TSTP Solution File: SWC016+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC016+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 : n002.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 20:49:11 EDT 2023
% Result : Theorem 32.14s 5.29s
% Output : Proof 69.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC016+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n002.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 16:08:49 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/sandbox2/benchmark/theBenchmark.p ...
% 0.20/0.65 Running up to 7 provers in parallel.
% 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 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 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 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 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
% 6.20/1.67 Prover 1: Preprocessing ...
% 6.20/1.67 Prover 4: Preprocessing ...
% 6.36/1.72 Prover 2: Preprocessing ...
% 6.36/1.72 Prover 5: Preprocessing ...
% 6.36/1.72 Prover 6: Preprocessing ...
% 6.36/1.72 Prover 3: Preprocessing ...
% 6.61/1.73 Prover 0: Preprocessing ...
% 19.74/3.51 Prover 2: Proving ...
% 21.04/3.70 Prover 5: Constructing countermodel ...
% 21.04/3.70 Prover 3: Constructing countermodel ...
% 21.04/3.71 Prover 1: Constructing countermodel ...
% 22.01/3.90 Prover 6: Proving ...
% 30.21/4.98 Prover 4: Constructing countermodel ...
% 32.14/5.28 Prover 3: proved (4617ms)
% 32.14/5.29
% 32.14/5.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 32.14/5.29
% 32.14/5.29 Prover 5: stopped
% 32.14/5.29 Prover 2: stopped
% 32.14/5.29 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 32.14/5.29 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 32.14/5.30 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 32.14/5.33 Prover 6: stopped
% 32.14/5.34 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 33.99/5.44 Prover 0: Proving ...
% 33.99/5.46 Prover 0: stopped
% 33.99/5.47 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 35.40/5.65 Prover 10: Preprocessing ...
% 36.57/5.78 Prover 8: Preprocessing ...
% 36.57/5.78 Prover 7: Preprocessing ...
% 36.57/5.79 Prover 11: Preprocessing ...
% 36.57/5.82 Prover 13: Preprocessing ...
% 37.61/6.02 Prover 10: Constructing countermodel ...
% 40.31/6.30 Prover 7: Constructing countermodel ...
% 41.60/6.47 Prover 13: Constructing countermodel ...
% 41.60/6.48 Prover 8: Warning: ignoring some quantifiers
% 41.60/6.55 Prover 8: Constructing countermodel ...
% 49.91/7.53 Prover 11: Constructing countermodel ...
% 68.58/10.00 Prover 1: Found proof (size 87)
% 68.58/10.00 Prover 1: proved (9330ms)
% 68.58/10.00 Prover 7: stopped
% 68.58/10.00 Prover 11: stopped
% 68.58/10.00 Prover 13: stopped
% 68.58/10.00 Prover 10: stopped
% 68.58/10.00 Prover 8: stopped
% 68.58/10.00 Prover 4: stopped
% 68.58/10.00
% 68.58/10.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 68.58/10.00
% 68.58/10.01 % SZS output start Proof for theBenchmark
% 68.58/10.02 Assumptions after simplification:
% 68.58/10.02 ---------------------------------
% 68.58/10.02
% 68.58/10.02 (ax15)
% 69.03/10.06 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 69.03/10.06 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 69.03/10.06 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 69.03/10.06
% 69.03/10.06 (ax17)
% 69.03/10.06 ssList(nil) = 0 & $i(nil)
% 69.03/10.06
% 69.03/10.06 (ax2)
% 69.03/10.07 ? [v0: $i] : (ssItem(v0) = 0 & $i(v0) & ? [v1: $i] : ( ~ (v1 = v0) &
% 69.03/10.07 ssItem(v1) = 0 & $i(v1)))
% 69.03/10.07
% 69.03/10.07 (ax20)
% 69.03/10.07 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1:
% 69.03/10.07 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 69.03/10.07 ssItem(v2) = 0 & $i(v2))))
% 69.03/10.07
% 69.03/10.07 (ax44)
% 69.03/10.07 ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1)
% 69.03/10.07 = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v0, v2) = v3) |
% 69.03/10.07 ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i]
% 69.03/10.07 : ! [v5: $i] : ! [v6: any] : ( ~ (frontsegP(v3, v5) = v6) | ~
% 69.03/10.07 (cons(v1, v4) = v5) | ~ $i(v4) | ? [v7: any] : ? [v8: any] :
% 69.03/10.07 (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 =
% 69.03/10.07 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 =
% 69.03/10.07 v0)))))))))
% 69.03/10.07
% 69.03/10.07 (co1)
% 69.03/10.08 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any]
% 69.03/10.08 : (ssList(v1) = 0 & neq(v1, nil) = v2 & $i(v1) & ( ~ (v2 = 0) | ? [v3: $i]
% 69.03/10.08 : (frontsegP(v1, v3) = 0 & frontsegP(v0, v3) = 0 & ssList(v3) = 0 &
% 69.03/10.08 neq(v3, nil) = 0 & $i(v3))) & ( ~ (v1 = nil) | v0 = nil) & ((v2 = 0 &
% 69.03/10.08 ! [v3: $i] : ( ~ (neq(v3, nil) = 0) | ~ $i(v3) | ? [v4: any] : ?
% 69.03/10.08 [v5: any] : ? [v6: any] : (frontsegP(v1, v3) = v5 & frontsegP(v0,
% 69.03/10.08 v3) = v6 & ssList(v3) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4
% 69.03/10.08 = 0))))) | (v1 = nil & ~ (v0 = nil)))))
% 69.03/10.08
% 69.03/10.08 (function-axioms)
% 69.03/10.08 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 69.03/10.08 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 69.03/10.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 69.03/10.08 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 69.03/10.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 69.03/10.08 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 69.03/10.08 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 69.03/10.09 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 69.03/10.09 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 69.03/10.09 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 69.03/10.09 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 69.03/10.09 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 69.03/10.09 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 69.03/10.09 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 69.03/10.09 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 69.03/10.09 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 69.03/10.09 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 69.03/10.09 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 69.03/10.09 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 69.03/10.09 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 69.03/10.09 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 69.03/10.09 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 69.03/10.09 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 69.03/10.09 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 69.03/10.09 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 69.03/10.09 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 69.03/10.09 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 69.03/10.09 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 69.03/10.09 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 69.03/10.09 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 69.03/10.09 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 69.03/10.09 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 69.03/10.09 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 69.03/10.09 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 69.03/10.09 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 69.03/10.09 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 69.03/10.09
% 69.03/10.09 Further assumptions not needed in the proof:
% 69.03/10.09 --------------------------------------------
% 69.03/10.09 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax21, ax22, ax23, ax24,
% 69.03/10.09 ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35, ax36,
% 69.03/10.09 ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax45, ax46, ax47, ax48, ax49,
% 69.03/10.09 ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59, ax6, ax60,
% 69.03/10.09 ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71, ax72,
% 69.03/10.09 ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83, ax84,
% 69.03/10.09 ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 69.03/10.09
% 69.03/10.09 Those formulas are unsatisfiable:
% 69.03/10.09 ---------------------------------
% 69.03/10.09
% 69.03/10.09 Begin of proof
% 69.03/10.09 |
% 69.03/10.09 | ALPHA: (ax17) implies:
% 69.03/10.09 | (1) ssList(nil) = 0
% 69.03/10.09 |
% 69.03/10.09 | ALPHA: (ax20) implies:
% 69.03/10.09 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 69.03/10.09 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 69.03/10.09 | ssItem(v2) = 0 & $i(v2))))
% 69.03/10.09 |
% 69.03/10.09 | ALPHA: (co1) implies:
% 69.03/10.09 | (3) $i(nil)
% 69.03/10.10 | (4) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : ? [v2: any] :
% 69.03/10.10 | (ssList(v1) = 0 & neq(v1, nil) = v2 & $i(v1) & ( ~ (v2 = 0) | ? [v3:
% 69.03/10.10 | $i] : (frontsegP(v1, v3) = 0 & frontsegP(v0, v3) = 0 &
% 69.03/10.10 | ssList(v3) = 0 & neq(v3, nil) = 0 & $i(v3))) & ( ~ (v1 = nil) |
% 69.03/10.10 | v0 = nil) & ((v2 = 0 & ! [v3: $i] : ( ~ (neq(v3, nil) = 0) | ~
% 69.03/10.10 | $i(v3) | ? [v4: any] : ? [v5: any] : ? [v6: any] :
% 69.03/10.10 | (frontsegP(v1, v3) = v5 & frontsegP(v0, v3) = v6 & ssList(v3)
% 69.03/10.10 | = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))) | (v1 =
% 69.03/10.10 | nil & ~ (v0 = nil)))))
% 69.03/10.10 |
% 69.03/10.10 | ALPHA: (function-axioms) implies:
% 69.03/10.10 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 69.03/10.10 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 69.03/10.10 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 69.03/10.10 | ! [v3: $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~
% 69.03/10.10 | (frontsegP(v3, v2) = v0))
% 69.03/10.10 |
% 69.03/10.10 | DELTA: instantiating (ax2) with fresh symbol all_91_0 gives:
% 69.03/10.10 | (7) ssItem(all_91_0) = 0 & $i(all_91_0) & ? [v0: any] : ( ~ (v0 =
% 69.03/10.10 | all_91_0) & ssItem(v0) = 0 & $i(v0))
% 69.03/10.10 |
% 69.03/10.10 | ALPHA: (7) implies:
% 69.03/10.10 | (8) ? [v0: any] : ( ~ (v0 = all_91_0) & ssItem(v0) = 0 & $i(v0))
% 69.03/10.10 |
% 69.03/10.10 | DELTA: instantiating (4) with fresh symbol all_93_0 gives:
% 69.03/10.10 | (9) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : ? [v1: any] :
% 69.03/10.10 | (ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ( ~ (v1 = 0) | ? [v2:
% 69.03/10.10 | $i] : (frontsegP(v0, v2) = 0 & frontsegP(all_93_0, v2) = 0 &
% 69.03/10.10 | ssList(v2) = 0 & neq(v2, nil) = 0 & $i(v2))) & ( ~ (v0 = nil) |
% 69.03/10.10 | all_93_0 = nil) & ((v1 = 0 & ! [v2: $i] : ( ~ (neq(v2, nil) = 0) |
% 69.03/10.10 | ~ $i(v2) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 69.03/10.10 | (frontsegP(v0, v2) = v4 & frontsegP(all_93_0, v2) = v5 &
% 69.03/10.10 | ssList(v2) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 =
% 69.03/10.10 | 0))))) | (v0 = nil & ~ (all_93_0 = nil))))
% 69.03/10.10 |
% 69.03/10.10 | ALPHA: (9) implies:
% 69.03/10.10 | (10) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 69.03/10.10 | $i(v0) & ( ~ (v1 = 0) | ? [v2: $i] : (frontsegP(v0, v2) = 0 &
% 69.03/10.10 | frontsegP(all_93_0, v2) = 0 & ssList(v2) = 0 & neq(v2, nil) = 0
% 69.03/10.10 | & $i(v2))) & ( ~ (v0 = nil) | all_93_0 = nil) & ((v1 = 0 & !
% 69.03/10.10 | [v2: $i] : ( ~ (neq(v2, nil) = 0) | ~ $i(v2) | ? [v3: any] :
% 69.03/10.10 | ? [v4: any] : ? [v5: any] : (frontsegP(v0, v2) = v4 &
% 69.03/10.10 | frontsegP(all_93_0, v2) = v5 & ssList(v2) = v3 & ( ~ (v5 =
% 69.03/10.11 | 0) | ~ (v4 = 0) | ~ (v3 = 0))))) | (v0 = nil & ~
% 69.03/10.11 | (all_93_0 = nil))))
% 69.03/10.11 |
% 69.03/10.11 | DELTA: instantiating (8) with fresh symbol all_95_0 gives:
% 69.03/10.11 | (11) ~ (all_95_0 = all_91_0) & ssItem(all_95_0) = 0 & $i(all_95_0)
% 69.03/10.11 |
% 69.03/10.11 | ALPHA: (11) implies:
% 69.03/10.11 | (12) $i(all_95_0)
% 69.03/10.11 | (13) ssItem(all_95_0) = 0
% 69.03/10.11 |
% 69.03/10.11 | DELTA: instantiating (10) with fresh symbols all_97_0, all_97_1 gives:
% 69.03/10.11 | (14) ssList(all_97_1) = 0 & neq(all_97_1, nil) = all_97_0 & $i(all_97_1) &
% 69.03/10.11 | ( ~ (all_97_0 = 0) | ? [v0: $i] : (frontsegP(all_97_1, v0) = 0 &
% 69.03/10.11 | frontsegP(all_93_0, v0) = 0 & ssList(v0) = 0 & neq(v0, nil) = 0 &
% 69.03/10.11 | $i(v0))) & ( ~ (all_97_1 = nil) | all_93_0 = nil) & ((all_97_0 = 0
% 69.03/10.11 | & ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | ? [v1: any]
% 69.03/10.11 | : ? [v2: any] : ? [v3: any] : (frontsegP(all_97_1, v0) = v2 &
% 69.03/10.11 | frontsegP(all_93_0, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0)
% 69.03/10.11 | | ~ (v2 = 0) | ~ (v1 = 0))))) | (all_97_1 = nil & ~
% 69.03/10.11 | (all_93_0 = nil)))
% 69.03/10.11 |
% 69.03/10.11 | ALPHA: (14) implies:
% 69.03/10.11 | (15) $i(all_97_1)
% 69.03/10.11 | (16) neq(all_97_1, nil) = all_97_0
% 69.03/10.11 | (17) ssList(all_97_1) = 0
% 69.03/10.11 | (18) (all_97_0 = 0 & ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | ?
% 69.03/10.11 | [v1: any] : ? [v2: any] : ? [v3: any] : (frontsegP(all_97_1, v0)
% 69.03/10.11 | = v2 & frontsegP(all_93_0, v0) = v3 & ssList(v0) = v1 & ( ~ (v3
% 69.03/10.11 | = 0) | ~ (v2 = 0) | ~ (v1 = 0))))) | (all_97_1 = nil & ~
% 69.03/10.11 | (all_93_0 = nil))
% 69.03/10.11 | (19) ~ (all_97_1 = nil) | all_93_0 = nil
% 69.03/10.11 | (20) ~ (all_97_0 = 0) | ? [v0: $i] : (frontsegP(all_97_1, v0) = 0 &
% 69.03/10.11 | frontsegP(all_93_0, v0) = 0 & ssList(v0) = 0 & neq(v0, nil) = 0 &
% 69.03/10.11 | $i(v0))
% 69.03/10.11 |
% 69.03/10.11 | GROUND_INST: instantiating (2) with all_97_1, simplifying with (15), (17)
% 69.03/10.11 | gives:
% 69.03/10.11 | (21) all_97_1 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i]
% 69.03/10.11 | : (cons(v1, v0) = all_97_1 & ssItem(v1) = 0 & $i(v1)))
% 69.03/10.11 |
% 69.03/10.11 | GROUND_INST: instantiating (ax15) with all_97_1, simplifying with (15), (17)
% 69.03/10.11 | gives:
% 69.03/10.11 | (22) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_1, v0) = v1) | ~ $i(v0)
% 69.03/10.11 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 69.03/10.11 | ~ (v0 = all_97_1)) & (v1 = 0 | v0 = all_97_1)))
% 69.03/10.11 |
% 69.03/10.11 | GROUND_INST: instantiating (22) with nil, all_97_0, simplifying with (3), (16)
% 69.03/10.11 | gives:
% 69.03/10.11 | (23) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_97_0 = 0)
% 69.03/10.11 | | ~ (all_97_1 = nil)) & (all_97_0 = 0 | all_97_1 = nil))
% 69.03/10.11 |
% 69.03/10.11 | BETA: splitting (18) gives:
% 69.03/10.11 |
% 69.03/10.11 | Case 1:
% 69.03/10.11 | |
% 69.03/10.11 | | (24) all_97_0 = 0 & ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | ?
% 69.03/10.11 | | [v1: any] : ? [v2: any] : ? [v3: any] : (frontsegP(all_97_1, v0)
% 69.03/10.11 | | = v2 & frontsegP(all_93_0, v0) = v3 & ssList(v0) = v1 & ( ~ (v3
% 69.03/10.11 | | = 0) | ~ (v2 = 0) | ~ (v1 = 0))))
% 69.03/10.11 | |
% 69.03/10.11 | | ALPHA: (24) implies:
% 69.03/10.12 | | (25) all_97_0 = 0
% 69.03/10.12 | | (26) ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 69.03/10.12 | | [v2: any] : ? [v3: any] : (frontsegP(all_97_1, v0) = v2 &
% 69.03/10.12 | | frontsegP(all_93_0, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) |
% 69.03/10.12 | | ~ (v2 = 0) | ~ (v1 = 0))))
% 69.03/10.12 | |
% 69.03/10.12 | | BETA: splitting (23) gives:
% 69.03/10.12 | |
% 69.03/10.12 | | Case 1:
% 69.03/10.12 | | |
% 69.03/10.12 | | | (27) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 69.03/10.12 | | |
% 69.03/10.12 | | | DELTA: instantiating (27) with fresh symbol all_274_0 gives:
% 69.03/10.12 | | | (28) ~ (all_274_0 = 0) & ssList(nil) = all_274_0
% 69.03/10.12 | | |
% 69.03/10.12 | | | ALPHA: (28) implies:
% 69.03/10.12 | | | (29) ~ (all_274_0 = 0)
% 69.03/10.12 | | | (30) ssList(nil) = all_274_0
% 69.03/10.12 | | |
% 69.03/10.12 | | | DELTA: instantiating (27) with fresh symbol all_276_0 gives:
% 69.03/10.12 | | | (31) ~ (all_276_0 = 0) & ssList(nil) = all_276_0
% 69.03/10.12 | | |
% 69.03/10.12 | | | ALPHA: (31) implies:
% 69.03/10.12 | | | (32) ssList(nil) = all_276_0
% 69.03/10.12 | | |
% 69.03/10.12 | | | GROUND_INST: instantiating (5) with 0, all_276_0, nil, simplifying with
% 69.03/10.12 | | | (1), (32) gives:
% 69.03/10.12 | | | (33) all_276_0 = 0
% 69.03/10.12 | | |
% 69.03/10.12 | | | GROUND_INST: instantiating (5) with all_274_0, all_276_0, nil, simplifying
% 69.03/10.12 | | | with (30), (32) gives:
% 69.03/10.12 | | | (34) all_276_0 = all_274_0
% 69.03/10.12 | | |
% 69.03/10.12 | | | COMBINE_EQS: (33), (34) imply:
% 69.03/10.12 | | | (35) all_274_0 = 0
% 69.03/10.12 | | |
% 69.03/10.12 | | | REDUCE: (29), (35) imply:
% 69.03/10.12 | | | (36) $false
% 69.03/10.12 | | |
% 69.03/10.12 | | | CLOSE: (36) is inconsistent.
% 69.03/10.12 | | |
% 69.03/10.12 | | Case 2:
% 69.03/10.12 | | |
% 69.03/10.12 | | | (37) ( ~ (all_97_0 = 0) | ~ (all_97_1 = nil)) & (all_97_0 = 0 |
% 69.03/10.12 | | | all_97_1 = nil)
% 69.03/10.12 | | |
% 69.03/10.12 | | | ALPHA: (37) implies:
% 69.03/10.12 | | | (38) ~ (all_97_0 = 0) | ~ (all_97_1 = nil)
% 69.03/10.12 | | |
% 69.03/10.12 | | | BETA: splitting (20) gives:
% 69.03/10.12 | | |
% 69.03/10.12 | | | Case 1:
% 69.03/10.12 | | | |
% 69.03/10.12 | | | | (39) ~ (all_97_0 = 0)
% 69.03/10.12 | | | |
% 69.03/10.12 | | | | REDUCE: (25), (39) imply:
% 69.03/10.12 | | | | (40) $false
% 69.03/10.12 | | | |
% 69.03/10.12 | | | | CLOSE: (40) is inconsistent.
% 69.03/10.12 | | | |
% 69.03/10.12 | | | Case 2:
% 69.03/10.12 | | | |
% 69.03/10.12 | | | | (41) ? [v0: $i] : (frontsegP(all_97_1, v0) = 0 & frontsegP(all_93_0,
% 69.03/10.12 | | | | v0) = 0 & ssList(v0) = 0 & neq(v0, nil) = 0 & $i(v0))
% 69.03/10.12 | | | |
% 69.03/10.12 | | | | DELTA: instantiating (41) with fresh symbol all_301_0 gives:
% 69.03/10.12 | | | | (42) frontsegP(all_97_1, all_301_0) = 0 & frontsegP(all_93_0,
% 69.03/10.12 | | | | all_301_0) = 0 & ssList(all_301_0) = 0 & neq(all_301_0, nil) =
% 69.03/10.12 | | | | 0 & $i(all_301_0)
% 69.03/10.12 | | | |
% 69.03/10.12 | | | | ALPHA: (42) implies:
% 69.03/10.12 | | | | (43) $i(all_301_0)
% 69.03/10.12 | | | | (44) neq(all_301_0, nil) = 0
% 69.03/10.12 | | | | (45) ssList(all_301_0) = 0
% 69.03/10.12 | | | | (46) frontsegP(all_93_0, all_301_0) = 0
% 69.03/10.12 | | | | (47) frontsegP(all_97_1, all_301_0) = 0
% 69.03/10.12 | | | |
% 69.03/10.12 | | | | BETA: splitting (38) gives:
% 69.03/10.12 | | | |
% 69.03/10.12 | | | | Case 1:
% 69.03/10.12 | | | | |
% 69.03/10.12 | | | | | (48) ~ (all_97_1 = nil)
% 69.03/10.12 | | | | |
% 69.03/10.12 | | | | | BETA: splitting (21) gives:
% 69.03/10.12 | | | | |
% 69.03/10.12 | | | | | Case 1:
% 69.03/10.12 | | | | | |
% 69.03/10.12 | | | | | | (49) all_97_1 = nil
% 69.03/10.12 | | | | | |
% 69.03/10.12 | | | | | | REDUCE: (48), (49) imply:
% 69.03/10.12 | | | | | | (50) $false
% 69.03/10.12 | | | | | |
% 69.03/10.12 | | | | | | CLOSE: (50) is inconsistent.
% 69.03/10.12 | | | | | |
% 69.03/10.12 | | | | | Case 2:
% 69.03/10.12 | | | | | |
% 69.03/10.12 | | | | | | (51) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] :
% 69.03/10.12 | | | | | | (cons(v1, v0) = all_97_1 & ssItem(v1) = 0 & $i(v1)))
% 69.03/10.12 | | | | | |
% 69.03/10.12 | | | | | | DELTA: instantiating (51) with fresh symbol all_311_0 gives:
% 69.03/10.12 | | | | | | (52) ssList(all_311_0) = 0 & $i(all_311_0) & ? [v0: $i] :
% 69.03/10.12 | | | | | | (cons(v0, all_311_0) = all_97_1 & ssItem(v0) = 0 & $i(v0))
% 69.03/10.12 | | | | | |
% 69.03/10.12 | | | | | | ALPHA: (52) implies:
% 69.03/10.12 | | | | | | (53) $i(all_311_0)
% 69.03/10.12 | | | | | | (54) ssList(all_311_0) = 0
% 69.03/10.13 | | | | | | (55) ? [v0: $i] : (cons(v0, all_311_0) = all_97_1 & ssItem(v0) =
% 69.03/10.13 | | | | | | 0 & $i(v0))
% 69.03/10.13 | | | | | |
% 69.03/10.13 | | | | | | DELTA: instantiating (55) with fresh symbol all_313_0 gives:
% 69.03/10.13 | | | | | | (56) cons(all_313_0, all_311_0) = all_97_1 & ssItem(all_313_0) =
% 69.03/10.13 | | | | | | 0 & $i(all_313_0)
% 69.03/10.13 | | | | | |
% 69.03/10.13 | | | | | | ALPHA: (56) implies:
% 69.03/10.13 | | | | | | (57) $i(all_313_0)
% 69.03/10.13 | | | | | | (58) ssItem(all_313_0) = 0
% 69.03/10.13 | | | | | | (59) cons(all_313_0, all_311_0) = all_97_1
% 69.03/10.13 | | | | | |
% 69.03/10.13 | | | | | | GROUND_INST: instantiating (ax44) with all_313_0, simplifying with
% 69.03/10.13 | | | | | | (57), (58) gives:
% 69.03/10.13 | | | | | | (60) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i]
% 69.03/10.13 | | | | | | : ! [v2: $i] : ( ~ (cons(all_313_0, v1) = v2) | ~ $i(v1)
% 69.03/10.13 | | | | | | | ? [v3: int] : ( ~ (v3 = 0) & ssList(v1) = v3) | !
% 69.03/10.13 | | | | | | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~
% 69.03/10.13 | | | | | | (frontsegP(v2, v4) = v5) | ~ (cons(v0, v3) = v4) | ~
% 69.03/10.13 | | | | | | $i(v3) | ? [v6: any] : ? [v7: any] : (frontsegP(v1,
% 69.03/10.13 | | | | | | v3) = v7 & ssList(v3) = v6 & ( ~ (v6 = 0) | (( ~
% 69.03/10.13 | | | | | | (v7 = 0) | ~ (v0 = all_313_0) | v5 = 0) & ( ~
% 69.03/10.13 | | | | | | (v5 = 0) | (v7 = 0 & v0 = all_313_0))))))))
% 69.03/10.13 | | | | | |
% 69.03/10.13 | | | | | | GROUND_INST: instantiating (26) with all_301_0, simplifying with
% 69.03/10.13 | | | | | | (43), (44) gives:
% 69.03/10.13 | | | | | | (61) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 69.03/10.13 | | | | | | (frontsegP(all_97_1, all_301_0) = v1 & frontsegP(all_93_0,
% 69.03/10.13 | | | | | | all_301_0) = v2 & ssList(all_301_0) = v0 & ( ~ (v2 = 0)
% 69.03/10.13 | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 69.03/10.13 | | | | | |
% 69.03/10.13 | | | | | | GROUND_INST: instantiating (60) with all_95_0, simplifying with
% 69.03/10.13 | | | | | | (12), (13) gives:
% 69.03/10.13 | | | | | | (62) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(all_313_0, v0) = v1) |
% 69.03/10.13 | | | | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)
% 69.03/10.13 | | | | | | | ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 69.03/10.13 | | | | | | (frontsegP(v1, v3) = v4) | ~ (cons(all_95_0, v2) = v3)
% 69.03/10.13 | | | | | | | ~ $i(v2) | ? [v5: any] : ? [v6: any] :
% 69.03/10.13 | | | | | | (frontsegP(v0, v2) = v6 & ssList(v2) = v5 & ( ~ (v5 = 0)
% 69.03/10.13 | | | | | | | (( ~ (v6 = 0) | ~ (all_313_0 = all_95_0) | v4 =
% 69.03/10.13 | | | | | | 0) & ( ~ (v4 = 0) | (v6 = 0 & all_313_0 =
% 69.03/10.13 | | | | | | all_95_0)))))))
% 69.03/10.13 | | | | | |
% 69.03/10.13 | | | | | | GROUND_INST: instantiating (62) with all_311_0, all_97_1,
% 69.03/10.13 | | | | | | simplifying with (53), (59) gives:
% 69.03/10.13 | | | | | | (63) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_311_0) = v0) | !
% 69.03/10.13 | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 69.03/10.13 | | | | | | (frontsegP(all_97_1, v1) = v2) | ~ (cons(all_95_0, v0) =
% 69.03/10.13 | | | | | | v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 69.03/10.13 | | | | | | (frontsegP(all_311_0, v0) = v4 & ssList(v0) = v3 & ( ~ (v3
% 69.03/10.13 | | | | | | = 0) | (( ~ (v4 = 0) | ~ (all_313_0 = all_95_0) |
% 69.03/10.13 | | | | | | v2 = 0) & ( ~ (v2 = 0) | (v4 = 0 & all_313_0 =
% 69.03/10.13 | | | | | | all_95_0))))))
% 69.03/10.13 | | | | | |
% 69.03/10.13 | | | | | | DELTA: instantiating (61) with fresh symbols all_680_0, all_680_1,
% 69.03/10.13 | | | | | | all_680_2 gives:
% 69.03/10.13 | | | | | | (64) frontsegP(all_97_1, all_301_0) = all_680_1 &
% 69.03/10.13 | | | | | | frontsegP(all_93_0, all_301_0) = all_680_0 &
% 69.03/10.13 | | | | | | ssList(all_301_0) = all_680_2 & ( ~ (all_680_0 = 0) | ~
% 69.03/10.13 | | | | | | (all_680_1 = 0) | ~ (all_680_2 = 0))
% 69.03/10.13 | | | | | |
% 69.03/10.13 | | | | | | ALPHA: (64) implies:
% 69.03/10.13 | | | | | | (65) ssList(all_301_0) = all_680_2
% 69.03/10.13 | | | | | | (66) frontsegP(all_93_0, all_301_0) = all_680_0
% 69.03/10.13 | | | | | | (67) frontsegP(all_97_1, all_301_0) = all_680_1
% 69.03/10.13 | | | | | | (68) ~ (all_680_0 = 0) | ~ (all_680_1 = 0) | ~ (all_680_2 = 0)
% 69.03/10.13 | | | | | |
% 69.03/10.13 | | | | | | BETA: splitting (63) gives:
% 69.03/10.13 | | | | | |
% 69.03/10.13 | | | | | | Case 1:
% 69.03/10.13 | | | | | | |
% 69.03/10.13 | | | | | | | (69) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_311_0) = v0)
% 69.03/10.13 | | | | | | |
% 69.03/10.13 | | | | | | | DELTA: instantiating (69) with fresh symbol all_707_0 gives:
% 69.03/10.13 | | | | | | | (70) ~ (all_707_0 = 0) & ssList(all_311_0) = all_707_0
% 69.03/10.13 | | | | | | |
% 69.03/10.13 | | | | | | | ALPHA: (70) implies:
% 69.03/10.13 | | | | | | | (71) ~ (all_707_0 = 0)
% 69.03/10.13 | | | | | | | (72) ssList(all_311_0) = all_707_0
% 69.03/10.13 | | | | | | |
% 69.03/10.13 | | | | | | | DELTA: instantiating (69) with fresh symbol all_709_0 gives:
% 69.03/10.13 | | | | | | | (73) ~ (all_709_0 = 0) & ssList(all_311_0) = all_709_0
% 69.03/10.13 | | | | | | |
% 69.03/10.13 | | | | | | | ALPHA: (73) implies:
% 69.03/10.13 | | | | | | | (74) ssList(all_311_0) = all_709_0
% 69.03/10.13 | | | | | | |
% 69.03/10.13 | | | | | | | DELTA: instantiating (69) with fresh symbol all_711_0 gives:
% 69.03/10.13 | | | | | | | (75) ~ (all_711_0 = 0) & ssList(all_311_0) = all_711_0
% 69.03/10.13 | | | | | | |
% 69.03/10.13 | | | | | | | ALPHA: (75) implies:
% 69.03/10.13 | | | | | | | (76) ssList(all_311_0) = all_711_0
% 69.03/10.13 | | | | | | |
% 69.03/10.13 | | | | | | | GROUND_INST: instantiating (5) with all_707_0, all_709_0,
% 69.03/10.13 | | | | | | | all_311_0, simplifying with (72), (74) gives:
% 69.03/10.14 | | | | | | | (77) all_709_0 = all_707_0
% 69.03/10.14 | | | | | | |
% 69.03/10.14 | | | | | | | GROUND_INST: instantiating (5) with 0, all_711_0, all_311_0,
% 69.03/10.14 | | | | | | | simplifying with (54), (76) gives:
% 69.03/10.14 | | | | | | | (78) all_711_0 = 0
% 69.03/10.14 | | | | | | |
% 69.03/10.14 | | | | | | | GROUND_INST: instantiating (5) with all_709_0, all_711_0,
% 69.03/10.14 | | | | | | | all_311_0, simplifying with (74), (76) gives:
% 69.03/10.14 | | | | | | | (79) all_711_0 = all_709_0
% 69.03/10.14 | | | | | | |
% 69.03/10.14 | | | | | | | COMBINE_EQS: (78), (79) imply:
% 69.03/10.14 | | | | | | | (80) all_709_0 = 0
% 69.03/10.14 | | | | | | |
% 69.03/10.14 | | | | | | | SIMP: (80) implies:
% 69.03/10.14 | | | | | | | (81) all_709_0 = 0
% 69.03/10.14 | | | | | | |
% 69.03/10.14 | | | | | | | COMBINE_EQS: (77), (81) imply:
% 69.03/10.14 | | | | | | | (82) all_707_0 = 0
% 69.03/10.14 | | | | | | |
% 69.03/10.14 | | | | | | | SIMP: (82) implies:
% 69.03/10.14 | | | | | | | (83) all_707_0 = 0
% 69.03/10.14 | | | | | | |
% 69.03/10.14 | | | | | | | REDUCE: (71), (83) imply:
% 69.03/10.14 | | | | | | | (84) $false
% 69.03/10.14 | | | | | | |
% 69.03/10.14 | | | | | | | CLOSE: (84) is inconsistent.
% 69.03/10.14 | | | | | | |
% 69.03/10.14 | | | | | | Case 2:
% 69.03/10.14 | | | | | | |
% 69.03/10.14 | | | | | | |
% 69.03/10.14 | | | | | | | GROUND_INST: instantiating (5) with 0, all_680_2, all_301_0,
% 69.03/10.14 | | | | | | | simplifying with (45), (65) gives:
% 69.03/10.14 | | | | | | | (85) all_680_2 = 0
% 69.03/10.14 | | | | | | |
% 69.03/10.14 | | | | | | | GROUND_INST: instantiating (6) with 0, all_680_0, all_301_0,
% 69.03/10.14 | | | | | | | all_93_0, simplifying with (46), (66) gives:
% 69.03/10.14 | | | | | | | (86) all_680_0 = 0
% 69.03/10.14 | | | | | | |
% 69.03/10.14 | | | | | | | GROUND_INST: instantiating (6) with 0, all_680_1, all_301_0,
% 69.03/10.14 | | | | | | | all_97_1, simplifying with (47), (67) gives:
% 69.03/10.14 | | | | | | | (87) all_680_1 = 0
% 69.03/10.14 | | | | | | |
% 69.03/10.14 | | | | | | | BETA: splitting (68) gives:
% 69.03/10.14 | | | | | | |
% 69.03/10.14 | | | | | | | Case 1:
% 69.03/10.14 | | | | | | | |
% 69.03/10.14 | | | | | | | | (88) ~ (all_680_0 = 0)
% 69.03/10.14 | | | | | | | |
% 69.03/10.14 | | | | | | | | REDUCE: (86), (88) imply:
% 69.03/10.14 | | | | | | | | (89) $false
% 69.03/10.14 | | | | | | | |
% 69.03/10.14 | | | | | | | | CLOSE: (89) is inconsistent.
% 69.03/10.14 | | | | | | | |
% 69.03/10.14 | | | | | | | Case 2:
% 69.03/10.14 | | | | | | | |
% 69.03/10.14 | | | | | | | | (90) ~ (all_680_1 = 0) | ~ (all_680_2 = 0)
% 69.03/10.14 | | | | | | | |
% 69.03/10.14 | | | | | | | | BETA: splitting (90) gives:
% 69.03/10.14 | | | | | | | |
% 69.03/10.14 | | | | | | | | Case 1:
% 69.03/10.14 | | | | | | | | |
% 69.25/10.14 | | | | | | | | | (91) ~ (all_680_1 = 0)
% 69.25/10.14 | | | | | | | | |
% 69.25/10.14 | | | | | | | | | REDUCE: (87), (91) imply:
% 69.25/10.14 | | | | | | | | | (92) $false
% 69.25/10.14 | | | | | | | | |
% 69.25/10.14 | | | | | | | | | CLOSE: (92) is inconsistent.
% 69.25/10.14 | | | | | | | | |
% 69.25/10.14 | | | | | | | | Case 2:
% 69.25/10.14 | | | | | | | | |
% 69.25/10.14 | | | | | | | | | (93) ~ (all_680_2 = 0)
% 69.25/10.14 | | | | | | | | |
% 69.25/10.14 | | | | | | | | | REDUCE: (85), (93) imply:
% 69.25/10.14 | | | | | | | | | (94) $false
% 69.25/10.14 | | | | | | | | |
% 69.25/10.14 | | | | | | | | | CLOSE: (94) is inconsistent.
% 69.25/10.14 | | | | | | | | |
% 69.25/10.14 | | | | | | | | End of split
% 69.25/10.14 | | | | | | | |
% 69.25/10.14 | | | | | | | End of split
% 69.25/10.14 | | | | | | |
% 69.25/10.14 | | | | | | End of split
% 69.25/10.14 | | | | | |
% 69.25/10.14 | | | | | End of split
% 69.25/10.14 | | | | |
% 69.25/10.14 | | | | Case 2:
% 69.25/10.14 | | | | |
% 69.25/10.14 | | | | | (95) ~ (all_97_0 = 0)
% 69.25/10.14 | | | | |
% 69.25/10.14 | | | | | REDUCE: (25), (95) imply:
% 69.25/10.14 | | | | | (96) $false
% 69.25/10.14 | | | | |
% 69.25/10.14 | | | | | CLOSE: (96) is inconsistent.
% 69.25/10.14 | | | | |
% 69.25/10.14 | | | | End of split
% 69.25/10.14 | | | |
% 69.25/10.14 | | | End of split
% 69.25/10.14 | | |
% 69.25/10.14 | | End of split
% 69.25/10.14 | |
% 69.25/10.14 | Case 2:
% 69.25/10.14 | |
% 69.25/10.14 | | (97) all_97_1 = nil & ~ (all_93_0 = nil)
% 69.25/10.14 | |
% 69.25/10.14 | | ALPHA: (97) implies:
% 69.25/10.14 | | (98) all_97_1 = nil
% 69.25/10.14 | | (99) ~ (all_93_0 = nil)
% 69.25/10.14 | |
% 69.25/10.14 | | BETA: splitting (19) gives:
% 69.25/10.14 | |
% 69.25/10.14 | | Case 1:
% 69.25/10.14 | | |
% 69.25/10.14 | | | (100) ~ (all_97_1 = nil)
% 69.25/10.14 | | |
% 69.25/10.14 | | | REDUCE: (98), (100) imply:
% 69.25/10.14 | | | (101) $false
% 69.25/10.14 | | |
% 69.25/10.14 | | | CLOSE: (101) is inconsistent.
% 69.25/10.14 | | |
% 69.25/10.14 | | Case 2:
% 69.25/10.14 | | |
% 69.25/10.14 | | | (102) all_93_0 = nil
% 69.25/10.14 | | |
% 69.25/10.14 | | | REDUCE: (99), (102) imply:
% 69.25/10.14 | | | (103) $false
% 69.25/10.14 | | |
% 69.25/10.14 | | | CLOSE: (103) is inconsistent.
% 69.25/10.14 | | |
% 69.25/10.14 | | End of split
% 69.25/10.14 | |
% 69.25/10.14 | End of split
% 69.25/10.14 |
% 69.25/10.14 End of proof
% 69.25/10.14 % SZS output end Proof for theBenchmark
% 69.25/10.14
% 69.25/10.14 9505ms
%------------------------------------------------------------------------------