (8) $i(all_93_1)
% 40.71/6.16 | (9) neq(all_93_1, nil) = all_93_0
% 40.71/6.16 | (10) ssList(all_93_1) = 0
% 40.71/6.16 | (11) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (rearsegP(v0, all_93_1) =
% 40.71/6.16 | v2 & ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ((v2 = 0 &
% 40.71/6.16 | all_93_0 = 0) | (v0 = nil & all_93_1 = nil)) & ((v1 = 0 & ( ~
% 40.71/6.16 | (v2 = 0) | ~ (all_93_0 = 0))) | (v0 = nil & ~ (all_93_1 =
% 40.71/6.16 | nil))))
% 40.71/6.16 |
% 40.71/6.16 | DELTA: instantiating (11) with fresh symbols all_97_0, all_97_1, all_97_2
% 40.71/6.16 | gives:
% 40.71/6.16 | (12) rearsegP(all_97_2, all_93_1) = all_97_0 & ssList(all_97_2) = 0 &
% 40.71/6.16 | neq(all_97_2, nil) = all_97_1 & $i(all_97_2) & ((all_97_0 = 0 &
% 40.71/6.16 | all_93_0 = 0) | (all_97_2 = nil & all_93_1 = nil)) & ((all_97_1 =
% 40.71/6.16 | 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0))) | (all_97_2 = nil &
% 40.71/6.16 | ~ (all_93_1 = nil)))
% 40.71/6.16 |
% 40.71/6.16 | ALPHA: (12) implies:
% 40.71/6.16 | (13) $i(all_97_2)
% 40.71/6.16 | (14) neq(all_97_2, nil) = all_97_1
% 40.71/6.16 | (15) ssList(all_97_2) = 0
% 40.71/6.16 | (16) rearsegP(all_97_2, all_93_1) = all_97_0
% 40.71/6.16 | (17) (all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0))) | (all_97_2 =
% 40.71/6.16 | nil & ~ (all_93_1 = nil))
% 40.71/6.16 | (18) (all_97_0 = 0 & all_93_0 = 0) | (all_97_2 = nil & all_93_1 = nil)
% 40.71/6.16 |
% 40.71/6.16 | GROUND_INST: instantiating (ax48) with nil, simplifying with (1), (3) gives:
% 40.71/6.16 | (19) ! [v0: $i] : (v0 = nil | ~ (rearsegP(nil, v0) = 0) | ~ $i(v0) | ?
% 40.71/6.16 | [v1: any] : ? [v2: any] : (rearsegP(v0, nil) = v2 & ssList(v0) = v1
% 40.71/6.16 | & ( ~ (v2 = 0) | ~ (v1 = 0))))
% 40.71/6.16 |
% 40.71/6.16 | GROUND_INST: instantiating (ax15) with all_93_1, simplifying with (8), (10)
% 40.71/6.16 | gives:
% 40.71/6.17 | (20) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_93_1, v0) = v1) | ~ $i(v0)
% 40.71/6.17 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 40.71/6.17 | ~ (v0 = all_93_1)) & (v1 = 0 | v0 = all_93_1)))
% 40.71/6.17 |
% 40.71/6.17 | GROUND_INST: instantiating (ax6) with all_97_2, simplifying with (13), (15)
% 40.71/6.17 | gives:
% 40.71/6.17 | (21) ! [v0: $i] : ! [v1: any] : ( ~ (rearsegP(all_97_2, v0) = v1) | ~
% 40.71/6.17 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 =
% 40.71/6.17 | 0) | ? [v2: $i] : (ssList(v2) = 0 & app(v2, v0) = all_97_2 &
% 40.71/6.17 | $i(v2))) & (v1 = 0 | ! [v2: $i] : ( ~ (app(v2, v0) =
% 40.71/6.17 | all_97_2) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 40.71/6.17 | ssList(v2) = v3)))))
% 40.71/6.17 |
% 40.71/6.17 | GROUND_INST: instantiating (21) with all_93_1, all_97_0, simplifying with (8),
% 40.71/6.17 | (16) gives:
% 40.71/6.17 | (22) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ (all_97_0
% 40.71/6.17 | = 0) | ? [v0: $i] : (ssList(v0) = 0 & app(v0, all_93_1) =
% 40.71/6.17 | all_97_2 & $i(v0))) & (all_97_0 = 0 | ! [v0: $i] : ( ~ (app(v0,
% 40.71/6.17 | all_93_1) = all_97_2) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 =
% 40.71/6.17 | 0) & ssList(v0) = v1))))
% 40.71/6.17 |
% 40.71/6.17 | GROUND_INST: instantiating (20) with nil, all_93_0, simplifying with (3), (9)
% 40.71/6.17 | gives:
% 40.71/6.17 | (23) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_93_0 = 0)
% 40.71/6.17 | | ~ (all_93_1 = nil)) & (all_93_0 = 0 | all_93_1 = nil))
% 40.71/6.17 |
% 40.71/6.17 | BETA: splitting (18) gives:
% 40.71/6.17 |
% 40.71/6.17 | Case 1:
% 40.71/6.17 | |
% 40.71/6.17 | | (24) all_97_0 = 0 & all_93_0 = 0
% 40.71/6.17 | |
% 40.71/6.17 | | ALPHA: (24) implies:
% 40.71/6.17 | | (25) all_93_0 = 0
% 40.71/6.17 | | (26) all_97_0 = 0
% 40.71/6.17 | |
% 40.71/6.17 | | REDUCE: (16), (26) imply:
% 40.71/6.17 | | (27) rearsegP(all_97_2, all_93_1) = 0
% 40.71/6.17 | |
% 40.71/6.17 | | BETA: splitting (17) gives:
% 40.71/6.17 | |
% 40.71/6.17 | | Case 1:
% 40.71/6.17 | | |
% 40.71/6.17 | | | (28) all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0))
% 40.71/6.17 | | |
% 40.71/6.17 | | | ALPHA: (28) implies:
% 40.71/6.17 | | | (29) ~ (all_97_0 = 0) | ~ (all_93_0 = 0)
% 40.71/6.17 | | |
% 40.71/6.17 | | | BETA: splitting (29) gives:
% 40.71/6.17 | | |
% 40.71/6.17 | | | Case 1:
% 40.71/6.17 | | | |
% 40.71/6.17 | | | | (30) ~ (all_97_0 = 0)
% 40.71/6.17 | | | |
% 40.71/6.17 | | | | REDUCE: (26), (30) imply:
% 40.71/6.17 | | | | (31) $false
% 40.71/6.17 | | | |
% 40.71/6.17 | | | | CLOSE: (31) is inconsistent.
% 40.71/6.17 | | | |
% 40.71/6.17 | | | Case 2:
% 40.71/6.17 | | | |
% 40.71/6.17 | | | | (32) ~ (all_93_0 = 0)
% 40.71/6.17 | | | |
% 40.71/6.17 | | | | REDUCE: (25), (32) imply:
% 40.71/6.17 | | | | (33) $false
% 40.71/6.17 | | | |
% 40.71/6.17 | | | | CLOSE: (33) is inconsistent.
% 40.71/6.17 | | | |
% 40.71/6.17 | | | End of split
% 40.71/6.17 | | |
% 40.71/6.17 | | Case 2:
% 40.71/6.17 | | |
% 40.98/6.17 | | | (34) all_97_2 = nil & ~ (all_93_1 = nil)
% 40.98/6.17 | | |
% 40.98/6.17 | | | ALPHA: (34) implies:
% 40.98/6.17 | | | (35) all_97_2 = nil
% 40.98/6.17 | | | (36) ~ (all_93_1 = nil)
% 40.98/6.17 | | |
% 40.98/6.17 | | | REDUCE: (27), (35) imply:
% 40.98/6.17 | | | (37) rearsegP(nil, all_93_1) = 0
% 40.98/6.17 | | |
% 40.98/6.17 | | | BETA: splitting (22) gives:
% 40.98/6.17 | | |
% 40.98/6.17 | | | Case 1:
% 40.98/6.17 | | | |
% 40.98/6.17 | | | | (38) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0)
% 40.98/6.17 | | | |
% 40.98/6.17 | | | | DELTA: instantiating (38) with fresh symbol all_314_0 gives:
% 40.98/6.17 | | | | (39) ~ (all_314_0 = 0) & ssList(all_93_1) = all_314_0
% 40.98/6.17 | | | |
% 40.98/6.17 | | | | ALPHA: (39) implies:
% 40.98/6.17 | | | | (40) ~ (all_314_0 = 0)
% 40.98/6.17 | | | | (41) ssList(all_93_1) = all_314_0
% 40.98/6.17 | | | |
% 40.98/6.17 | | | | GROUND_INST: instantiating (5) with 0, all_314_0, all_93_1, simplifying
% 40.98/6.17 | | | | with (10), (41) gives:
% 40.98/6.17 | | | | (42) all_314_0 = 0
% 40.98/6.17 | | | |
% 40.98/6.17 | | | | REDUCE: (40), (42) imply:
% 40.98/6.17 | | | | (43) $false
% 40.98/6.17 | | | |
% 40.98/6.17 | | | | CLOSE: (43) is inconsistent.
% 40.98/6.17 | | | |
% 40.98/6.17 | | | Case 2:
% 40.98/6.17 | | | |
% 40.98/6.18 | | | | (44) ( ~ (all_97_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 & app(v0,
% 40.98/6.18 | | | | all_93_1) = all_97_2 & $i(v0))) & (all_97_0 = 0 | ! [v0:
% 40.98/6.18 | | | | $i] : ( ~ (app(v0, all_93_1) = all_97_2) | ~ $i(v0) | ?
% 40.98/6.18 | | | | [v1: int] : ( ~ (v1 = 0) & ssList(v0) = v1)))
% 40.98/6.18 | | | |
% 40.98/6.18 | | | | ALPHA: (44) implies:
% 40.98/6.18 | | | | (45) ~ (all_97_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 & app(v0,
% 40.98/6.18 | | | | all_93_1) = all_97_2 & $i(v0))
% 40.98/6.18 | | | |
% 40.98/6.18 | | | | BETA: splitting (45) gives:
% 40.98/6.18 | | | |
% 40.98/6.18 | | | | Case 1:
% 40.98/6.18 | | | | |
% 40.98/6.18 | | | | | (46) ~ (all_97_0 = 0)
% 40.98/6.18 | | | | |
% 40.98/6.18 | | | | | REDUCE: (26), (46) imply:
% 40.98/6.18 | | | | | (47) $false
% 40.98/6.18 | | | | |
% 40.98/6.18 | | | | | CLOSE: (47) is inconsistent.
% 40.98/6.18 | | | | |
% 40.98/6.18 | | | | Case 2:
% 40.98/6.18 | | | | |
% 40.98/6.18 | | | | | (48) ? [v0: $i] : (ssList(v0) = 0 & app(v0, all_93_1) = all_97_2 &
% 40.98/6.18 | | | | | $i(v0))
% 40.98/6.18 | | | | |
% 40.98/6.18 | | | | | DELTA: instantiating (48) with fresh symbol all_320_0 gives:
% 40.98/6.18 | | | | | (49) ssList(all_320_0) = 0 & app(all_320_0, all_93_1) = all_97_2 &
% 40.98/6.18 | | | | | $i(all_320_0)
% 40.98/6.18 | | | | |
% 40.98/6.18 | | | | | ALPHA: (49) implies:
% 40.98/6.18 | | | | | (50) $i(all_320_0)
% 40.98/6.18 | | | | | (51) app(all_320_0, all_93_1) = all_97_2
% 40.98/6.18 | | | | | (52) ssList(all_320_0) = 0
% 40.98/6.18 | | | | |
% 40.98/6.18 | | | | | REDUCE: (35), (51) imply:
% 40.98/6.18 | | | | | (53) app(all_320_0, all_93_1) = nil
% 40.98/6.18 | | | | |
% 40.98/6.18 | | | | | GROUND_INST: instantiating (2) with all_320_0, simplifying with (50),
% 40.98/6.18 | | | | | (52) gives:
% 40.98/6.18 | | | | | (54) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_320_0, v0) = v1) | ~
% 40.98/6.18 | | | | | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | ((
% 40.98/6.18 | | | | | ~ (v1 = nil) | (v0 = nil & all_320_0 = nil)) & ( ~ (v0 =
% 40.98/6.18 | | | | | nil) | ~ (all_320_0 = nil) | v1 = nil)))
% 40.98/6.18 | | | | |
% 40.98/6.18 | | | | | GROUND_INST: instantiating (19) with all_93_1, simplifying with (8),
% 40.98/6.18 | | | | | (37) gives:
% 40.98/6.18 | | | | | (55) all_93_1 = nil | ? [v0: any] : ? [v1: any] :
% 40.98/6.18 | | | | | (rearsegP(all_93_1, nil) = v1 & ssList(all_93_1) = v0 & ( ~
% 40.98/6.18 | | | | | (v1 = 0) | ~ (v0 = 0)))
% 40.98/6.18 | | | | |
% 40.98/6.18 | | | | | GROUND_INST: instantiating (54) with all_93_1, nil, simplifying with
% 40.98/6.18 | | | | | (8), (53) gives:
% 40.98/6.18 | | | | | (56) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) |
% 40.98/6.18 | | | | | (all_320_0 = nil & all_93_1 = nil)
% 40.98/6.18 | | | | |
% 40.98/6.18 | | | | | BETA: splitting (56) gives:
% 40.98/6.18 | | | | |
% 40.98/6.18 | | | | | Case 1:
% 40.98/6.18 | | | | | |
% 40.98/6.18 | | | | | | (57) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0)
% 40.98/6.18 | | | | | |
% 40.98/6.18 | | | | | | DELTA: instantiating (57) with fresh symbol all_505_0 gives:
% 40.98/6.18 | | | | | | (58) ~ (all_505_0 = 0) & ssList(all_93_1) = all_505_0
% 40.98/6.18 | | | | | |
% 40.98/6.18 | | | | | | ALPHA: (58) implies:
% 40.98/6.18 | | | | | | (59) ~ (all_505_0 = 0)
% 40.98/6.18 | | | | | | (60) ssList(all_93_1) = all_505_0
% 40.98/6.18 | | | | | |
% 40.98/6.18 | | | | | | DELTA: instantiating (57) with fresh symbol all_509_0 gives:
% 40.98/6.18 | | | | | | (61) ~ (all_509_0 = 0) & ssList(all_93_1) = all_509_0
% 40.98/6.18 | | | | | |
% 40.98/6.18 | | | | | | ALPHA: (61) implies:
% 40.98/6.18 | | | | | | (62) ssList(all_93_1) = all_509_0
% 40.98/6.18 | | | | | |
% 40.98/6.18 | | | | | | BETA: splitting (55) gives:
% 40.98/6.18 | | | | | |
% 40.98/6.18 | | | | | | Case 1:
% 40.98/6.18 | | | | | | |
% 40.98/6.18 | | | | | | | (63) all_93_1 = nil
% 40.98/6.18 | | | | | | |
% 40.98/6.18 | | | | | | | REDUCE: (36), (63) imply:
% 40.98/6.18 | | | | | | | (64) $false
% 40.98/6.18 | | | | | | |
% 40.98/6.18 | | | | | | | CLOSE: (64) is inconsistent.
% 40.98/6.18 | | | | | | |
% 40.98/6.18 | | | | | | Case 2:
% 40.98/6.18 | | | | | | |
% 40.98/6.18 | | | | | | | (65) ? [v0: any] : ? [v1: any] : (rearsegP(all_93_1, nil) =
% 40.98/6.18 | | | | | | | v1 & ssList(all_93_1) = v0 & ( ~ (v1 = 0) | ~ (v0 =
% 40.98/6.18 | | | | | | | 0)))
% 40.98/6.18 | | | | | | |
% 40.98/6.18 | | | | | | | DELTA: instantiating (65) with fresh symbols all_522_0, all_522_1
% 40.98/6.18 | | | | | | | gives:
% 40.98/6.18 | | | | | | | (66) rearsegP(all_93_1, nil) = all_522_0 & ssList(all_93_1) =
% 40.98/6.18 | | | | | | | all_522_1 & ( ~ (all_522_0 = 0) | ~ (all_522_1 = 0))
% 40.98/6.18 | | | | | | |
% 40.98/6.18 | | | | | | | ALPHA: (66) implies:
% 40.98/6.18 | | | | | | | (67) ssList(all_93_1) = all_522_1
% 40.98/6.18 | | | | | | |
% 40.98/6.18 | | | | | | | DELTA: instantiating (57) with fresh symbol all_528_0 gives:
% 40.98/6.18 | | | | | | | (68) ~ (all_528_0 = 0) & ssList(all_93_1) = all_528_0
% 40.98/6.18 | | | | | | |
% 40.98/6.18 | | | | | | | ALPHA: (68) implies:
% 40.98/6.18 | | | | | | | (69) ssList(all_93_1) = all_528_0
% 40.98/6.18 | | | | | | |
% 40.98/6.18 | | | | | | | GROUND_INST: instantiating (5) with 0, all_522_1, all_93_1,
% 40.98/6.18 | | | | | | | simplifying with (10), (67) gives:
% 40.98/6.18 | | | | | | | (70) all_522_1 = 0
% 40.98/6.18 | | | | | | |
% 40.98/6.18 | | | | | | | GROUND_INST: instantiating (5) with all_509_0, all_522_1,
% 40.98/6.18 | | | | | | | all_93_1, simplifying with (62), (67) gives:
% 40.98/6.18 | | | | | | | (71) all_522_1 = all_509_0
% 40.98/6.18 | | | | | | |
% 40.98/6.18 | | | | | | | GROUND_INST: instantiating (5) with all_509_0, all_528_0,
% 40.98/6.18 | | | | | | | all_93_1, simplifying with (62), (69) gives:
% 40.98/6.18 | | | | | | | (72) all_528_0 = all_509_0
% 40.98/6.18 | | | | | | |
% 40.98/6.19 | | | | | | | GROUND_INST: instantiating (5) with all_505_0, all_528_0,
% 40.98/6.19 | | | | | | | all_93_1, simplifying with (60), (69) gives:
% 40.98/6.19 | | | | | | | (73) all_528_0 = all_505_0
% 40.98/6.19 | | | | | | |
% 40.98/6.19 | | | | | | | COMBINE_EQS: (72), (73) imply:
% 40.98/6.19 | | | | | | | (74) all_509_0 = all_505_0
% 40.98/6.19 | | | | | | |
% 40.98/6.19 | | | | | | | SIMP: (74) implies:
% 40.98/6.19 | | | | | | | (75) all_509_0 = all_505_0
% 40.98/6.19 | | | | | | |
% 40.98/6.19 | | | | | | | COMBINE_EQS: (70), (71) imply:
% 40.98/6.19 | | | | | | | (76) all_509_0 = 0
% 40.98/6.19 | | | | | | |
% 40.98/6.19 | | | | | | | SIMP: (76) implies:
% 40.98/6.19 | | | | | | | (77) all_509_0 = 0
% 40.98/6.19 | | | | | | |
% 40.98/6.19 | | | | | | | COMBINE_EQS: (75), (77) imply:
% 40.98/6.19 | | | | | | | (78) all_505_0 = 0
% 40.98/6.19 | | | | | | |
% 40.98/6.19 | | | | | | | REDUCE: (59), (78) imply:
% 40.98/6.19 | | | | | | | (79) $false
% 40.98/6.19 | | | | | | |
% 40.98/6.19 | | | | | | | CLOSE: (79) is inconsistent.
% 40.98/6.19 | | | | | | |
% 40.98/6.19 | | | | | | End of split
% 40.98/6.19 | | | | | |
% 40.98/6.19 | | | | | Case 2:
% 40.98/6.19 | | | | | |
% 40.98/6.19 | | | | | | (80) all_320_0 = nil & all_93_1 = nil
% 40.98/6.19 | | | | | |
% 40.98/6.19 | | | | | | ALPHA: (80) implies:
% 40.98/6.19 | | | | | | (81) all_93_1 = nil
% 40.98/6.19 | | | | | |
% 40.98/6.19 | | | | | | REDUCE: (36), (81) imply:
% 40.98/6.19 | | | | | | (82) $false
% 40.98/6.19 | | | | | |
% 40.98/6.19 | | | | | | CLOSE: (82) is inconsistent.
% 40.98/6.19 | | | | | |
% 40.98/6.19 | | | | | End of split
% 40.98/6.19 | | | | |
% 40.98/6.19 | | | | End of split
% 40.98/6.19 | | | |
% 40.98/6.19 | | | End of split
% 40.98/6.19 | | |
% 40.98/6.19 | | End of split
% 40.98/6.19 | |
% 40.98/6.19 | Case 2:
% 40.98/6.19 | |
% 40.98/6.19 | | (83) all_97_2 = nil & all_93_1 = nil
% 40.98/6.19 | |
% 40.98/6.19 | | ALPHA: (83) implies:
% 40.98/6.19 | | (84) all_93_1 = nil
% 40.98/6.19 | | (85) all_97_2 = nil
% 40.98/6.19 | |
% 40.98/6.19 | | REDUCE: (14), (85) imply:
% 40.98/6.19 | | (86) neq(nil, nil) = all_97_1
% 40.98/6.19 | |
% 40.98/6.19 | | REDUCE: (9), (84) imply:
% 40.98/6.19 | | (87) neq(nil, nil) = all_93_0
% 40.98/6.19 | |
% 40.98/6.19 | | BETA: splitting (17) gives:
% 40.98/6.19 | |
% 40.98/6.19 | | Case 1:
% 40.98/6.19 | | |
% 40.98/6.19 | | | (88) all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0))
% 40.98/6.19 | | |
% 40.98/6.19 | | | ALPHA: (88) implies:
% 40.98/6.19 | | | (89) all_97_1 = 0
% 40.98/6.19 | | |
% 40.98/6.19 | | | REDUCE: (86), (89) imply:
% 40.98/6.19 | | | (90) neq(nil, nil) = 0
% 40.98/6.19 | | |
% 40.98/6.19 | | | BETA: splitting (23) gives:
% 40.98/6.19 | | |
% 40.98/6.19 | | | Case 1:
% 40.98/6.19 | | | |
% 40.98/6.19 | | | | (91) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 40.98/6.19 | | | |
% 40.98/6.19 | | | | DELTA: instantiating (91) with fresh symbol all_306_0 gives:
% 40.98/6.19 | | | | (92) ~ (all_306_0 = 0) & ssList(nil) = all_306_0
% 40.98/6.19 | | | |
% 40.98/6.19 | | | | ALPHA: (92) implies:
% 40.98/6.19 | | | | (93) ~ (all_306_0 = 0)
% 40.98/6.19 | | | | (94) ssList(nil) = all_306_0
% 40.98/6.19 | | | |
% 40.98/6.19 | | | | DELTA: instantiating (91) with fresh symbol all_311_0 gives:
% 40.98/6.19 | | | | (95) ~ (all_311_0 = 0) & ssList(nil) = all_311_0
% 40.98/6.19 | | | |
% 40.98/6.19 | | | | ALPHA: (95) implies:
% 40.98/6.19 | | | | (96) ssList(nil) = all_311_0
% 40.98/6.19 | | | |
% 40.98/6.19 | | | | GROUND_INST: instantiating (5) with 0, all_311_0, nil, simplifying with
% 40.98/6.19 | | | | (1), (96) gives:
% 40.98/6.19 | | | | (97) all_311_0 = 0
% 40.98/6.19 | | | |
% 40.98/6.19 | | | | GROUND_INST: instantiating (5) with all_306_0, all_311_0, nil,
% 40.98/6.19 | | | | simplifying with (94), (96) gives:
% 40.98/6.19 | | | | (98) all_311_0 = all_306_0
% 40.98/6.19 | | | |
% 40.98/6.19 | | | | COMBINE_EQS: (97), (98) imply:
% 40.98/6.19 | | | | (99) all_306_0 = 0
% 40.98/6.19 | | | |
% 40.98/6.19 | | | | REDUCE: (93), (99) imply:
% 40.98/6.19 | | | | (100) $false
% 40.98/6.19 | | | |
% 40.98/6.19 | | | | CLOSE: (100) is inconsistent.
% 40.98/6.19 | | | |
% 40.98/6.19 | | | Case 2:
% 40.98/6.19 | | | |
% 40.98/6.19 | | | | (101) ( ~ (all_93_0 = 0) | ~ (all_93_1 = nil)) & (all_93_0 = 0 |
% 40.98/6.19 | | | | all_93_1 = nil)
% 40.98/6.19 | | | |
% 40.98/6.19 | | | | ALPHA: (101) implies:
% 40.98/6.19 | | | | (102) ~ (all_93_0 = 0) | ~ (all_93_1 = nil)
% 40.98/6.19 | | | |
% 40.98/6.19 | | | | BETA: splitting (102) gives:
% 40.98/6.19 | | | |
% 40.98/6.19 | | | | Case 1:
% 40.98/6.19 | | | | |
% 40.98/6.19 | | | | | (103) ~ (all_93_1 = nil)
% 40.98/6.19 | | | | |
% 40.98/6.19 | | | | | REDUCE: (84), (103) imply:
% 40.98/6.19 | | | | | (104) $false
% 40.98/6.19 | | | | |
% 40.98/6.19 | | | | | CLOSE: (104) is inconsistent.
% 40.98/6.19 | | | | |
% 40.98/6.19 | | | | Case 2:
% 40.98/6.19 | | | | |
% 40.98/6.19 | | | | | (105) ~ (all_93_0 = 0)
% 40.98/6.19 | | | | |
% 40.98/6.19 | | | | | GROUND_INST: instantiating (6) with 0, all_93_0, nil, nil, simplifying
% 40.98/6.19 | | | | | with (87), (90) gives:
% 40.98/6.19 | | | | | (106) all_93_0 = 0
% 40.98/6.19 | | | | |
% 40.98/6.19 | | | | | REDUCE: (105), (106) imply:
% 40.98/6.19 | | | | | (107) $false
% 40.98/6.19 | | | | |
% 40.98/6.19 | | | | | CLOSE: (107) is inconsistent.
% 40.98/6.19 | | | | |
% 40.98/6.19 | | | | End of split
% 40.98/6.19 | | | |
% 40.98/6.19 | | | End of split
% 40.98/6.19 | | |
% 40.98/6.19 | | Case 2:
% 40.98/6.19 | | |
% 40.98/6.19 | | | (108) all_97_2 = nil & ~ (all_93_1 = nil)
% 40.98/6.19 | | |
% 40.98/6.19 | | | ALPHA: (108) implies:
% 40.98/6.19 | | | (109) ~ (all_93_1 = nil)
% 40.98/6.19 | | |
% 40.98/6.19 | | | REDUCE: (84), (109) imply:
% 40.98/6.19 | | | (110) $false
% 40.98/6.19 | | |
% 40.98/6.19 | | | CLOSE: (110) is inconsistent.
% 40.98/6.19 | | |
% 40.98/6.19 | | End of split
% 40.98/6.19 | |
% 40.98/6.19 | End of split
% 40.98/6.19 |
% 40.98/6.19 End of proof
% 40.98/6.19 % SZS output end Proof for theBenchmark
% 40.98/6.19
% 40.98/6.19 5590ms
%------------------------------------------------------------------------------