TSTP Solution File: SWC069+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC069+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 : n008.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 20:49:29 EDT 2023
% Result : Theorem 25.34s 4.16s
% Output : Proof 50.87s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SWC069+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.35 % Computer : n008.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Aug 28 18:18:47 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.62 ________ _____
% 0.21/0.62 ___ __ \_________(_)________________________________
% 0.21/0.62 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.62 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.62 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.62
% 0.21/0.62 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.62 (2023-06-19)
% 0.21/0.62
% 0.21/0.62 (c) Philipp Rümmer, 2009-2023
% 0.21/0.62 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.62 Amanda Stjerna.
% 0.21/0.62 Free software under BSD-3-Clause.
% 0.21/0.62
% 0.21/0.62 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.62
% 0.21/0.62 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.63 Running up to 7 provers in parallel.
% 0.21/0.65 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.65 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.65 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.65 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.65 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.65 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.65 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.53/1.46 Prover 1: Preprocessing ...
% 4.53/1.48 Prover 4: Preprocessing ...
% 5.00/1.52 Prover 3: Preprocessing ...
% 5.00/1.52 Prover 5: Preprocessing ...
% 5.00/1.52 Prover 6: Preprocessing ...
% 5.00/1.53 Prover 2: Preprocessing ...
% 5.00/1.53 Prover 0: Preprocessing ...
% 14.77/2.86 Prover 2: Proving ...
% 14.77/2.93 Prover 5: Constructing countermodel ...
% 15.73/2.97 Prover 1: Constructing countermodel ...
% 17.06/3.10 Prover 6: Proving ...
% 17.06/3.10 Prover 3: Constructing countermodel ...
% 23.74/3.99 Prover 4: Constructing countermodel ...
% 25.34/4.16 Prover 3: proved (3513ms)
% 25.34/4.16
% 25.34/4.16 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 25.34/4.16
% 25.34/4.16 Prover 6: stopped
% 25.34/4.16 Prover 2: stopped
% 25.34/4.16 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 25.34/4.16 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 25.34/4.17 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 25.34/4.17 Prover 5: stopped
% 25.34/4.19 Prover 0: Proving ...
% 25.34/4.19 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 25.34/4.19 Prover 0: stopped
% 25.34/4.20 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 26.06/4.44 Prover 11: Preprocessing ...
% 26.06/4.44 Prover 7: Preprocessing ...
% 26.88/4.47 Prover 10: Preprocessing ...
% 26.88/4.49 Prover 8: Preprocessing ...
% 26.88/4.51 Prover 13: Preprocessing ...
% 30.15/4.80 Prover 10: Constructing countermodel ...
% 30.15/4.81 Prover 7: Constructing countermodel ...
% 31.65/5.04 Prover 13: Constructing countermodel ...
% 31.65/5.11 Prover 8: Warning: ignoring some quantifiers
% 31.65/5.12 Prover 8: Constructing countermodel ...
% 39.79/6.07 Prover 11: Constructing countermodel ...
% 48.88/7.42 Prover 1: Found proof (size 84)
% 48.88/7.42 Prover 1: proved (6782ms)
% 48.88/7.42 Prover 7: stopped
% 48.88/7.42 Prover 10: stopped
% 48.88/7.43 Prover 8: stopped
% 48.88/7.43 Prover 11: stopped
% 48.88/7.43 Prover 13: stopped
% 48.88/7.43 Prover 4: stopped
% 48.88/7.43
% 48.88/7.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 48.88/7.43
% 48.88/7.43 % SZS output start Proof for theBenchmark
% 48.88/7.44 Assumptions after simplification:
% 48.88/7.44 ---------------------------------
% 48.88/7.44
% 48.88/7.44 (ax15)
% 50.34/7.46 ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2: any] :
% 50.34/7.46 ( ~ (neq(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 50.34/7.46 ssList(v1) = v3) | (( ~ (v2 = 0) | ~ (v1 = v0)) & (v2 = 0 | v1 = v0))))
% 50.34/7.46
% 50.34/7.47 (ax17)
% 50.34/7.47 ssList(nil) = 0 & $i(nil)
% 50.34/7.47
% 50.34/7.47 (ax20)
% 50.34/7.47 $i(nil) & ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1:
% 50.34/7.47 $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 50.34/7.47 ssItem(v2) = 0 & $i(v2))))
% 50.34/7.47
% 50.34/7.47 (ax44)
% 50.34/7.47 ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ( ~ (ssItem(v1)
% 50.34/7.47 = 0) | ~ $i(v1) | ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v0, v2) = v3) |
% 50.34/7.47 ~ $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v2) = v4) | ! [v4: $i]
% 50.34/7.47 : ! [v5: $i] : ! [v6: any] : ( ~ (frontsegP(v3, v5) = v6) | ~
% 50.34/7.47 (cons(v1, v4) = v5) | ~ $i(v4) | ? [v7: any] : ? [v8: any] :
% 50.34/7.47 (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 =
% 50.34/7.47 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 =
% 50.34/7.47 v0)))))))))
% 50.34/7.47
% 50.34/7.47 (co1)
% 50.34/7.48 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) =
% 50.34/7.48 0 & $i(v1) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: any] : (v2 =
% 50.34/7.48 v0 & neq(v1, nil) = v3 & ! [v4: $i] : ( ~ (neq(v4, nil) = 0) | ~
% 50.34/7.48 $i(v4) | ? [v5: any] : ? [v6: any] : ? [v7: any] : (segmentP(v1,
% 50.34/7.48 v4) = v6 & segmentP(v0, v4) = v7 & ssList(v4) = v5 & ( ~ (v7 =
% 50.34/7.48 0) | ~ (v6 = 0) | ~ (v5 = 0)))) & ( ~ (v3 = 0) | ? [v4: $i]
% 50.34/7.48 : (segmentP(v1, v4) = 0 & segmentP(v0, v4) = 0 & ssList(v4) = 0 &
% 50.34/7.48 neq(v4, nil) = 0 & $i(v4))) & ( ~ (v1 = nil) | ~ (v0 = nil)) & (
% 50.34/7.48 ~ (v1 = nil) | v0 = nil)))))
% 50.34/7.48
% 50.34/7.48 (function-axioms)
% 50.34/7.49 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 50.34/7.49 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 50.34/7.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 50.34/7.49 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 50.34/7.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 50.34/7.49 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 50.34/7.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 50.34/7.49 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 50.34/7.49 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 50.34/7.49 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 50.34/7.49 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 50.34/7.49 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 50.34/7.49 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 50.34/7.49 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 50.34/7.49 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 50.34/7.49 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 50.34/7.49 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 50.34/7.49 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 50.34/7.49 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 50.34/7.49 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 50.34/7.49 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 50.34/7.49 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 50.34/7.49 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 50.34/7.49 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 50.34/7.49 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 50.34/7.49 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 50.34/7.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 50.34/7.49 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 50.34/7.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 50.34/7.49 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 50.34/7.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 50.34/7.49 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 50.34/7.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 50.34/7.49 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 50.34/7.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 50.34/7.49 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 50.34/7.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 50.34/7.49 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 50.34/7.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 50.34/7.49 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 50.34/7.49 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 50.34/7.49 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 50.34/7.49 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 50.34/7.49
% 50.34/7.49 Further assumptions not needed in the proof:
% 50.34/7.49 --------------------------------------------
% 50.34/7.49 ax1, ax10, ax11, ax12, ax13, ax14, ax16, ax18, ax19, ax2, ax21, ax22, ax23,
% 50.34/7.49 ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32, ax33, ax34, ax35,
% 50.34/7.49 ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax45, ax46, ax47, ax48,
% 50.34/7.49 ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56, ax57, ax58, ax59, ax6,
% 50.34/7.49 ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68, ax69, ax7, ax70, ax71,
% 50.34/7.49 ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8, ax80, ax81, ax82, ax83,
% 50.34/7.49 ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92, ax93, ax94, ax95
% 50.34/7.49
% 50.34/7.49 Those formulas are unsatisfiable:
% 50.34/7.49 ---------------------------------
% 50.34/7.49
% 50.34/7.49 Begin of proof
% 50.34/7.49 |
% 50.34/7.49 | ALPHA: (ax17) implies:
% 50.34/7.49 | (1) ssList(nil) = 0
% 50.34/7.49 |
% 50.34/7.49 | ALPHA: (ax20) implies:
% 50.34/7.49 | (2) ! [v0: $i] : (v0 = nil | ~ (ssList(v0) = 0) | ~ $i(v0) | ? [v1: $i]
% 50.34/7.49 | : (ssList(v1) = 0 & $i(v1) & ? [v2: $i] : (cons(v2, v1) = v0 &
% 50.34/7.49 | ssItem(v2) = 0 & $i(v2))))
% 50.34/7.49 |
% 50.34/7.49 | ALPHA: (co1) implies:
% 50.34/7.50 | (3) $i(nil)
% 50.62/7.50 | (4) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0
% 50.62/7.50 | & $i(v1) & ? [v2: $i] : (ssList(v2) = 0 & $i(v2) & ? [v3: any] :
% 50.62/7.50 | (v2 = v0 & neq(v1, nil) = v3 & ! [v4: $i] : ( ~ (neq(v4, nil) =
% 50.62/7.50 | 0) | ~ $i(v4) | ? [v5: any] : ? [v6: any] : ? [v7: any]
% 50.62/7.50 | : (segmentP(v1, v4) = v6 & segmentP(v0, v4) = v7 & ssList(v4)
% 50.62/7.50 | = v5 & ( ~ (v7 = 0) | ~ (v6 = 0) | ~ (v5 = 0)))) & ( ~
% 50.62/7.50 | (v3 = 0) | ? [v4: $i] : (segmentP(v1, v4) = 0 & segmentP(v0,
% 50.62/7.50 | v4) = 0 & ssList(v4) = 0 & neq(v4, nil) = 0 & $i(v4))) &
% 50.62/7.50 | ( ~ (v1 = nil) | ~ (v0 = nil)) & ( ~ (v1 = nil) | v0 =
% 50.62/7.50 | nil)))))
% 50.62/7.50 |
% 50.62/7.50 | ALPHA: (function-axioms) implies:
% 50.62/7.51 | (5) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 50.62/7.51 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 50.62/7.51 | (6) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 50.62/7.51 | ! [v3: $i] : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3,
% 50.62/7.51 | v2) = v0))
% 50.62/7.51 |
% 50.62/7.51 | DELTA: instantiating (4) with fresh symbol all_93_0 gives:
% 50.62/7.51 | (7) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : (ssList(v0) = 0 &
% 50.62/7.51 | $i(v0) & ? [v1: $i] : (ssList(v1) = 0 & $i(v1) & ? [v2: any] : (v1
% 50.62/7.51 | = all_93_0 & neq(v0, nil) = v2 & ! [v3: $i] : ( ~ (neq(v3, nil)
% 50.62/7.51 | = 0) | ~ $i(v3) | ? [v4: any] : ? [v5: any] : ? [v6: any]
% 50.62/7.51 | : (segmentP(v0, v3) = v5 & segmentP(all_93_0, v3) = v6 &
% 50.62/7.51 | ssList(v3) = v4 & ( ~ (v6 = 0) | ~ (v5 = 0) | ~ (v4 = 0))))
% 50.62/7.51 | & ( ~ (v2 = 0) | ? [v3: $i] : (segmentP(v0, v3) = 0 &
% 50.62/7.51 | segmentP(all_93_0, v3) = 0 & ssList(v3) = 0 & neq(v3, nil) =
% 50.62/7.51 | 0 & $i(v3))) & ( ~ (v0 = nil) | ~ (all_93_0 = nil)) & ( ~
% 50.62/7.51 | (v0 = nil) | all_93_0 = nil))))
% 50.62/7.51 |
% 50.62/7.51 | ALPHA: (7) implies:
% 50.62/7.51 | (8) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0
% 50.62/7.51 | & $i(v1) & ? [v2: any] : (v1 = all_93_0 & neq(v0, nil) = v2 & !
% 50.62/7.51 | [v3: $i] : ( ~ (neq(v3, nil) = 0) | ~ $i(v3) | ? [v4: any] : ?
% 50.62/7.51 | [v5: any] : ? [v6: any] : (segmentP(v0, v3) = v5 &
% 50.62/7.51 | segmentP(all_93_0, v3) = v6 & ssList(v3) = v4 & ( ~ (v6 = 0)
% 50.62/7.51 | | ~ (v5 = 0) | ~ (v4 = 0)))) & ( ~ (v2 = 0) | ? [v3: $i]
% 50.62/7.51 | : (segmentP(v0, v3) = 0 & segmentP(all_93_0, v3) = 0 &
% 50.62/7.51 | ssList(v3) = 0 & neq(v3, nil) = 0 & $i(v3))) & ( ~ (v0 = nil)
% 50.62/7.51 | | ~ (all_93_0 = nil)) & ( ~ (v0 = nil) | all_93_0 = nil))))
% 50.62/7.51 |
% 50.62/7.51 | DELTA: instantiating (8) with fresh symbol all_97_0 gives:
% 50.62/7.51 | (9) ssList(all_97_0) = 0 & $i(all_97_0) & ? [v0: $i] : (ssList(v0) = 0 &
% 50.62/7.51 | $i(v0) & ? [v1: any] : (v0 = all_93_0 & neq(all_97_0, nil) = v1 & !
% 50.62/7.51 | [v2: $i] : ( ~ (neq(v2, nil) = 0) | ~ $i(v2) | ? [v3: any] : ?
% 50.62/7.51 | [v4: any] : ? [v5: any] : (segmentP(all_97_0, v2) = v4 &
% 50.62/7.51 | segmentP(all_93_0, v2) = v5 & ssList(v2) = v3 & ( ~ (v5 = 0) |
% 50.62/7.51 | ~ (v4 = 0) | ~ (v3 = 0)))) & ( ~ (v1 = 0) | ? [v2: $i] :
% 50.62/7.51 | (segmentP(all_97_0, v2) = 0 & segmentP(all_93_0, v2) = 0 &
% 50.62/7.51 | ssList(v2) = 0 & neq(v2, nil) = 0 & $i(v2))) & ( ~ (all_97_0 =
% 50.62/7.51 | nil) | ~ (all_93_0 = nil)) & ( ~ (all_97_0 = nil) | all_93_0 =
% 50.62/7.51 | nil)))
% 50.62/7.51 |
% 50.62/7.51 | ALPHA: (9) implies:
% 50.62/7.51 | (10) $i(all_97_0)
% 50.62/7.52 | (11) ssList(all_97_0) = 0
% 50.62/7.52 | (12) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: any] : (v0 = all_93_0
% 50.62/7.52 | & neq(all_97_0, nil) = v1 & ! [v2: $i] : ( ~ (neq(v2, nil) = 0) |
% 50.62/7.52 | ~ $i(v2) | ? [v3: any] : ? [v4: any] : ? [v5: any] :
% 50.62/7.52 | (segmentP(all_97_0, v2) = v4 & segmentP(all_93_0, v2) = v5 &
% 50.62/7.52 | ssList(v2) = v3 & ( ~ (v5 = 0) | ~ (v4 = 0) | ~ (v3 = 0))))
% 50.62/7.52 | & ( ~ (v1 = 0) | ? [v2: $i] : (segmentP(all_97_0, v2) = 0 &
% 50.62/7.52 | segmentP(all_93_0, v2) = 0 & ssList(v2) = 0 & neq(v2, nil) = 0
% 50.62/7.52 | & $i(v2))) & ( ~ (all_97_0 = nil) | ~ (all_93_0 = nil)) & ( ~
% 50.62/7.52 | (all_97_0 = nil) | all_93_0 = nil)))
% 50.62/7.52 |
% 50.62/7.52 | DELTA: instantiating (12) with fresh symbol all_99_0 gives:
% 50.62/7.52 | (13) ssList(all_99_0) = 0 & $i(all_99_0) & ? [v0: any] : (all_99_0 =
% 50.62/7.52 | all_93_0 & neq(all_97_0, nil) = v0 & ! [v1: $i] : ( ~ (neq(v1, nil)
% 50.62/7.52 | = 0) | ~ $i(v1) | ? [v2: any] : ? [v3: any] : ? [v4: any] :
% 50.62/7.52 | (segmentP(all_97_0, v1) = v3 & segmentP(all_93_0, v1) = v4 &
% 50.62/7.52 | ssList(v1) = v2 & ( ~ (v4 = 0) | ~ (v3 = 0) | ~ (v2 = 0)))) &
% 50.62/7.52 | ( ~ (v0 = 0) | ? [v1: $i] : (segmentP(all_97_0, v1) = 0 &
% 50.62/7.52 | segmentP(all_93_0, v1) = 0 & ssList(v1) = 0 & neq(v1, nil) = 0 &
% 50.62/7.52 | $i(v1))) & ( ~ (all_97_0 = nil) | ~ (all_93_0 = nil)) & ( ~
% 50.62/7.52 | (all_97_0 = nil) | all_93_0 = nil))
% 50.62/7.52 |
% 50.62/7.52 | ALPHA: (13) implies:
% 50.62/7.52 | (14) ? [v0: any] : (all_99_0 = all_93_0 & neq(all_97_0, nil) = v0 & !
% 50.62/7.52 | [v1: $i] : ( ~ (neq(v1, nil) = 0) | ~ $i(v1) | ? [v2: any] : ?
% 50.62/7.52 | [v3: any] : ? [v4: any] : (segmentP(all_97_0, v1) = v3 &
% 50.62/7.52 | segmentP(all_93_0, v1) = v4 & ssList(v1) = v2 & ( ~ (v4 = 0) |
% 50.62/7.52 | ~ (v3 = 0) | ~ (v2 = 0)))) & ( ~ (v0 = 0) | ? [v1: $i] :
% 50.62/7.52 | (segmentP(all_97_0, v1) = 0 & segmentP(all_93_0, v1) = 0 &
% 50.62/7.52 | ssList(v1) = 0 & neq(v1, nil) = 0 & $i(v1))) & ( ~ (all_97_0 =
% 50.62/7.52 | nil) | ~ (all_93_0 = nil)) & ( ~ (all_97_0 = nil) | all_93_0 =
% 50.62/7.52 | nil))
% 50.62/7.52 |
% 50.62/7.52 | DELTA: instantiating (14) with fresh symbol all_101_0 gives:
% 50.62/7.52 | (15) all_99_0 = all_93_0 & neq(all_97_0, nil) = all_101_0 & ! [v0: $i] : (
% 50.62/7.52 | ~ (neq(v0, nil) = 0) | ~ $i(v0) | ? [v1: any] : ? [v2: any] : ?
% 50.62/7.52 | [v3: any] : (segmentP(all_97_0, v0) = v2 & segmentP(all_93_0, v0) =
% 50.62/7.52 | v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))
% 50.62/7.52 | & ( ~ (all_101_0 = 0) | ? [v0: $i] : (segmentP(all_97_0, v0) = 0 &
% 50.62/7.52 | segmentP(all_93_0, v0) = 0 & ssList(v0) = 0 & neq(v0, nil) = 0 &
% 50.62/7.52 | $i(v0))) & ( ~ (all_97_0 = nil) | ~ (all_93_0 = nil)) & ( ~
% 50.62/7.52 | (all_97_0 = nil) | all_93_0 = nil)
% 50.62/7.52 |
% 50.62/7.52 | ALPHA: (15) implies:
% 50.62/7.52 | (16) neq(all_97_0, nil) = all_101_0
% 50.62/7.52 | (17) ~ (all_97_0 = nil) | all_93_0 = nil
% 50.62/7.52 | (18) ~ (all_97_0 = nil) | ~ (all_93_0 = nil)
% 50.62/7.53 | (19) ~ (all_101_0 = 0) | ? [v0: $i] : (segmentP(all_97_0, v0) = 0 &
% 50.62/7.53 | segmentP(all_93_0, v0) = 0 & ssList(v0) = 0 & neq(v0, nil) = 0 &
% 50.62/7.53 | $i(v0))
% 50.62/7.53 | (20) ! [v0: $i] : ( ~ (neq(v0, nil) = 0) | ~ $i(v0) | ? [v1: any] : ?
% 50.62/7.53 | [v2: any] : ? [v3: any] : (segmentP(all_97_0, v0) = v2 &
% 50.62/7.53 | segmentP(all_93_0, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | ~
% 50.62/7.53 | (v2 = 0) | ~ (v1 = 0))))
% 50.62/7.53 |
% 50.62/7.53 | GROUND_INST: instantiating (2) with all_97_0, simplifying with (10), (11)
% 50.62/7.53 | gives:
% 50.62/7.53 | (21) all_97_0 = nil | ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i]
% 50.62/7.53 | : (cons(v1, v0) = all_97_0 & ssItem(v1) = 0 & $i(v1)))
% 50.62/7.53 |
% 50.62/7.53 | GROUND_INST: instantiating (ax15) with all_97_0, simplifying with (10), (11)
% 50.62/7.53 | gives:
% 50.62/7.53 | (22) ! [v0: $i] : ! [v1: any] : ( ~ (neq(all_97_0, v0) = v1) | ~ $i(v0)
% 50.62/7.53 | | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = 0) |
% 50.62/7.53 | ~ (v0 = all_97_0)) & (v1 = 0 | v0 = all_97_0)))
% 50.62/7.53 |
% 50.62/7.53 | GROUND_INST: instantiating (22) with nil, all_101_0, simplifying with (3),
% 50.62/7.53 | (16) gives:
% 50.62/7.53 | (23) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0) | (( ~ (all_101_0 = 0)
% 50.62/7.53 | | ~ (all_97_0 = nil)) & (all_101_0 = 0 | all_97_0 = nil))
% 50.62/7.53 |
% 50.62/7.53 | BETA: splitting (17) gives:
% 50.62/7.53 |
% 50.62/7.53 | Case 1:
% 50.62/7.53 | |
% 50.62/7.53 | | (24) ~ (all_97_0 = nil)
% 50.62/7.53 | |
% 50.62/7.53 | | BETA: splitting (23) gives:
% 50.62/7.53 | |
% 50.62/7.53 | | Case 1:
% 50.62/7.53 | | |
% 50.62/7.53 | | | (25) ? [v0: int] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 50.62/7.53 | | |
% 50.62/7.53 | | | DELTA: instantiating (25) with fresh symbol all_279_0 gives:
% 50.62/7.53 | | | (26) ~ (all_279_0 = 0) & ssList(nil) = all_279_0
% 50.62/7.53 | | |
% 50.62/7.53 | | | ALPHA: (26) implies:
% 50.62/7.53 | | | (27) ~ (all_279_0 = 0)
% 50.62/7.53 | | | (28) ssList(nil) = all_279_0
% 50.62/7.53 | | |
% 50.62/7.53 | | | DELTA: instantiating (25) with fresh symbol all_281_0 gives:
% 50.62/7.53 | | | (29) ~ (all_281_0 = 0) & ssList(nil) = all_281_0
% 50.62/7.53 | | |
% 50.62/7.53 | | | ALPHA: (29) implies:
% 50.62/7.53 | | | (30) ssList(nil) = all_281_0
% 50.62/7.53 | | |
% 50.62/7.53 | | | GROUND_INST: instantiating (5) with 0, all_281_0, nil, simplifying with
% 50.62/7.53 | | | (1), (30) gives:
% 50.62/7.53 | | | (31) all_281_0 = 0
% 50.62/7.53 | | |
% 50.62/7.53 | | | GROUND_INST: instantiating (5) with all_279_0, all_281_0, nil, simplifying
% 50.62/7.53 | | | with (28), (30) gives:
% 50.62/7.53 | | | (32) all_281_0 = all_279_0
% 50.62/7.53 | | |
% 50.62/7.53 | | | COMBINE_EQS: (31), (32) imply:
% 50.62/7.53 | | | (33) all_279_0 = 0
% 50.62/7.53 | | |
% 50.62/7.53 | | | REDUCE: (27), (33) imply:
% 50.62/7.53 | | | (34) $false
% 50.62/7.53 | | |
% 50.62/7.54 | | | CLOSE: (34) is inconsistent.
% 50.62/7.54 | | |
% 50.62/7.54 | | Case 2:
% 50.62/7.54 | | |
% 50.62/7.54 | | | (35) ( ~ (all_101_0 = 0) | ~ (all_97_0 = nil)) & (all_101_0 = 0 |
% 50.62/7.54 | | | all_97_0 = nil)
% 50.62/7.54 | | |
% 50.62/7.54 | | | ALPHA: (35) implies:
% 50.62/7.54 | | | (36) all_101_0 = 0 | all_97_0 = nil
% 50.62/7.54 | | |
% 50.62/7.54 | | | BETA: splitting (36) gives:
% 50.62/7.54 | | |
% 50.62/7.54 | | | Case 1:
% 50.62/7.54 | | | |
% 50.62/7.54 | | | | (37) all_97_0 = nil
% 50.62/7.54 | | | |
% 50.62/7.54 | | | | REDUCE: (24), (37) imply:
% 50.62/7.54 | | | | (38) $false
% 50.62/7.54 | | | |
% 50.62/7.54 | | | | CLOSE: (38) is inconsistent.
% 50.62/7.54 | | | |
% 50.62/7.54 | | | Case 2:
% 50.62/7.54 | | | |
% 50.62/7.54 | | | | (39) all_101_0 = 0
% 50.62/7.54 | | | |
% 50.62/7.54 | | | | BETA: splitting (21) gives:
% 50.62/7.54 | | | |
% 50.62/7.54 | | | | Case 1:
% 50.62/7.54 | | | | |
% 50.62/7.54 | | | | | (40) all_97_0 = nil
% 50.62/7.54 | | | | |
% 50.62/7.54 | | | | | REDUCE: (24), (40) imply:
% 50.62/7.54 | | | | | (41) $false
% 50.62/7.54 | | | | |
% 50.62/7.54 | | | | | CLOSE: (41) is inconsistent.
% 50.62/7.54 | | | | |
% 50.62/7.54 | | | | Case 2:
% 50.62/7.54 | | | | |
% 50.62/7.54 | | | | | (42) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] :
% 50.62/7.54 | | | | | (cons(v1, v0) = all_97_0 & ssItem(v1) = 0 & $i(v1)))
% 50.62/7.54 | | | | |
% 50.62/7.54 | | | | | DELTA: instantiating (42) with fresh symbol all_309_0 gives:
% 50.62/7.54 | | | | | (43) ssList(all_309_0) = 0 & $i(all_309_0) & ? [v0: $i] :
% 50.62/7.54 | | | | | (cons(v0, all_309_0) = all_97_0 & ssItem(v0) = 0 & $i(v0))
% 50.62/7.54 | | | | |
% 50.62/7.54 | | | | | ALPHA: (43) implies:
% 50.62/7.54 | | | | | (44) $i(all_309_0)
% 50.62/7.54 | | | | | (45) ssList(all_309_0) = 0
% 50.62/7.54 | | | | | (46) ? [v0: $i] : (cons(v0, all_309_0) = all_97_0 & ssItem(v0) = 0
% 50.62/7.54 | | | | | & $i(v0))
% 50.62/7.54 | | | | |
% 50.62/7.54 | | | | | DELTA: instantiating (46) with fresh symbol all_311_0 gives:
% 50.62/7.54 | | | | | (47) cons(all_311_0, all_309_0) = all_97_0 & ssItem(all_311_0) = 0
% 50.62/7.54 | | | | | & $i(all_311_0)
% 50.62/7.54 | | | | |
% 50.62/7.54 | | | | | ALPHA: (47) implies:
% 50.62/7.54 | | | | | (48) $i(all_311_0)
% 50.62/7.54 | | | | | (49) ssItem(all_311_0) = 0
% 50.62/7.54 | | | | | (50) cons(all_311_0, all_309_0) = all_97_0
% 50.62/7.54 | | | | |
% 50.62/7.54 | | | | | BETA: splitting (19) gives:
% 50.62/7.54 | | | | |
% 50.62/7.54 | | | | | Case 1:
% 50.62/7.54 | | | | | |
% 50.62/7.54 | | | | | | (51) ~ (all_101_0 = 0)
% 50.62/7.54 | | | | | |
% 50.62/7.54 | | | | | | REDUCE: (39), (51) imply:
% 50.62/7.54 | | | | | | (52) $false
% 50.62/7.54 | | | | | |
% 50.62/7.54 | | | | | | CLOSE: (52) is inconsistent.
% 50.62/7.54 | | | | | |
% 50.62/7.54 | | | | | Case 2:
% 50.62/7.54 | | | | | |
% 50.62/7.54 | | | | | | (53) ? [v0: $i] : (segmentP(all_97_0, v0) = 0 &
% 50.62/7.54 | | | | | | segmentP(all_93_0, v0) = 0 & ssList(v0) = 0 & neq(v0, nil)
% 50.62/7.54 | | | | | | = 0 & $i(v0))
% 50.62/7.54 | | | | | |
% 50.62/7.54 | | | | | | DELTA: instantiating (53) with fresh symbol all_317_0 gives:
% 50.62/7.54 | | | | | | (54) segmentP(all_97_0, all_317_0) = 0 & segmentP(all_93_0,
% 50.62/7.54 | | | | | | all_317_0) = 0 & ssList(all_317_0) = 0 & neq(all_317_0,
% 50.62/7.54 | | | | | | nil) = 0 & $i(all_317_0)
% 50.62/7.54 | | | | | |
% 50.62/7.54 | | | | | | ALPHA: (54) implies:
% 50.62/7.54 | | | | | | (55) $i(all_317_0)
% 50.62/7.54 | | | | | | (56) neq(all_317_0, nil) = 0
% 50.62/7.54 | | | | | | (57) ssList(all_317_0) = 0
% 50.62/7.54 | | | | | | (58) segmentP(all_93_0, all_317_0) = 0
% 50.62/7.54 | | | | | | (59) segmentP(all_97_0, all_317_0) = 0
% 50.62/7.54 | | | | | |
% 50.62/7.54 | | | | | | GROUND_INST: instantiating (ax44) with all_311_0, simplifying with
% 50.62/7.54 | | | | | | (48), (49) gives:
% 50.62/7.54 | | | | | | (60) ! [v0: $i] : ( ~ (ssItem(v0) = 0) | ~ $i(v0) | ! [v1: $i]
% 50.62/7.55 | | | | | | : ! [v2: $i] : ( ~ (cons(all_311_0, v1) = v2) | ~ $i(v1)
% 50.62/7.55 | | | | | | | ? [v3: int] : ( ~ (v3 = 0) & ssList(v1) = v3) | !
% 50.62/7.55 | | | | | | [v3: $i] : ! [v4: $i] : ! [v5: any] : ( ~
% 50.62/7.55 | | | | | | (frontsegP(v2, v4) = v5) | ~ (cons(v0, v3) = v4) | ~
% 50.62/7.55 | | | | | | $i(v3) | ? [v6: any] : ? [v7: any] : (frontsegP(v1,
% 50.62/7.55 | | | | | | v3) = v7 & ssList(v3) = v6 & ( ~ (v6 = 0) | (( ~
% 50.62/7.55 | | | | | | (v7 = 0) | ~ (v0 = all_311_0) | v5 = 0) & ( ~
% 50.62/7.55 | | | | | | (v5 = 0) | (v7 = 0 & v0 = all_311_0))))))))
% 50.62/7.55 | | | | | |
% 50.62/7.55 | | | | | | GROUND_INST: instantiating (20) with all_317_0, simplifying with
% 50.62/7.55 | | | | | | (55), (56) gives:
% 50.62/7.55 | | | | | | (61) ? [v0: any] : ? [v1: any] : ? [v2: any] :
% 50.62/7.55 | | | | | | (segmentP(all_97_0, all_317_0) = v1 & segmentP(all_93_0,
% 50.62/7.55 | | | | | | all_317_0) = v2 & ssList(all_317_0) = v0 & ( ~ (v2 = 0)
% 50.62/7.55 | | | | | | | ~ (v1 = 0) | ~ (v0 = 0)))
% 50.62/7.55 | | | | | |
% 50.62/7.55 | | | | | | GROUND_INST: instantiating (60) with all_311_0, simplifying with
% 50.62/7.55 | | | | | | (48), (49) gives:
% 50.62/7.55 | | | | | | (62) ! [v0: $i] : ! [v1: $i] : ( ~ (cons(all_311_0, v0) = v1) |
% 50.62/7.55 | | | | | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2)
% 50.62/7.55 | | | | | | | ! [v2: $i] : ! [v3: $i] : ! [v4: any] : ( ~
% 50.62/7.55 | | | | | | (frontsegP(v1, v3) = v4) | ~ (cons(all_311_0, v2) = v3)
% 50.62/7.55 | | | | | | | ~ $i(v2) | ? [v5: any] : ? [v6: any] :
% 50.62/7.55 | | | | | | (frontsegP(v0, v2) = v6 & ssList(v2) = v5 & ( ~ (v5 = 0)
% 50.62/7.55 | | | | | | | (( ~ (v6 = 0) | v4 = 0) & ( ~ (v4 = 0) | v6 =
% 50.62/7.55 | | | | | | 0))))))
% 50.62/7.55 | | | | | |
% 50.62/7.55 | | | | | | GROUND_INST: instantiating (62) with all_309_0, all_97_0,
% 50.62/7.55 | | | | | | simplifying with (44), (50) gives:
% 50.62/7.55 | | | | | | (63) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_309_0) = v0) | !
% 50.62/7.55 | | | | | | [v0: $i] : ! [v1: $i] : ! [v2: any] : ( ~
% 50.62/7.55 | | | | | | (frontsegP(all_97_0, v1) = v2) | ~ (cons(all_311_0, v0) =
% 50.62/7.55 | | | | | | v1) | ~ $i(v0) | ? [v3: any] : ? [v4: any] :
% 50.62/7.55 | | | | | | (frontsegP(all_309_0, v0) = v4 & ssList(v0) = v3 & ( ~ (v3
% 50.62/7.55 | | | | | | = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 =
% 50.62/7.55 | | | | | | 0)))))
% 50.62/7.55 | | | | | |
% 50.62/7.55 | | | | | | DELTA: instantiating (61) with fresh symbols all_684_0, all_684_1,
% 50.62/7.55 | | | | | | all_684_2 gives:
% 50.62/7.55 | | | | | | (64) segmentP(all_97_0, all_317_0) = all_684_1 &
% 50.62/7.55 | | | | | | segmentP(all_93_0, all_317_0) = all_684_0 &
% 50.62/7.55 | | | | | | ssList(all_317_0) = all_684_2 & ( ~ (all_684_0 = 0) | ~
% 50.62/7.55 | | | | | | (all_684_1 = 0) | ~ (all_684_2 = 0))
% 50.62/7.55 | | | | | |
% 50.62/7.55 | | | | | | ALPHA: (64) implies:
% 50.62/7.55 | | | | | | (65) ssList(all_317_0) = all_684_2
% 50.62/7.55 | | | | | | (66) segmentP(all_93_0, all_317_0) = all_684_0
% 50.62/7.55 | | | | | | (67) segmentP(all_97_0, all_317_0) = all_684_1
% 50.62/7.55 | | | | | | (68) ~ (all_684_0 = 0) | ~ (all_684_1 = 0) | ~ (all_684_2 = 0)
% 50.62/7.55 | | | | | |
% 50.62/7.55 | | | | | | BETA: splitting (63) gives:
% 50.62/7.55 | | | | | |
% 50.62/7.55 | | | | | | Case 1:
% 50.62/7.55 | | | | | | |
% 50.62/7.55 | | | | | | | (69) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_309_0) = v0)
% 50.62/7.55 | | | | | | |
% 50.62/7.55 | | | | | | | DELTA: instantiating (69) with fresh symbol all_711_0 gives:
% 50.62/7.55 | | | | | | | (70) ~ (all_711_0 = 0) & ssList(all_309_0) = all_711_0
% 50.62/7.55 | | | | | | |
% 50.62/7.55 | | | | | | | ALPHA: (70) implies:
% 50.62/7.55 | | | | | | | (71) ~ (all_711_0 = 0)
% 50.62/7.55 | | | | | | | (72) ssList(all_309_0) = all_711_0
% 50.62/7.55 | | | | | | |
% 50.62/7.55 | | | | | | | DELTA: instantiating (69) with fresh symbol all_713_0 gives:
% 50.62/7.55 | | | | | | | (73) ~ (all_713_0 = 0) & ssList(all_309_0) = all_713_0
% 50.62/7.55 | | | | | | |
% 50.62/7.55 | | | | | | | ALPHA: (73) implies:
% 50.62/7.55 | | | | | | | (74) ssList(all_309_0) = all_713_0
% 50.62/7.55 | | | | | | |
% 50.62/7.55 | | | | | | | DELTA: instantiating (69) with fresh symbol all_715_0 gives:
% 50.62/7.55 | | | | | | | (75) ~ (all_715_0 = 0) & ssList(all_309_0) = all_715_0
% 50.62/7.55 | | | | | | |
% 50.62/7.55 | | | | | | | ALPHA: (75) implies:
% 50.62/7.55 | | | | | | | (76) ssList(all_309_0) = all_715_0
% 50.62/7.55 | | | | | | |
% 50.62/7.55 | | | | | | | GROUND_INST: instantiating (5) with 0, all_715_0, all_309_0,
% 50.62/7.55 | | | | | | | simplifying with (45), (76) gives:
% 50.87/7.55 | | | | | | | (77) all_715_0 = 0
% 50.87/7.55 | | | | | | |
% 50.87/7.55 | | | | | | | GROUND_INST: instantiating (5) with all_713_0, all_715_0,
% 50.87/7.55 | | | | | | | all_309_0, simplifying with (74), (76) gives:
% 50.87/7.55 | | | | | | | (78) all_715_0 = all_713_0
% 50.87/7.55 | | | | | | |
% 50.87/7.55 | | | | | | | GROUND_INST: instantiating (5) with all_711_0, all_715_0,
% 50.87/7.55 | | | | | | | all_309_0, simplifying with (72), (76) gives:
% 50.87/7.55 | | | | | | | (79) all_715_0 = all_711_0
% 50.87/7.55 | | | | | | |
% 50.87/7.55 | | | | | | | COMBINE_EQS: (78), (79) imply:
% 50.87/7.55 | | | | | | | (80) all_713_0 = all_711_0
% 50.87/7.55 | | | | | | |
% 50.87/7.55 | | | | | | | COMBINE_EQS: (77), (78) imply:
% 50.87/7.55 | | | | | | | (81) all_713_0 = 0
% 50.87/7.55 | | | | | | |
% 50.87/7.55 | | | | | | | COMBINE_EQS: (80), (81) imply:
% 50.87/7.55 | | | | | | | (82) all_711_0 = 0
% 50.87/7.55 | | | | | | |
% 50.87/7.55 | | | | | | | REDUCE: (71), (82) imply:
% 50.87/7.55 | | | | | | | (83) $false
% 50.87/7.55 | | | | | | |
% 50.87/7.55 | | | | | | | CLOSE: (83) is inconsistent.
% 50.87/7.55 | | | | | | |
% 50.87/7.55 | | | | | | Case 2:
% 50.87/7.55 | | | | | | |
% 50.87/7.55 | | | | | | |
% 50.87/7.55 | | | | | | | GROUND_INST: instantiating (5) with 0, all_684_2, all_317_0,
% 50.87/7.55 | | | | | | | simplifying with (57), (65) gives:
% 50.87/7.56 | | | | | | | (84) all_684_2 = 0
% 50.87/7.56 | | | | | | |
% 50.87/7.56 | | | | | | | GROUND_INST: instantiating (6) with 0, all_684_0, all_317_0,
% 50.87/7.56 | | | | | | | all_93_0, simplifying with (58), (66) gives:
% 50.87/7.56 | | | | | | | (85) all_684_0 = 0
% 50.87/7.56 | | | | | | |
% 50.87/7.56 | | | | | | | GROUND_INST: instantiating (6) with 0, all_684_1, all_317_0,
% 50.87/7.56 | | | | | | | all_97_0, simplifying with (59), (67) gives:
% 50.87/7.56 | | | | | | | (86) all_684_1 = 0
% 50.87/7.56 | | | | | | |
% 50.87/7.56 | | | | | | | BETA: splitting (68) gives:
% 50.87/7.56 | | | | | | |
% 50.87/7.56 | | | | | | | Case 1:
% 50.87/7.56 | | | | | | | |
% 50.87/7.56 | | | | | | | | (87) ~ (all_684_0 = 0)
% 50.87/7.56 | | | | | | | |
% 50.87/7.56 | | | | | | | | REDUCE: (85), (87) imply:
% 50.87/7.56 | | | | | | | | (88) $false
% 50.87/7.56 | | | | | | | |
% 50.87/7.56 | | | | | | | | CLOSE: (88) is inconsistent.
% 50.87/7.56 | | | | | | | |
% 50.87/7.56 | | | | | | | Case 2:
% 50.87/7.56 | | | | | | | |
% 50.87/7.56 | | | | | | | | (89) ~ (all_684_1 = 0) | ~ (all_684_2 = 0)
% 50.87/7.56 | | | | | | | |
% 50.87/7.56 | | | | | | | | BETA: splitting (89) gives:
% 50.87/7.56 | | | | | | | |
% 50.87/7.56 | | | | | | | | Case 1:
% 50.87/7.56 | | | | | | | | |
% 50.87/7.56 | | | | | | | | | (90) ~ (all_684_1 = 0)
% 50.87/7.56 | | | | | | | | |
% 50.87/7.56 | | | | | | | | | REDUCE: (86), (90) imply:
% 50.87/7.56 | | | | | | | | | (91) $false
% 50.87/7.56 | | | | | | | | |
% 50.87/7.56 | | | | | | | | | CLOSE: (91) is inconsistent.
% 50.87/7.56 | | | | | | | | |
% 50.87/7.56 | | | | | | | | Case 2:
% 50.87/7.56 | | | | | | | | |
% 50.87/7.56 | | | | | | | | | (92) ~ (all_684_2 = 0)
% 50.87/7.56 | | | | | | | | |
% 50.87/7.56 | | | | | | | | | REDUCE: (84), (92) imply:
% 50.87/7.56 | | | | | | | | | (93) $false
% 50.87/7.56 | | | | | | | | |
% 50.87/7.56 | | | | | | | | | CLOSE: (93) is inconsistent.
% 50.87/7.56 | | | | | | | | |
% 50.87/7.56 | | | | | | | | End of split
% 50.87/7.56 | | | | | | | |
% 50.87/7.56 | | | | | | | End of split
% 50.87/7.56 | | | | | | |
% 50.87/7.56 | | | | | | End of split
% 50.87/7.56 | | | | | |
% 50.87/7.56 | | | | | End of split
% 50.87/7.56 | | | | |
% 50.87/7.56 | | | | End of split
% 50.87/7.56 | | | |
% 50.87/7.56 | | | End of split
% 50.87/7.56 | | |
% 50.87/7.56 | | End of split
% 50.87/7.56 | |
% 50.87/7.56 | Case 2:
% 50.87/7.56 | |
% 50.87/7.56 | | (94) all_93_0 = nil
% 50.87/7.56 | | (95) all_97_0 = nil
% 50.87/7.56 | |
% 50.87/7.56 | | BETA: splitting (18) gives:
% 50.87/7.56 | |
% 50.87/7.56 | | Case 1:
% 50.87/7.56 | | |
% 50.87/7.56 | | | (96) ~ (all_97_0 = nil)
% 50.87/7.56 | | |
% 50.87/7.56 | | | REDUCE: (95), (96) imply:
% 50.87/7.56 | | | (97) $false
% 50.87/7.56 | | |
% 50.87/7.56 | | | CLOSE: (97) is inconsistent.
% 50.87/7.56 | | |
% 50.87/7.56 | | Case 2:
% 50.87/7.56 | | |
% 50.87/7.56 | | | (98) ~ (all_93_0 = nil)
% 50.87/7.56 | | |
% 50.87/7.56 | | | REDUCE: (94), (98) imply:
% 50.87/7.56 | | | (99) $false
% 50.87/7.56 | | |
% 50.87/7.56 | | | CLOSE: (99) is inconsistent.
% 50.87/7.56 | | |
% 50.87/7.56 | | End of split
% 50.87/7.56 | |
% 50.87/7.56 | End of split
% 50.87/7.56 |
% 50.87/7.56 End of proof
% 50.87/7.56 % SZS output end Proof for theBenchmark
% 50.87/7.56
% 50.87/7.56 6938ms
%------------------------------------------------------------------------------