TSTP Solution File: SWC100+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC100+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 20:49:39 EDT 2023
% Result : Theorem 22.56s 3.83s
% Output : Proof 33.84s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWC100+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.15/0.33 % Computer : n001.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Mon Aug 28 18:18:20 EDT 2023
% 0.17/0.34 % 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/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.61 Running up to 7 provers in parallel.
% 0.19/0.63 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.63 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.63 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.63 Prover 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 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.63 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.63 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.15/1.55 Prover 1: Preprocessing ...
% 5.15/1.55 Prover 4: Preprocessing ...
% 5.85/1.58 Prover 3: Preprocessing ...
% 5.85/1.58 Prover 2: Preprocessing ...
% 5.85/1.58 Prover 5: Preprocessing ...
% 5.85/1.58 Prover 6: Preprocessing ...
% 5.85/1.60 Prover 0: Preprocessing ...
% 15.41/2.90 Prover 2: Proving ...
% 15.41/2.93 Prover 1: Constructing countermodel ...
% 15.41/2.94 Prover 5: Constructing countermodel ...
% 16.32/3.02 Prover 3: Constructing countermodel ...
% 16.57/3.05 Prover 6: Proving ...
% 21.37/3.67 Prover 4: Constructing countermodel ...
% 22.56/3.83 Prover 3: proved (3196ms)
% 22.56/3.83
% 22.56/3.83 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 22.56/3.83
% 22.56/3.83 Prover 2: stopped
% 22.56/3.83 Prover 6: stopped
% 22.56/3.84 Prover 5: stopped
% 22.76/3.86 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 22.76/3.86 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 22.76/3.86 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 22.76/3.86 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 23.21/3.95 Prover 0: Proving ...
% 23.21/3.96 Prover 0: stopped
% 23.54/3.99 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 24.08/4.19 Prover 10: Preprocessing ...
% 24.08/4.22 Prover 8: Preprocessing ...
% 25.30/4.25 Prover 7: Preprocessing ...
% 25.82/4.29 Prover 11: Preprocessing ...
% 26.17/4.38 Prover 13: Preprocessing ...
% 26.79/4.42 Prover 10: Constructing countermodel ...
% 26.79/4.48 Prover 7: Constructing countermodel ...
% 28.36/4.66 Prover 8: Warning: ignoring some quantifiers
% 28.36/4.69 Prover 8: Constructing countermodel ...
% 29.05/4.72 Prover 13: Constructing countermodel ...
% 31.89/5.18 Prover 1: Found proof (size 117)
% 31.89/5.18 Prover 1: proved (4560ms)
% 31.89/5.18 Prover 7: stopped
% 31.89/5.18 Prover 8: stopped
% 31.89/5.18 Prover 4: stopped
% 31.89/5.18 Prover 13: stopped
% 31.89/5.18 Prover 10: stopped
% 33.00/5.38 Prover 11: Constructing countermodel ...
% 33.00/5.40 Prover 11: stopped
% 33.00/5.40
% 33.00/5.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 33.00/5.40
% 33.00/5.42 % SZS output start Proof for theBenchmark
% 33.00/5.43 Assumptions after simplification:
% 33.00/5.43 ---------------------------------
% 33.00/5.43
% 33.00/5.43 (ax15)
% 33.00/5.47 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 33.00/5.47 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 33.00/5.47 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 33.00/5.47
% 33.00/5.47 (ax17)
% 33.00/5.47 ssList(nil) = 0 & $i(nil)
% 33.00/5.47
% 33.00/5.47 (ax5)
% 33.00/5.48 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 33.00/5.48 ( ~ (frontsegP(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 33.00/5.48 ssList(v1) = v3) | (( ~ (v2 = 0) | ? [v3: $i] : (ssList(v3) = 0 &
% 33.00/5.48 app(v1, v3) = v0 & $i(v3))) & (v2 = 0 | ! [v3: $i] : ( ~ (app(v1,
% 33.00/5.48 v3) = v0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v3)
% 33.00/5.48 = v4))))))
% 33.00/5.48
% 33.00/5.48 (ax83)
% 33.00/5.48 $i(nil) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : !
% 33.00/5.48 [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0)
% 33.00/5.48 & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = nil)) & ( ~ (v1
% 33.00/5.48 = nil) | ~ (v0 = nil) | v2 = nil))))
% 33.00/5.48
% 33.00/5.48 (co1)
% 33.00/5.48 $i(nil) & ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 33.00/5.48 $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] : (frontsegP(v2, v0) = v4
% 33.00/5.48 & ssList(v2) = 0 & neq(v2, nil) = v3 & $i(v2) & ? [v5: any] :
% 33.00/5.48 (strictorderedP(v0) = v5 & ? [v6: $i] : (v5 = 0 & ssList(v6) = 0 &
% 33.00/5.48 app(v0, v6) = v2 & $i(v6) & ! [v7: $i] : ! [v8: $i] : ( ~ (cons(v7,
% 33.00/5.48 nil) = v8) | ~ $i(v7) | ? [v9: int] : ( ~ (v9 = 0) &
% 33.00/5.48 ssItem(v7) = v9) | ! [v9: $i] : ( ~ (app(v8, v9) = v6) | ~
% 33.00/5.48 $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & ssList(v9) = v10) | !
% 33.00/5.48 [v10: $i] : ! [v11: $i] : ( ~ (cons(v10, nil) = v11) | ~ $i(v10)
% 33.00/5.48 | ? [v12: any] : ? [v13: any] : (lt(v10, v7) = v13 &
% 33.00/5.48 ssItem(v10) = v12 & ( ~ (v12 = 0) | ! [v14: $i] : ( ~ (v13 =
% 33.00/5.48 0) | ~ (app(v14, v11) = v0) | ~ $i(v14) | ? [v15:
% 33.00/5.48 int] : ( ~ (v15 = 0) & ssList(v14) = v15)))))))) & ( ~
% 33.00/5.48 (v0 = nil) | v2 = nil) & ((v3 = 0 & ( ~ (v4 = 0) | ~ (v1 = 0))) | (v2
% 33.00/5.48 = nil & ~ (v0 = nil))))))
% 33.00/5.48
% 33.00/5.48 (function-axioms)
% 33.00/5.49 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 33.00/5.49 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 33.00/5.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 33.00/5.49 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 33.00/5.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 33.00/5.49 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 33.00/5.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 33.00/5.49 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 33.00/5.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 33.00/5.49 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 33.00/5.49 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 33.00/5.49 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 33.00/5.49 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 33.00/5.49 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 33.00/5.49 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 33.00/5.49 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 33.00/5.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 33.00/5.49 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 33.00/5.49 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 33.00/5.49 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 33.00/5.49 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 33.00/5.49 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 33.00/5.49 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 33.00/5.49 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 33.00/5.49 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 33.00/5.49 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 33.00/5.49 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 33.00/5.49 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 33.00/5.49 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 33.00/5.49 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 33.00/5.49 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 33.00/5.49 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 33.00/5.49 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 33.00/5.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 33.00/5.49 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 33.00/5.49 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 33.00/5.49
% 33.00/5.49 Further assumptions not needed in the proof:
% 33.00/5.49 --------------------------------------------
% 33.00/5.50 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax20, ax21, ax22,
% 33.00/5.50 ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34,
% 33.00/5.50 ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44, ax45, ax46,
% 33.00/5.50 ax47, ax48, ax49, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59,
% 33.00/5.50 ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70,
% 33.00/5.50 ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82,
% 33.00/5.50 ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 33.00/5.50
% 33.00/5.50 Those formulas are unsatisfiable:
% 33.00/5.50 ---------------------------------
% 33.00/5.50
% 33.00/5.50 Begin of proof
% 33.00/5.50 |
% 33.00/5.50 | ALPHA: (ax17) implies:
% 33.00/5.50 | (1) ssList(nil) = 0
% 33.00/5.50 |
% 33.00/5.50 | ALPHA: (ax83) implies:
% 33.00/5.50 | (2) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2:
% 33.00/5.50 | $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 =
% 33.00/5.50 | 0) & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 =
% 33.00/5.50 | nil)) & ( ~ (v1 = nil) | ~ (v0 = nil) | v2 = nil))))
% 33.00/5.50 |
% 33.00/5.50 | ALPHA: (co1) implies:
% 33.00/5.50 | (3) $i(nil)
% 33.00/5.50 | (4) ? [v0: $i] : ? [v1: any] : (ssList(v0) = 0 & neq(v0, nil) = v1 &
% 33.00/5.50 | $i(v0) & ? [v2: $i] : ? [v3: any] : ? [v4: any] : (frontsegP(v2,
% 33.00/5.50 | v0) = v4 & ssList(v2) = 0 & neq(v2, nil) = v3 & $i(v2) & ? [v5:
% 33.00/5.50 | any] : (strictorderedP(v0) = v5 & ? [v6: $i] : (v5 = 0 &
% 33.00/5.50 | ssList(v6) = 0 & app(v0, v6) = v2 & $i(v6) & ! [v7: $i] : !
% 33.00/5.50 | [v8: $i] : ( ~ (cons(v7, nil) = v8) | ~ $i(v7) | ? [v9: int]
% 33.00/5.50 | : ( ~ (v9 = 0) & ssItem(v7) = v9) | ! [v9: $i] : ( ~
% 33.00/5.50 | (app(v8, v9) = v6) | ~ $i(v9) | ? [v10: int] : ( ~ (v10 =
% 33.00/5.50 | 0) & ssList(v9) = v10) | ! [v10: $i] : ! [v11: $i] :
% 33.00/5.50 | ( ~ (cons(v10, nil) = v11) | ~ $i(v10) | ? [v12: any] :
% 33.00/5.50 | ? [v13: any] : (lt(v10, v7) = v13 & ssItem(v10) = v12 & (
% 33.00/5.50 | ~ (v12 = 0) | ! [v14: $i] : ( ~ (v13 = 0) | ~
% 33.00/5.50 | (app(v14, v11) = v0) | ~ $i(v14) | ? [v15: int] :
% 33.00/5.50 | ( ~ (v15 = 0) & ssList(v14) = v15)))))))) & ( ~ (v0
% 33.00/5.50 | = nil) | v2 = nil) & ((v3 = 0 & ( ~ (v4 = 0) | ~ (v1 = 0)))
% 33.00/5.50 | | (v2 = nil & ~ (v0 = nil))))))
% 33.00/5.50 |
% 33.00/5.50 | ALPHA: (function-axioms) implies:
% 33.84/5.50 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 33.84/5.50 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 33.84/5.50 |
% 33.84/5.51 | DELTA: instantiating (4) with fresh symbols all_93_0, all_93_1 gives:
% 33.84/5.51 | (6) ssList(all_93_1) = 0 & neq(all_93_1, nil) = all_93_0 & $i(all_93_1) &
% 33.84/5.51 | ? [v0: $i] : ? [v1: any] : ? [v2: any] : (frontsegP(v0, all_93_1) =
% 33.84/5.51 | v2 & ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ? [v3: any] :
% 33.84/5.51 | (strictorderedP(all_93_1) = v3 & ? [v4: $i] : (v3 = 0 & ssList(v4) =
% 33.84/5.51 | 0 & app(all_93_1, v4) = v0 & $i(v4) & ! [v5: $i] : ! [v6: $i] :
% 33.84/5.51 | ( ~ (cons(v5, nil) = v6) | ~ $i(v5) | ? [v7: int] : ( ~ (v7 =
% 33.84/5.51 | 0) & ssItem(v5) = v7) | ! [v7: $i] : ( ~ (app(v6, v7) =
% 33.84/5.51 | v4) | ~ $i(v7) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v7)
% 33.84/5.51 | = v8) | ! [v8: $i] : ! [v9: $i] : ( ~ (cons(v8, nil) =
% 33.84/5.51 | v9) | ~ $i(v8) | ? [v10: any] : ? [v11: any] : (lt(v8,
% 33.84/5.51 | v5) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | ! [v12:
% 33.84/5.51 | $i] : ( ~ (v11 = 0) | ~ (app(v12, v9) = all_93_1) |
% 33.84/5.51 | ~ $i(v12) | ? [v13: int] : ( ~ (v13 = 0) &
% 33.84/5.51 | ssList(v12) = v13)))))))) & ( ~ (all_93_1 = nil) |
% 33.84/5.51 | v0 = nil) & ((v1 = 0 & ( ~ (v2 = 0) | ~ (all_93_0 = 0))) | (v0 =
% 33.84/5.51 | nil & ~ (all_93_1 = nil)))))
% 33.84/5.51 |
% 33.84/5.51 | ALPHA: (6) implies:
% 33.84/5.51 | (7) $i(all_93_1)
% 33.84/5.51 | (8) neq(all_93_1, nil) = all_93_0
% 33.84/5.51 | (9) ssList(all_93_1) = 0
% 33.84/5.51 | (10) ? [v0: $i] : ? [v1: any] : ? [v2: any] : (frontsegP(v0, all_93_1) =
% 33.84/5.51 | v2 & ssList(v0) = 0 & neq(v0, nil) = v1 & $i(v0) & ? [v3: any] :
% 33.84/5.51 | (strictorderedP(all_93_1) = v3 & ? [v4: $i] : (v3 = 0 & ssList(v4)
% 33.84/5.51 | = 0 & app(all_93_1, v4) = v0 & $i(v4) & ! [v5: $i] : ! [v6:
% 33.84/5.51 | $i] : ( ~ (cons(v5, nil) = v6) | ~ $i(v5) | ? [v7: int] : (
% 33.84/5.51 | ~ (v7 = 0) & ssItem(v5) = v7) | ! [v7: $i] : ( ~ (app(v6,
% 33.84/5.51 | v7) = v4) | ~ $i(v7) | ? [v8: int] : ( ~ (v8 = 0) &
% 33.84/5.51 | ssList(v7) = v8) | ! [v8: $i] : ! [v9: $i] : ( ~
% 33.84/5.51 | (cons(v8, nil) = v9) | ~ $i(v8) | ? [v10: any] : ?
% 33.84/5.51 | [v11: any] : (lt(v8, v5) = v11 & ssItem(v8) = v10 & ( ~
% 33.84/5.51 | (v10 = 0) | ! [v12: $i] : ( ~ (v11 = 0) | ~
% 33.84/5.51 | (app(v12, v9) = all_93_1) | ~ $i(v12) | ? [v13:
% 33.84/5.51 | int] : ( ~ (v13 = 0) & ssList(v12) = v13)))))))) &
% 33.84/5.51 | ( ~ (all_93_1 = nil) | v0 = nil) & ((v1 = 0 & ( ~ (v2 = 0) | ~
% 33.84/5.51 | (all_93_0 = 0))) | (v0 = nil & ~ (all_93_1 = nil)))))
% 33.84/5.51 |
% 33.84/5.51 | DELTA: instantiating (10) with fresh symbols all_97_0, all_97_1, all_97_2
% 33.84/5.51 | gives:
% 33.84/5.52 | (11) frontsegP(all_97_2, all_93_1) = all_97_0 & ssList(all_97_2) = 0 &
% 33.84/5.52 | neq(all_97_2, nil) = all_97_1 & $i(all_97_2) & ? [v0: any] :
% 33.84/5.52 | (strictorderedP(all_93_1) = v0 & ? [v1: $i] : (v0 = 0 & ssList(v1) =
% 33.84/5.52 | 0 & app(all_93_1, v1) = all_97_2 & $i(v1) & ! [v2: $i] : ! [v3:
% 33.84/5.52 | $i] : ( ~ (cons(v2, nil) = v3) | ~ $i(v2) | ? [v4: int] : ( ~
% 33.84/5.52 | (v4 = 0) & ssItem(v2) = v4) | ! [v4: $i] : ( ~ (app(v3, v4) =
% 33.84/5.52 | v1) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) & ssList(v4) =
% 33.84/5.52 | v5) | ! [v5: $i] : ! [v6: $i] : ( ~ (cons(v5, nil) = v6) |
% 33.84/5.52 | ~ $i(v5) | ? [v7: any] : ? [v8: any] : (lt(v5, v2) = v8 &
% 33.84/5.52 | ssItem(v5) = v7 & ( ~ (v7 = 0) | ! [v9: $i] : ( ~ (v8 =
% 33.84/5.52 | 0) | ~ (app(v9, v6) = all_93_1) | ~ $i(v9) | ?
% 33.84/5.52 | [v10: int] : ( ~ (v10 = 0) & ssList(v9) = v10))))))))
% 33.84/5.52 | & ( ~ (all_93_1 = nil) | all_97_2 = nil) & ((all_97_1 = 0 & ( ~
% 33.84/5.52 | (all_97_0 = 0) | ~ (all_93_0 = 0))) | (all_97_2 = nil & ~
% 33.84/5.52 | (all_93_1 = nil))))
% 33.84/5.52 |
% 33.84/5.52 | ALPHA: (11) implies:
% 33.84/5.52 | (12) $i(all_97_2)
% 33.84/5.52 | (13) neq(all_97_2, nil) = all_97_1
% 33.84/5.52 | (14) ssList(all_97_2) = 0
% 33.84/5.52 | (15) frontsegP(all_97_2, all_93_1) = all_97_0
% 33.84/5.52 | (16) ? [v0: any] : (strictorderedP(all_93_1) = v0 & ? [v1: $i] : (v0 = 0
% 33.84/5.52 | & ssList(v1) = 0 & app(all_93_1, v1) = all_97_2 & $i(v1) & ! [v2:
% 33.84/5.52 | $i] : ! [v3: $i] : ( ~ (cons(v2, nil) = v3) | ~ $i(v2) | ?
% 33.84/5.52 | [v4: int] : ( ~ (v4 = 0) & ssItem(v2) = v4) | ! [v4: $i] : ( ~
% 33.84/5.52 | (app(v3, v4) = v1) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) &
% 33.84/5.52 | ssList(v4) = v5) | ! [v5: $i] : ! [v6: $i] : ( ~ (cons(v5,
% 33.84/5.52 | nil) = v6) | ~ $i(v5) | ? [v7: any] : ? [v8: any] :
% 33.84/5.52 | (lt(v5, v2) = v8 & ssItem(v5) = v7 & ( ~ (v7 = 0) | ! [v9:
% 33.84/5.52 | $i] : ( ~ (v8 = 0) | ~ (app(v9, v6) = all_93_1) | ~
% 33.84/5.52 | $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & ssList(v9) =
% 33.84/5.52 | v10)))))))) & ( ~ (all_93_1 = nil) | all_97_2 = nil)
% 33.84/5.52 | & ((all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0))) |
% 33.84/5.52 | (all_97_2 = nil & ~ (all_93_1 = nil))))
% 33.84/5.52 |
% 33.84/5.52 | DELTA: instantiating (16) with fresh symbol all_99_0 gives:
% 33.84/5.52 | (17) strictorderedP(all_93_1) = all_99_0 & ? [v0: $i] : (all_99_0 = 0 &
% 33.84/5.52 | ssList(v0) = 0 & app(all_93_1, v0) = all_97_2 & $i(v0) & ! [v1: $i]
% 33.84/5.52 | : ! [v2: $i] : ( ~ (cons(v1, nil) = v2) | ~ $i(v1) | ? [v3: int]
% 33.84/5.52 | : ( ~ (v3 = 0) & ssItem(v1) = v3) | ! [v3: $i] : ( ~ (app(v2, v3)
% 33.84/5.53 | = v0) | ~ $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v3) =
% 33.84/5.53 | v4) | ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v4, nil) = v5) |
% 33.84/5.53 | ~ $i(v4) | ? [v6: any] : ? [v7: any] : (lt(v4, v1) = v7 &
% 33.84/5.53 | ssItem(v4) = v6 & ( ~ (v6 = 0) | ! [v8: $i] : ( ~ (v7 = 0)
% 33.84/5.53 | | ~ (app(v8, v5) = all_93_1) | ~ $i(v8) | ? [v9: int]
% 33.84/5.53 | : ( ~ (v9 = 0) & ssList(v8) = v9)))))))) & ( ~ (all_93_1
% 33.84/5.53 | = nil) | all_97_2 = nil) & ((all_97_1 = 0 & ( ~ (all_97_0 = 0) |
% 33.84/5.53 | ~ (all_93_0 = 0))) | (all_97_2 = nil & ~ (all_93_1 = nil)))
% 33.84/5.53 |
% 33.84/5.53 | ALPHA: (17) implies:
% 33.84/5.53 | (18) (all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0))) | (all_97_2 =
% 33.84/5.53 | nil & ~ (all_93_1 = nil))
% 33.84/5.53 | (19) ~ (all_93_1 = nil) | all_97_2 = nil
% 33.84/5.53 | (20) ? [v0: $i] : (all_99_0 = 0 & ssList(v0) = 0 & app(all_93_1, v0) =
% 33.84/5.53 | all_97_2 & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, nil) =
% 33.84/5.53 | v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3)
% 33.84/5.53 | | ! [v3: $i] : ( ~ (app(v2, v3) = v0) | ~ $i(v3) | ? [v4: int]
% 33.84/5.53 | : ( ~ (v4 = 0) & ssList(v3) = v4) | ! [v4: $i] : ! [v5: $i] :
% 33.84/5.53 | ( ~ (cons(v4, nil) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7:
% 33.84/5.53 | any] : (lt(v4, v1) = v7 & ssItem(v4) = v6 & ( ~ (v6 = 0) |
% 33.84/5.53 | ! [v8: $i] : ( ~ (v7 = 0) | ~ (app(v8, v5) = all_93_1) |
% 33.84/5.53 | ~ $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & ssList(v8) =
% 33.84/5.53 | v9))))))))
% 33.84/5.53 |
% 33.84/5.53 | DELTA: instantiating (20) with fresh symbol all_101_0 gives:
% 33.84/5.53 | (21) all_99_0 = 0 & ssList(all_101_0) = 0 & app(all_93_1, all_101_0) =
% 33.84/5.53 | all_97_2 & $i(all_101_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0,
% 33.84/5.53 | nil) = v1) | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) &
% 33.84/5.53 | ssItem(v0) = v2) | ! [v2: $i] : ( ~ (app(v1, v2) = all_101_0) |
% 33.84/5.53 | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) & ssList(v2) = v3) | !
% 33.84/5.53 | [v3: $i] : ! [v4: $i] : ( ~ (cons(v3, nil) = v4) | ~ $i(v3) | ?
% 33.84/5.53 | [v5: any] : ? [v6: any] : (lt(v3, v0) = v6 & ssItem(v3) = v5 &
% 33.84/5.53 | ( ~ (v5 = 0) | ! [v7: $i] : ( ~ (v6 = 0) | ~ (app(v7, v4) =
% 33.84/5.53 | all_93_1) | ~ $i(v7) | ? [v8: int] : ( ~ (v8 = 0) &
% 33.84/5.53 | ssList(v7) = v8)))))))
% 33.84/5.53 |
% 33.84/5.53 | ALPHA: (21) implies:
% 33.84/5.53 | (22) $i(all_101_0)
% 33.84/5.53 | (23) app(all_93_1, all_101_0) = all_97_2
% 33.84/5.53 | (24) ssList(all_101_0) = 0
% 33.84/5.53 |
% 33.84/5.53 | GROUND_INST: instantiating (2) with all_93_1, simplifying with (7), (9) gives:
% 33.84/5.53 | (25) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_93_1, v0) = v1) | ~ $i(v0) |
% 33.84/5.53 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = nil) |
% 33.84/5.53 | (v0 = nil & all_93_1 = nil)) & ( ~ (v0 = nil) | ~ (all_93_1 =
% 33.84/5.53 | nil) | v1 = nil)))
% 33.84/5.53 |
% 33.84/5.53 | GROUND_INST: instantiating (ax15) with all_93_1, simplifying with (7), (9)
% 33.84/5.53 | gives:
% 33.84/5.53 | (26) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_93_1, v0) = v1) | ~ $i(v0)
% 33.84/5.53 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 33.84/5.53 | ~ (v0 = all_93_1)) & (v1 = 0 | v0 = all_93_1)))
% 33.84/5.53 |
% 33.84/5.53 | GROUND_INST: instantiating (ax5) with all_97_2, simplifying with (12), (14)
% 33.84/5.54 | gives:
% 33.84/5.54 | (27) ! [v0: $i] : ! [v1: any] : ( ~ (frontsegP(all_97_2, v0) = v1) | ~
% 33.84/5.54 | $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 =
% 33.84/5.54 | 0) | ? [v2: $i] : (ssList(v2) = 0 & app(v0, v2) = all_97_2 &
% 33.84/5.54 | $i(v2))) & (v1 = 0 | ! [v2: $i] : ( ~ (app(v0, v2) =
% 33.84/5.54 | all_97_2) | ~ $i(v2) | ? [v3: int] : ( ~ (v3 = 0) &
% 33.84/5.54 | ssList(v2) = v3)))))
% 33.84/5.54 |
% 33.84/5.54 | GROUND_INST: instantiating (ax15) with all_97_2, simplifying with (12), (14)
% 33.84/5.54 | gives:
% 33.84/5.54 | (28) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_2, v0) = v1) | ~ $i(v0)
% 33.84/5.54 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 33.84/5.54 | ~ (v0 = all_97_2)) & (v1 = 0 | v0 = all_97_2)))
% 33.84/5.54 |
% 33.84/5.54 | GROUND_INST: instantiating (26) with nil, all_93_0, simplifying with (3), (8)
% 33.84/5.54 | gives:
% 33.84/5.54 | (29) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_93_0 = 0)
% 33.84/5.54 | | ~ (all_93_1 = nil)) & (all_93_0 = 0 | all_93_1 = nil))
% 33.84/5.54 |
% 33.84/5.54 | GROUND_INST: instantiating (28) with nil, all_97_1, simplifying with (3), (13)
% 33.84/5.54 | gives:
% 33.84/5.54 | (30) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_97_1 = 0)
% 33.84/5.54 | | ~ (all_97_2 = nil)) & (all_97_1 = 0 | all_97_2 = nil))
% 33.84/5.54 |
% 33.84/5.54 | GROUND_INST: instantiating (27) with all_93_1, all_97_0, simplifying with (7),
% 33.84/5.54 | (15) gives:
% 33.84/5.54 | (31) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0) | (( ~ (all_97_0
% 33.84/5.54 | = 0) | ? [v0: $i] : (ssList(v0) = 0 & app(all_93_1, v0) =
% 33.84/5.54 | all_97_2 & $i(v0))) & (all_97_0 = 0 | ! [v0: $i] : ( ~
% 33.84/5.54 | (app(all_93_1, v0) = all_97_2) | ~ $i(v0) | ? [v1: int] : ( ~
% 33.84/5.54 | (v1 = 0) & ssList(v0) = v1))))
% 33.84/5.54 |
% 33.84/5.54 | GROUND_INST: instantiating (25) with all_101_0, all_97_2, simplifying with
% 33.84/5.54 | (22), (23) gives:
% 33.84/5.54 | (32) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) = v0) | (( ~
% 33.84/5.54 | (all_101_0 = nil) | ~ (all_93_1 = nil) | all_97_2 = nil) & ( ~
% 33.84/5.54 | (all_97_2 = nil) | (all_101_0 = nil & all_93_1 = nil)))
% 33.84/5.54 |
% 33.84/5.54 | BETA: splitting (19) gives:
% 33.84/5.54 |
% 33.84/5.54 | Case 1:
% 33.84/5.54 | |
% 33.84/5.54 | | (33) ~ (all_93_1 = nil)
% 33.84/5.54 | |
% 33.84/5.54 | | BETA: splitting (29) gives:
% 33.84/5.54 | |
% 33.84/5.54 | | Case 1:
% 33.84/5.54 | | |
% 33.84/5.54 | | | (34) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 33.84/5.54 | | |
% 33.84/5.54 | | | DELTA: instantiating (34) with fresh symbol all_357_0 gives:
% 33.84/5.54 | | | (35) ~ (all_357_0 = 0) & ssList(nil) = all_357_0
% 33.84/5.54 | | |
% 33.84/5.54 | | | ALPHA: (35) implies:
% 33.84/5.54 | | | (36) ~ (all_357_0 = 0)
% 33.84/5.54 | | | (37) ssList(nil) = all_357_0
% 33.84/5.54 | | |
% 33.84/5.54 | | | GROUND_INST: instantiating (5) with 0, all_357_0, nil, simplifying with
% 33.84/5.54 | | | (1), (37) gives:
% 33.84/5.54 | | | (38) all_357_0 = 0
% 33.84/5.54 | | |
% 33.84/5.54 | | | REDUCE: (36), (38) imply:
% 33.84/5.55 | | | (39) $false
% 33.84/5.55 | | |
% 33.84/5.55 | | | CLOSE: (39) is inconsistent.
% 33.84/5.55 | | |
% 33.84/5.55 | | Case 2:
% 33.84/5.55 | | |
% 33.84/5.55 | | | (40) ( ~ (all_93_0 = 0) | ~ (all_93_1 = nil)) & (all_93_0 = 0 |
% 33.84/5.55 | | | all_93_1 = nil)
% 33.84/5.55 | | |
% 33.84/5.55 | | | ALPHA: (40) implies:
% 33.84/5.55 | | | (41) all_93_0 = 0 | all_93_1 = nil
% 33.84/5.55 | | |
% 33.84/5.55 | | | BETA: splitting (32) gives:
% 33.84/5.55 | | |
% 33.84/5.55 | | | Case 1:
% 33.84/5.55 | | | |
% 33.84/5.55 | | | | (42) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) = v0)
% 33.84/5.55 | | | |
% 33.84/5.55 | | | | DELTA: instantiating (42) with fresh symbol all_366_0 gives:
% 33.84/5.55 | | | | (43) ~ (all_366_0 = 0) & ssList(all_101_0) = all_366_0
% 33.84/5.55 | | | |
% 33.84/5.55 | | | | ALPHA: (43) implies:
% 33.84/5.55 | | | | (44) ~ (all_366_0 = 0)
% 33.84/5.55 | | | | (45) ssList(all_101_0) = all_366_0
% 33.84/5.55 | | | |
% 33.84/5.55 | | | | GROUND_INST: instantiating (5) with 0, all_366_0, all_101_0, simplifying
% 33.84/5.55 | | | | with (24), (45) gives:
% 33.84/5.55 | | | | (46) all_366_0 = 0
% 33.84/5.55 | | | |
% 33.84/5.55 | | | | REDUCE: (44), (46) imply:
% 33.84/5.55 | | | | (47) $false
% 33.84/5.55 | | | |
% 33.84/5.55 | | | | CLOSE: (47) is inconsistent.
% 33.84/5.55 | | | |
% 33.84/5.55 | | | Case 2:
% 33.84/5.55 | | | |
% 33.84/5.55 | | | | (48) ( ~ (all_101_0 = nil) | ~ (all_93_1 = nil) | all_97_2 = nil) &
% 33.84/5.55 | | | | ( ~ (all_97_2 = nil) | (all_101_0 = nil & all_93_1 = nil))
% 33.84/5.55 | | | |
% 33.84/5.55 | | | | ALPHA: (48) implies:
% 33.84/5.55 | | | | (49) ~ (all_97_2 = nil) | (all_101_0 = nil & all_93_1 = nil)
% 33.84/5.55 | | | |
% 33.84/5.55 | | | | BETA: splitting (49) gives:
% 33.84/5.55 | | | |
% 33.84/5.55 | | | | Case 1:
% 33.84/5.55 | | | | |
% 33.84/5.55 | | | | | (50) ~ (all_97_2 = nil)
% 33.84/5.55 | | | | |
% 33.84/5.55 | | | | | BETA: splitting (18) gives:
% 33.84/5.55 | | | | |
% 33.84/5.55 | | | | | Case 1:
% 33.84/5.55 | | | | | |
% 33.84/5.55 | | | | | | (51) all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0))
% 33.84/5.55 | | | | | |
% 33.84/5.55 | | | | | | ALPHA: (51) implies:
% 33.84/5.55 | | | | | | (52) ~ (all_97_0 = 0) | ~ (all_93_0 = 0)
% 33.84/5.55 | | | | | |
% 33.84/5.55 | | | | | | BETA: splitting (41) gives:
% 33.84/5.55 | | | | | |
% 33.84/5.55 | | | | | | Case 1:
% 33.84/5.55 | | | | | | |
% 33.84/5.55 | | | | | | | (53) all_93_1 = nil
% 33.84/5.55 | | | | | | |
% 33.84/5.55 | | | | | | | REDUCE: (33), (53) imply:
% 33.84/5.55 | | | | | | | (54) $false
% 33.84/5.55 | | | | | | |
% 33.84/5.55 | | | | | | | CLOSE: (54) is inconsistent.
% 33.84/5.55 | | | | | | |
% 33.84/5.55 | | | | | | Case 2:
% 33.84/5.55 | | | | | | |
% 33.84/5.55 | | | | | | | (55) all_93_0 = 0
% 33.84/5.55 | | | | | | |
% 33.84/5.55 | | | | | | | BETA: splitting (52) gives:
% 33.84/5.55 | | | | | | |
% 33.84/5.55 | | | | | | | Case 1:
% 33.84/5.55 | | | | | | | |
% 33.84/5.55 | | | | | | | | (56) ~ (all_97_0 = 0)
% 33.84/5.55 | | | | | | | |
% 33.84/5.55 | | | | | | | | BETA: splitting (31) gives:
% 33.84/5.55 | | | | | | | |
% 33.84/5.55 | | | | | | | | Case 1:
% 33.84/5.55 | | | | | | | | |
% 33.84/5.55 | | | | | | | | | (57) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_93_1) = v0)
% 33.84/5.55 | | | | | | | | |
% 33.84/5.55 | | | | | | | | | DELTA: instantiating (57) with fresh symbol all_391_0 gives:
% 33.84/5.55 | | | | | | | | | (58) ~ (all_391_0 = 0) & ssList(all_93_1) = all_391_0
% 33.84/5.55 | | | | | | | | |
% 33.84/5.55 | | | | | | | | | ALPHA: (58) implies:
% 33.84/5.55 | | | | | | | | | (59) ~ (all_391_0 = 0)
% 33.84/5.55 | | | | | | | | | (60) ssList(all_93_1) = all_391_0
% 33.84/5.55 | | | | | | | | |
% 33.84/5.55 | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_391_0, all_93_1,
% 33.84/5.55 | | | | | | | | | simplifying with (9), (60) gives:
% 33.84/5.55 | | | | | | | | | (61) all_391_0 = 0
% 33.84/5.55 | | | | | | | | |
% 33.84/5.55 | | | | | | | | | REDUCE: (59), (61) imply:
% 33.84/5.55 | | | | | | | | | (62) $false
% 33.84/5.55 | | | | | | | | |
% 33.84/5.55 | | | | | | | | | CLOSE: (62) is inconsistent.
% 33.84/5.55 | | | | | | | | |
% 33.84/5.55 | | | | | | | | Case 2:
% 33.84/5.55 | | | | | | | | |
% 33.84/5.55 | | | | | | | | | (63) ( ~ (all_97_0 = 0) | ? [v0: $i] : (ssList(v0) = 0 &
% 33.84/5.55 | | | | | | | | | app(all_93_1, v0) = all_97_2 & $i(v0))) &
% 33.84/5.55 | | | | | | | | | (all_97_0 = 0 | ! [v0: $i] : ( ~ (app(all_93_1, v0) =
% 33.84/5.55 | | | | | | | | | all_97_2) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 =
% 33.84/5.55 | | | | | | | | | 0) & ssList(v0) = v1)))
% 33.84/5.55 | | | | | | | | |
% 33.84/5.55 | | | | | | | | | ALPHA: (63) implies:
% 33.84/5.55 | | | | | | | | | (64) all_97_0 = 0 | ! [v0: $i] : ( ~ (app(all_93_1, v0) =
% 33.84/5.55 | | | | | | | | | all_97_2) | ~ $i(v0) | ? [v1: int] : ( ~ (v1 =
% 33.84/5.55 | | | | | | | | | 0) & ssList(v0) = v1))
% 33.84/5.55 | | | | | | | | |
% 33.84/5.55 | | | | | | | | | BETA: splitting (64) gives:
% 33.84/5.55 | | | | | | | | |
% 33.84/5.55 | | | | | | | | | Case 1:
% 33.84/5.55 | | | | | | | | | |
% 33.84/5.55 | | | | | | | | | | (65) all_97_0 = 0
% 33.84/5.55 | | | | | | | | | |
% 33.84/5.55 | | | | | | | | | | REDUCE: (56), (65) imply:
% 33.84/5.55 | | | | | | | | | | (66) $false
% 33.84/5.55 | | | | | | | | | |
% 33.84/5.55 | | | | | | | | | | CLOSE: (66) is inconsistent.
% 33.84/5.55 | | | | | | | | | |
% 33.84/5.55 | | | | | | | | | Case 2:
% 33.84/5.55 | | | | | | | | | |
% 33.84/5.55 | | | | | | | | | | (67) ! [v0: $i] : ( ~ (app(all_93_1, v0) = all_97_2) |
% 33.84/5.55 | | | | | | | | | | ~ $i(v0) | ? [v1: int] : ( ~ (v1 = 0) &
% 33.84/5.55 | | | | | | | | | | ssList(v0) = v1))
% 33.84/5.55 | | | | | | | | | |
% 33.84/5.55 | | | | | | | | | | GROUND_INST: instantiating (67) with all_101_0, simplifying
% 33.84/5.55 | | | | | | | | | | with (22), (23) gives:
% 33.84/5.55 | | | | | | | | | | (68) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) =
% 33.84/5.55 | | | | | | | | | | v0)
% 33.84/5.55 | | | | | | | | | |
% 33.84/5.55 | | | | | | | | | | DELTA: instantiating (68) with fresh symbol all_395_0 gives:
% 33.84/5.55 | | | | | | | | | | (69) ~ (all_395_0 = 0) & ssList(all_101_0) = all_395_0
% 33.84/5.55 | | | | | | | | | |
% 33.84/5.55 | | | | | | | | | | ALPHA: (69) implies:
% 33.84/5.55 | | | | | | | | | | (70) ~ (all_395_0 = 0)
% 33.84/5.55 | | | | | | | | | | (71) ssList(all_101_0) = all_395_0
% 33.84/5.55 | | | | | | | | | |
% 33.84/5.56 | | | | | | | | | | GROUND_INST: instantiating (5) with 0, all_395_0, all_101_0,
% 33.84/5.56 | | | | | | | | | | simplifying with (24), (71) gives:
% 33.84/5.56 | | | | | | | | | | (72) all_395_0 = 0
% 33.84/5.56 | | | | | | | | | |
% 33.84/5.56 | | | | | | | | | | REDUCE: (70), (72) imply:
% 33.84/5.56 | | | | | | | | | | (73) $false
% 33.84/5.56 | | | | | | | | | |
% 33.84/5.56 | | | | | | | | | | CLOSE: (73) is inconsistent.
% 33.84/5.56 | | | | | | | | | |
% 33.84/5.56 | | | | | | | | | End of split
% 33.84/5.56 | | | | | | | | |
% 33.84/5.56 | | | | | | | | End of split
% 33.84/5.56 | | | | | | | |
% 33.84/5.56 | | | | | | | Case 2:
% 33.84/5.56 | | | | | | | |
% 33.84/5.56 | | | | | | | | (74) ~ (all_93_0 = 0)
% 33.84/5.56 | | | | | | | |
% 33.84/5.56 | | | | | | | | REDUCE: (55), (74) imply:
% 33.84/5.56 | | | | | | | | (75) $false
% 33.84/5.56 | | | | | | | |
% 33.84/5.56 | | | | | | | | CLOSE: (75) is inconsistent.
% 33.84/5.56 | | | | | | | |
% 33.84/5.56 | | | | | | | End of split
% 33.84/5.56 | | | | | | |
% 33.84/5.56 | | | | | | End of split
% 33.84/5.56 | | | | | |
% 33.84/5.56 | | | | | Case 2:
% 33.84/5.56 | | | | | |
% 33.84/5.56 | | | | | | (76) all_97_2 = nil & ~ (all_93_1 = nil)
% 33.84/5.56 | | | | | |
% 33.84/5.56 | | | | | | ALPHA: (76) implies:
% 33.84/5.56 | | | | | | (77) all_97_2 = nil
% 33.84/5.56 | | | | | |
% 33.84/5.56 | | | | | | REDUCE: (50), (77) imply:
% 33.84/5.56 | | | | | | (78) $false
% 33.84/5.56 | | | | | |
% 33.84/5.56 | | | | | | CLOSE: (78) is inconsistent.
% 33.84/5.56 | | | | | |
% 33.84/5.56 | | | | | End of split
% 33.84/5.56 | | | | |
% 33.84/5.56 | | | | Case 2:
% 33.84/5.56 | | | | |
% 33.84/5.56 | | | | | (79) all_97_2 = nil
% 33.84/5.56 | | | | | (80) all_101_0 = nil & all_93_1 = nil
% 33.84/5.56 | | | | |
% 33.84/5.56 | | | | | ALPHA: (80) implies:
% 33.84/5.56 | | | | | (81) all_93_1 = nil
% 33.84/5.56 | | | | |
% 33.84/5.56 | | | | | REF_CLOSE: (1), (5), (18), (30), (79), (81) are inconsistent by
% 33.84/5.56 | | | | | sub-proof #1.
% 33.84/5.56 | | | | |
% 33.84/5.56 | | | | End of split
% 33.84/5.56 | | | |
% 33.84/5.56 | | | End of split
% 33.84/5.56 | | |
% 33.84/5.56 | | End of split
% 33.84/5.56 | |
% 33.84/5.56 | Case 2:
% 33.84/5.56 | |
% 33.84/5.56 | | (82) all_93_1 = nil
% 33.84/5.56 | | (83) all_97_2 = nil
% 33.84/5.56 | |
% 33.84/5.56 | | REF_CLOSE: (1), (5), (18), (30), (82), (83) are inconsistent by sub-proof
% 33.84/5.56 | | #1.
% 33.84/5.56 | |
% 33.84/5.56 | End of split
% 33.84/5.56 |
% 33.84/5.56 End of proof
% 33.84/5.56
% 33.84/5.56 Sub-proof #1 shows that the following formulas are inconsistent:
% 33.84/5.56 ----------------------------------------------------------------
% 33.84/5.56 (1) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 33.84/5.56 (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 33.84/5.56 (2) ssList(nil) = 0
% 33.84/5.56 (3) all_93_1 = nil
% 33.84/5.56 (4) (all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0))) | (all_97_2 =
% 33.84/5.56 nil & ~ (all_93_1 = nil))
% 33.84/5.56 (5) all_97_2 = nil
% 33.84/5.56 (6) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_97_1 = 0) |
% 33.84/5.56 ~ (all_97_2 = nil)) & (all_97_1 = 0 | all_97_2 = nil))
% 33.84/5.56
% 33.84/5.56 Begin of proof
% 33.84/5.56 |
% 33.84/5.56 | BETA: splitting (4) gives:
% 33.84/5.56 |
% 33.84/5.56 | Case 1:
% 33.84/5.56 | |
% 33.84/5.56 | | (7) all_97_1 = 0 & ( ~ (all_97_0 = 0) | ~ (all_93_0 = 0))
% 33.84/5.56 | |
% 33.84/5.56 | | ALPHA: (7) implies:
% 33.84/5.56 | | (8) all_97_1 = 0
% 33.84/5.56 | |
% 33.84/5.56 | | BETA: splitting (6) gives:
% 33.84/5.56 | |
% 33.84/5.56 | | Case 1:
% 33.84/5.56 | | |
% 33.84/5.56 | | | (9) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 33.84/5.56 | | |
% 33.84/5.56 | | | DELTA: instantiating (9) with fresh symbol all_361_0 gives:
% 33.84/5.56 | | | (10) ~ (all_361_0 = 0) & ssList(nil) = all_361_0
% 33.84/5.56 | | |
% 33.84/5.56 | | | ALPHA: (10) implies:
% 33.84/5.56 | | | (11) ~ (all_361_0 = 0)
% 33.84/5.56 | | | (12) ssList(nil) = all_361_0
% 33.84/5.56 | | |
% 33.84/5.56 | | | DELTA: instantiating (9) with fresh symbol all_366_0 gives:
% 33.84/5.56 | | | (13) ~ (all_366_0 = 0) & ssList(nil) = all_366_0
% 33.84/5.56 | | |
% 33.84/5.56 | | | ALPHA: (13) implies:
% 33.84/5.56 | | | (14) ssList(nil) = all_366_0
% 33.84/5.56 | | |
% 33.84/5.56 | | | GROUND_INST: instantiating (1) with 0, all_366_0, nil, simplifying with
% 33.84/5.56 | | | (2), (14) gives:
% 33.84/5.56 | | | (15) all_366_0 = 0
% 33.84/5.56 | | |
% 33.84/5.56 | | | GROUND_INST: instantiating (1) with all_361_0, all_366_0, nil, simplifying
% 33.84/5.56 | | | with (12), (14) gives:
% 33.84/5.56 | | | (16) all_366_0 = all_361_0
% 33.84/5.56 | | |
% 33.84/5.56 | | | COMBINE_EQS: (15), (16) imply:
% 33.84/5.56 | | | (17) all_361_0 = 0
% 33.84/5.56 | | |
% 33.84/5.56 | | | REDUCE: (11), (17) imply:
% 33.84/5.56 | | | (18) $false
% 33.84/5.56 | | |
% 33.84/5.56 | | | CLOSE: (18) is inconsistent.
% 33.84/5.56 | | |
% 33.84/5.56 | | Case 2:
% 33.84/5.56 | | |
% 33.84/5.56 | | | (19) ( ~ (all_97_1 = 0) | ~ (all_97_2 = nil)) & (all_97_1 = 0 |
% 33.84/5.56 | | | all_97_2 = nil)
% 33.84/5.56 | | |
% 33.84/5.56 | | | ALPHA: (19) implies:
% 33.84/5.56 | | | (20) ~ (all_97_1 = 0) | ~ (all_97_2 = nil)
% 33.84/5.56 | | |
% 33.84/5.56 | | | BETA: splitting (20) gives:
% 33.84/5.56 | | |
% 33.84/5.56 | | | Case 1:
% 33.84/5.56 | | | |
% 33.84/5.56 | | | | (21) ~ (all_97_2 = nil)
% 33.84/5.56 | | | |
% 33.84/5.56 | | | | REDUCE: (5), (21) imply:
% 33.84/5.56 | | | | (22) $false
% 33.84/5.56 | | | |
% 33.84/5.56 | | | | CLOSE: (22) is inconsistent.
% 33.84/5.56 | | | |
% 33.84/5.56 | | | Case 2:
% 33.84/5.56 | | | |
% 33.84/5.56 | | | | (23) ~ (all_97_1 = 0)
% 33.84/5.56 | | | |
% 33.84/5.56 | | | | REDUCE: (8), (23) imply:
% 33.84/5.56 | | | | (24) $false
% 33.84/5.56 | | | |
% 33.84/5.56 | | | | CLOSE: (24) is inconsistent.
% 33.84/5.56 | | | |
% 33.84/5.56 | | | End of split
% 33.84/5.56 | | |
% 33.84/5.56 | | End of split
% 33.84/5.56 | |
% 33.84/5.56 | Case 2:
% 33.84/5.56 | |
% 33.84/5.56 | | (25) all_97_2 = nil & ~ (all_93_1 = nil)
% 33.84/5.56 | |
% 33.84/5.56 | | ALPHA: (25) implies:
% 33.84/5.56 | | (26) ~ (all_93_1 = nil)
% 33.84/5.56 | |
% 33.84/5.56 | | REDUCE: (3), (26) imply:
% 33.84/5.56 | | (27) $false
% 33.84/5.56 | |
% 33.84/5.56 | | CLOSE: (27) is inconsistent.
% 33.84/5.56 | |
% 33.84/5.56 | End of split
% 33.84/5.56 |
% 33.84/5.56 End of proof
% 33.84/5.56 % SZS output end Proof for theBenchmark
% 33.84/5.56
% 33.84/5.56 4963ms
%------------------------------------------------------------------------------