TSTP Solution File: SWC043+1 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SWC043+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 : n032.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 20:49:21 EDT 2023
% Result : Theorem 18.94s 3.22s
% Output : Proof 27.75s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SWC043+1 : TPTP v8.1.2. Released v2.4.0.
% 0.10/0.11 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.11/0.31 % Computer : n032.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Aug 28 18:32:45 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.16/0.53 ________ _____
% 0.16/0.53 ___ __ \_________(_)________________________________
% 0.16/0.53 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.16/0.53 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.16/0.53 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.16/0.53
% 0.16/0.53 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.16/0.53 (2023-06-19)
% 0.16/0.53
% 0.16/0.53 (c) Philipp Rümmer, 2009-2023
% 0.16/0.53 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.16/0.53 Amanda Stjerna.
% 0.16/0.53 Free software under BSD-3-Clause.
% 0.16/0.53
% 0.16/0.53 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.16/0.53
% 0.16/0.53 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.16/0.54 Running up to 7 provers in parallel.
% 0.16/0.55 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.16/0.55 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.16/0.55 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.16/0.55 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.16/0.55 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.16/0.55 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.16/0.55 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.25/1.33 Prover 4: Preprocessing ...
% 4.25/1.33 Prover 1: Preprocessing ...
% 4.25/1.38 Prover 3: Preprocessing ...
% 4.25/1.38 Prover 0: Preprocessing ...
% 4.25/1.38 Prover 2: Preprocessing ...
% 4.25/1.38 Prover 5: Preprocessing ...
% 4.25/1.38 Prover 6: Preprocessing ...
% 13.22/2.50 Prover 2: Proving ...
% 13.22/2.53 Prover 5: Constructing countermodel ...
% 14.22/2.58 Prover 6: Proving ...
% 14.22/2.59 Prover 1: Constructing countermodel ...
% 14.22/2.62 Prover 3: Constructing countermodel ...
% 18.94/3.21 Prover 3: proved (2662ms)
% 18.94/3.21
% 18.94/3.22 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.94/3.22
% 18.94/3.22 Prover 5: stopped
% 18.94/3.23 Prover 6: stopped
% 18.94/3.24 Prover 2: stopped
% 19.35/3.25 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 19.35/3.25 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 19.35/3.25 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 19.35/3.25 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 20.22/3.43 Prover 7: Preprocessing ...
% 20.22/3.44 Prover 11: Preprocessing ...
% 20.94/3.46 Prover 4: Constructing countermodel ...
% 20.94/3.47 Prover 8: Preprocessing ...
% 20.94/3.47 Prover 10: Preprocessing ...
% 22.17/3.69 Prover 0: Proving ...
% 22.17/3.70 Prover 7: Constructing countermodel ...
% 22.17/3.71 Prover 0: stopped
% 22.17/3.72 Prover 10: Constructing countermodel ...
% 22.17/3.72 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 22.66/3.83 Prover 13: Preprocessing ...
% 23.91/3.87 Prover 1: Found proof (size 23)
% 23.91/3.87 Prover 1: proved (3322ms)
% 23.91/3.87 Prover 10: stopped
% 23.91/3.87 Prover 7: stopped
% 23.91/3.87 Prover 4: stopped
% 23.91/3.88 Prover 8: Warning: ignoring some quantifiers
% 24.25/3.89 Prover 8: Constructing countermodel ...
% 24.25/3.91 Prover 8: stopped
% 24.25/3.91 Prover 13: stopped
% 26.89/4.55 Prover 11: Constructing countermodel ...
% 26.89/4.58 Prover 11: stopped
% 26.89/4.58
% 26.89/4.58 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 26.89/4.58
% 27.25/4.59 % SZS output start Proof for theBenchmark
% 27.25/4.60 Assumptions after simplification:
% 27.25/4.60 ---------------------------------
% 27.25/4.60
% 27.25/4.60 (ax83)
% 27.25/4.63 $i(nil) & ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : !
% 27.25/4.63 [v2: $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0)
% 27.25/4.63 & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 = nil)) & ( ~ (v1
% 27.25/4.63 = nil) | ~ (v0 = nil) | v2 = nil))))
% 27.25/4.63
% 27.25/4.63 (co1)
% 27.25/4.64 $i(nil) & ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) =
% 27.25/4.64 0 & $i(v1) & ? [v2: any] : (v1 = nil & ~ (v0 = nil) & strictorderedP(v0)
% 27.25/4.64 = v2 & ssList(nil) = 0 & ? [v3: $i] : (v2 = 0 & ssList(v3) = 0 &
% 27.25/4.64 app(v0, v3) = nil & $i(v3) & ! [v4: $i] : ! [v5: $i] : ( ~ (cons(v4,
% 27.25/4.64 nil) = v5) | ~ $i(v4) | ? [v6: int] : ( ~ (v6 = 0) &
% 27.25/4.64 ssItem(v4) = v6) | ! [v6: $i] : ( ~ (app(v5, v6) = v3) | ~
% 27.25/4.64 $i(v6) | ? [v7: int] : ( ~ (v7 = 0) & ssList(v6) = v7) | ! [v7:
% 27.25/4.64 $i] : ! [v8: $i] : ( ~ (cons(v7, nil) = v8) | ~ $i(v7) | ?
% 27.25/4.64 [v9: any] : ? [v10: any] : (lt(v7, v4) = v10 & ssItem(v7) = v9
% 27.25/4.64 & ( ~ (v9 = 0) | ! [v11: $i] : ( ~ (v10 = 0) | ~ (app(v11,
% 27.25/4.64 v8) = v0) | ~ $i(v11) | ? [v12: int] : ( ~ (v12 = 0)
% 27.25/4.64 & ssList(v11) = v12)))))))))))
% 27.25/4.64
% 27.25/4.64 (function-axioms)
% 27.25/4.66 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 27.25/4.66 [v3: $i] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0:
% 27.25/4.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.25/4.66 : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0:
% 27.25/4.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.25/4.66 : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0:
% 27.25/4.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.25/4.66 : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0:
% 27.25/4.66 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 27.25/4.66 : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & !
% 27.25/4.66 [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 27.25/4.66 $i] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) &
% 27.25/4.66 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3:
% 27.25/4.66 $i] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 27.25/4.66 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 27.25/4.66 [v3: $i] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) &
% 27.25/4.66 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 27.25/4.66 (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0: $i] : ! [v1: $i] :
% 27.25/4.66 ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2)
% 27.25/4.66 = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 27.25/4.66 $i] : ! [v3: $i] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) =
% 27.25/4.66 v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 = v0 | ~ (tl(v2) =
% 27.25/4.66 v1) | ~ (tl(v2) = v0)) & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : (v1 =
% 27.25/4.66 v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0: MultipleValueBool] : !
% 27.25/4.66 [v1: MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (equalelemsP(v2) = v1) |
% 27.25/4.66 ~ (equalelemsP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.25/4.66 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) |
% 27.25/4.66 ~ (duplicatefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.25/4.66 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderedP(v2) = v1) |
% 27.25/4.66 ~ (strictorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.25/4.66 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderedP(v2) = v1) |
% 27.25/4.66 ~ (totalorderedP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.25/4.66 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (strictorderP(v2) = v1) |
% 27.25/4.66 ~ (strictorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.25/4.66 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~
% 27.25/4.66 (totalorderP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.25/4.66 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~
% 27.25/4.66 (cyclefreeP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.25/4.66 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~
% 27.25/4.66 (singletonP(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1:
% 27.25/4.66 MultipleValueBool] : ! [v2: $i] : (v1 = v0 | ~ (ssList(v2) = v1) | ~
% 27.25/4.66 (ssList(v2) = v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool]
% 27.25/4.66 : ! [v2: $i] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 27.25/4.66
% 27.25/4.66 Further assumptions not needed in the proof:
% 27.25/4.66 --------------------------------------------
% 27.25/4.66 ax1, ax10, ax11, ax12, ax13, ax14, ax15, ax16, ax17, ax18, ax19, ax2, ax20,
% 27.25/4.66 ax21, ax22, ax23, ax24, ax25, ax26, ax27, ax28, ax29, ax3, ax30, ax31, ax32,
% 27.25/4.66 ax33, ax34, ax35, ax36, ax37, ax38, ax39, ax4, ax40, ax41, ax42, ax43, ax44,
% 27.25/4.66 ax45, ax46, ax47, ax48, ax49, ax5, ax50, ax51, ax52, ax53, ax54, ax55, ax56,
% 27.25/4.66 ax57, ax58, ax59, ax6, ax60, ax61, ax62, ax63, ax64, ax65, ax66, ax67, ax68,
% 27.25/4.66 ax69, ax7, ax70, ax71, ax72, ax73, ax74, ax75, ax76, ax77, ax78, ax79, ax8,
% 27.25/4.66 ax80, ax81, ax82, ax84, ax85, ax86, ax87, ax88, ax89, ax9, ax90, ax91, ax92,
% 27.25/4.66 ax93, ax94, ax95
% 27.25/4.66
% 27.25/4.66 Those formulas are unsatisfiable:
% 27.25/4.66 ---------------------------------
% 27.25/4.66
% 27.25/4.66 Begin of proof
% 27.25/4.66 |
% 27.25/4.66 | ALPHA: (ax83) implies:
% 27.25/4.67 | (1) ! [v0: $i] : ( ~ (ssList(v0) = 0) | ~ $i(v0) | ! [v1: $i] : ! [v2:
% 27.25/4.67 | $i] : ( ~ (app(v0, v1) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 =
% 27.25/4.67 | 0) & ssList(v1) = v3) | (( ~ (v2 = nil) | (v1 = nil & v0 =
% 27.25/4.67 | nil)) & ( ~ (v1 = nil) | ~ (v0 = nil) | v2 = nil))))
% 27.25/4.67 |
% 27.25/4.67 | ALPHA: (co1) implies:
% 27.25/4.67 | (2) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: $i] : (ssList(v1) = 0
% 27.25/4.67 | & $i(v1) & ? [v2: any] : (v1 = nil & ~ (v0 = nil) &
% 27.25/4.67 | strictorderedP(v0) = v2 & ssList(nil) = 0 & ? [v3: $i] : (v2 = 0
% 27.25/4.67 | & ssList(v3) = 0 & app(v0, v3) = nil & $i(v3) & ! [v4: $i] :
% 27.25/4.67 | ! [v5: $i] : ( ~ (cons(v4, nil) = v5) | ~ $i(v4) | ? [v6:
% 27.25/4.67 | int] : ( ~ (v6 = 0) & ssItem(v4) = v6) | ! [v6: $i] : ( ~
% 27.25/4.67 | (app(v5, v6) = v3) | ~ $i(v6) | ? [v7: int] : ( ~ (v7 =
% 27.25/4.67 | 0) & ssList(v6) = v7) | ! [v7: $i] : ! [v8: $i] : ( ~
% 27.25/4.67 | (cons(v7, nil) = v8) | ~ $i(v7) | ? [v9: any] : ?
% 27.25/4.67 | [v10: any] : (lt(v7, v4) = v10 & ssItem(v7) = v9 & ( ~
% 27.25/4.67 | (v9 = 0) | ! [v11: $i] : ( ~ (v10 = 0) | ~
% 27.25/4.67 | (app(v11, v8) = v0) | ~ $i(v11) | ? [v12: int] :
% 27.25/4.67 | ( ~ (v12 = 0) & ssList(v11) = v12)))))))))))
% 27.25/4.67 |
% 27.25/4.67 | ALPHA: (function-axioms) implies:
% 27.25/4.67 | (3) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 27.25/4.67 | (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 27.25/4.67 |
% 27.25/4.67 | DELTA: instantiating (2) with fresh symbol all_93_0 gives:
% 27.25/4.67 | (4) ssList(all_93_0) = 0 & $i(all_93_0) & ? [v0: $i] : (ssList(v0) = 0 &
% 27.25/4.67 | $i(v0) & ? [v1: any] : (v0 = nil & ~ (all_93_0 = nil) &
% 27.25/4.67 | strictorderedP(all_93_0) = v1 & ssList(nil) = 0 & ? [v2: $i] : (v1
% 27.25/4.67 | = 0 & ssList(v2) = 0 & app(all_93_0, v2) = nil & $i(v2) & ! [v3:
% 27.25/4.67 | $i] : ! [v4: $i] : ( ~ (cons(v3, nil) = v4) | ~ $i(v3) | ?
% 27.25/4.67 | [v5: int] : ( ~ (v5 = 0) & ssItem(v3) = v5) | ! [v5: $i] : ( ~
% 27.25/4.67 | (app(v4, v5) = v2) | ~ $i(v5) | ? [v6: int] : ( ~ (v6 = 0)
% 27.25/4.67 | & ssList(v5) = v6) | ! [v6: $i] : ! [v7: $i] : ( ~
% 27.25/4.67 | (cons(v6, nil) = v7) | ~ $i(v6) | ? [v8: any] : ? [v9:
% 27.25/4.67 | any] : (lt(v6, v3) = v9 & ssItem(v6) = v8 & ( ~ (v8 = 0)
% 27.25/4.67 | | ! [v10: $i] : ( ~ (v9 = 0) | ~ (app(v10, v7) =
% 27.25/4.67 | all_93_0) | ~ $i(v10) | ? [v11: int] : ( ~ (v11 =
% 27.25/4.67 | 0) & ssList(v10) = v11))))))))))
% 27.25/4.67 |
% 27.25/4.67 | ALPHA: (4) implies:
% 27.25/4.68 | (5) $i(all_93_0)
% 27.25/4.68 | (6) ssList(all_93_0) = 0
% 27.25/4.68 | (7) ? [v0: $i] : (ssList(v0) = 0 & $i(v0) & ? [v1: any] : (v0 = nil & ~
% 27.25/4.68 | (all_93_0 = nil) & strictorderedP(all_93_0) = v1 & ssList(nil) = 0
% 27.25/4.68 | & ? [v2: $i] : (v1 = 0 & ssList(v2) = 0 & app(all_93_0, v2) = nil
% 27.25/4.68 | & $i(v2) & ! [v3: $i] : ! [v4: $i] : ( ~ (cons(v3, nil) = v4) |
% 27.25/4.68 | ~ $i(v3) | ? [v5: int] : ( ~ (v5 = 0) & ssItem(v3) = v5) | !
% 27.25/4.68 | [v5: $i] : ( ~ (app(v4, v5) = v2) | ~ $i(v5) | ? [v6: int] :
% 27.25/4.68 | ( ~ (v6 = 0) & ssList(v5) = v6) | ! [v6: $i] : ! [v7: $i] :
% 27.25/4.68 | ( ~ (cons(v6, nil) = v7) | ~ $i(v6) | ? [v8: any] : ? [v9:
% 27.25/4.68 | any] : (lt(v6, v3) = v9 & ssItem(v6) = v8 & ( ~ (v8 = 0)
% 27.25/4.68 | | ! [v10: $i] : ( ~ (v9 = 0) | ~ (app(v10, v7) =
% 27.25/4.68 | all_93_0) | ~ $i(v10) | ? [v11: int] : ( ~ (v11 =
% 27.25/4.68 | 0) & ssList(v10) = v11))))))))))
% 27.69/4.68 |
% 27.69/4.68 | DELTA: instantiating (7) with fresh symbol all_97_0 gives:
% 27.69/4.68 | (8) ssList(all_97_0) = 0 & $i(all_97_0) & ? [v0: any] : (all_97_0 = nil &
% 27.69/4.68 | ~ (all_93_0 = nil) & strictorderedP(all_93_0) = v0 & ssList(nil) = 0
% 27.69/4.68 | & ? [v1: $i] : (v0 = 0 & ssList(v1) = 0 & app(all_93_0, v1) = nil &
% 27.69/4.68 | $i(v1) & ! [v2: $i] : ! [v3: $i] : ( ~ (cons(v2, nil) = v3) | ~
% 27.69/4.68 | $i(v2) | ? [v4: int] : ( ~ (v4 = 0) & ssItem(v2) = v4) | ! [v4:
% 27.69/4.68 | $i] : ( ~ (app(v3, v4) = v1) | ~ $i(v4) | ? [v5: int] : ( ~
% 27.69/4.68 | (v5 = 0) & ssList(v4) = v5) | ! [v5: $i] : ! [v6: $i] : ( ~
% 27.69/4.68 | (cons(v5, nil) = v6) | ~ $i(v5) | ? [v7: any] : ? [v8:
% 27.69/4.68 | any] : (lt(v5, v2) = v8 & ssItem(v5) = v7 & ( ~ (v7 = 0) |
% 27.69/4.68 | ! [v9: $i] : ( ~ (v8 = 0) | ~ (app(v9, v6) = all_93_0) |
% 27.69/4.68 | ~ $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & ssList(v9)
% 27.69/4.68 | = v10)))))))))
% 27.69/4.68 |
% 27.69/4.68 | ALPHA: (8) implies:
% 27.69/4.68 | (9) ? [v0: any] : (all_97_0 = nil & ~ (all_93_0 = nil) &
% 27.69/4.68 | strictorderedP(all_93_0) = v0 & ssList(nil) = 0 & ? [v1: $i] : (v0 =
% 27.69/4.68 | 0 & ssList(v1) = 0 & app(all_93_0, v1) = nil & $i(v1) & ! [v2: $i]
% 27.69/4.68 | : ! [v3: $i] : ( ~ (cons(v2, nil) = v3) | ~ $i(v2) | ? [v4: int]
% 27.69/4.68 | : ( ~ (v4 = 0) & ssItem(v2) = v4) | ! [v4: $i] : ( ~ (app(v3,
% 27.69/4.68 | v4) = v1) | ~ $i(v4) | ? [v5: int] : ( ~ (v5 = 0) &
% 27.69/4.68 | ssList(v4) = v5) | ! [v5: $i] : ! [v6: $i] : ( ~ (cons(v5,
% 27.69/4.68 | nil) = v6) | ~ $i(v5) | ? [v7: any] : ? [v8: any] :
% 27.69/4.68 | (lt(v5, v2) = v8 & ssItem(v5) = v7 & ( ~ (v7 = 0) | ! [v9:
% 27.69/4.68 | $i] : ( ~ (v8 = 0) | ~ (app(v9, v6) = all_93_0) | ~
% 27.69/4.68 | $i(v9) | ? [v10: int] : ( ~ (v10 = 0) & ssList(v9) =
% 27.69/4.68 | v10)))))))))
% 27.69/4.68 |
% 27.69/4.68 | DELTA: instantiating (9) with fresh symbol all_99_0 gives:
% 27.69/4.69 | (10) all_97_0 = nil & ~ (all_93_0 = nil) & strictorderedP(all_93_0) =
% 27.69/4.69 | all_99_0 & ssList(nil) = 0 & ? [v0: $i] : (all_99_0 = 0 & ssList(v0)
% 27.69/4.69 | = 0 & app(all_93_0, v0) = nil & $i(v0) & ! [v1: $i] : ! [v2: $i] :
% 27.69/4.69 | ( ~ (cons(v1, nil) = v2) | ~ $i(v1) | ? [v3: int] : ( ~ (v3 = 0) &
% 27.69/4.69 | ssItem(v1) = v3) | ! [v3: $i] : ( ~ (app(v2, v3) = v0) | ~
% 27.69/4.69 | $i(v3) | ? [v4: int] : ( ~ (v4 = 0) & ssList(v3) = v4) | !
% 27.69/4.69 | [v4: $i] : ! [v5: $i] : ( ~ (cons(v4, nil) = v5) | ~ $i(v4) |
% 27.69/4.69 | ? [v6: any] : ? [v7: any] : (lt(v4, v1) = v7 & ssItem(v4) =
% 27.69/4.69 | v6 & ( ~ (v6 = 0) | ! [v8: $i] : ( ~ (v7 = 0) | ~ (app(v8,
% 27.69/4.69 | v5) = all_93_0) | ~ $i(v8) | ? [v9: int] : ( ~ (v9
% 27.69/4.69 | = 0) & ssList(v8) = v9))))))))
% 27.69/4.69 |
% 27.69/4.69 | ALPHA: (10) implies:
% 27.69/4.69 | (11) ~ (all_93_0 = nil)
% 27.69/4.69 | (12) ? [v0: $i] : (all_99_0 = 0 & ssList(v0) = 0 & app(all_93_0, v0) = nil
% 27.69/4.69 | & $i(v0) & ! [v1: $i] : ! [v2: $i] : ( ~ (cons(v1, nil) = v2) | ~
% 27.69/4.69 | $i(v1) | ? [v3: int] : ( ~ (v3 = 0) & ssItem(v1) = v3) | ! [v3:
% 27.69/4.69 | $i] : ( ~ (app(v2, v3) = v0) | ~ $i(v3) | ? [v4: int] : ( ~
% 27.69/4.69 | (v4 = 0) & ssList(v3) = v4) | ! [v4: $i] : ! [v5: $i] : ( ~
% 27.69/4.69 | (cons(v4, nil) = v5) | ~ $i(v4) | ? [v6: any] : ? [v7: any]
% 27.69/4.69 | : (lt(v4, v1) = v7 & ssItem(v4) = v6 & ( ~ (v6 = 0) | ! [v8:
% 27.69/4.69 | $i] : ( ~ (v7 = 0) | ~ (app(v8, v5) = all_93_0) | ~
% 27.69/4.69 | $i(v8) | ? [v9: int] : ( ~ (v9 = 0) & ssList(v8) =
% 27.69/4.69 | v9))))))))
% 27.69/4.69 |
% 27.69/4.69 | DELTA: instantiating (12) with fresh symbol all_101_0 gives:
% 27.69/4.69 | (13) all_99_0 = 0 & ssList(all_101_0) = 0 & app(all_93_0, all_101_0) = nil
% 27.69/4.69 | & $i(all_101_0) & ! [v0: $i] : ! [v1: $i] : ( ~ (cons(v0, nil) = v1)
% 27.69/4.69 | | ~ $i(v0) | ? [v2: int] : ( ~ (v2 = 0) & ssItem(v0) = v2) | !
% 27.69/4.69 | [v2: $i] : ( ~ (app(v1, v2) = all_101_0) | ~ $i(v2) | ? [v3: int]
% 27.69/4.69 | : ( ~ (v3 = 0) & ssList(v2) = v3) | ! [v3: $i] : ! [v4: $i] : (
% 27.69/4.69 | ~ (cons(v3, nil) = v4) | ~ $i(v3) | ? [v5: any] : ? [v6: any]
% 27.69/4.69 | : (lt(v3, v0) = v6 & ssItem(v3) = v5 & ( ~ (v5 = 0) | ! [v7:
% 27.69/4.69 | $i] : ( ~ (v6 = 0) | ~ (app(v7, v4) = all_93_0) | ~
% 27.69/4.69 | $i(v7) | ? [v8: int] : ( ~ (v8 = 0) & ssList(v7) =
% 27.69/4.69 | v8)))))))
% 27.69/4.69 |
% 27.69/4.69 | ALPHA: (13) implies:
% 27.69/4.69 | (14) $i(all_101_0)
% 27.69/4.69 | (15) app(all_93_0, all_101_0) = nil
% 27.69/4.69 | (16) ssList(all_101_0) = 0
% 27.69/4.69 |
% 27.75/4.69 | GROUND_INST: instantiating (1) with all_93_0, simplifying with (5), (6) gives:
% 27.75/4.69 | (17) ! [v0: $i] : ! [v1: $i] : ( ~ (app(all_93_0, v0) = v1) | ~ $i(v0) |
% 27.75/4.69 | ? [v2: int] : ( ~ (v2 = 0) & ssList(v0) = v2) | (( ~ (v1 = nil) |
% 27.75/4.69 | (v0 = nil & all_93_0 = nil)) & ( ~ (v0 = nil) | ~ (all_93_0 =
% 27.75/4.69 | nil) | v1 = nil)))
% 27.75/4.69 |
% 27.75/4.69 | GROUND_INST: instantiating (17) with all_101_0, nil, simplifying with (14),
% 27.75/4.69 | (15) gives:
% 27.75/4.69 | (18) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) = v0) | (all_101_0 =
% 27.75/4.69 | nil & all_93_0 = nil)
% 27.75/4.69 |
% 27.75/4.69 | BETA: splitting (18) gives:
% 27.75/4.69 |
% 27.75/4.69 | Case 1:
% 27.75/4.69 | |
% 27.75/4.69 | | (19) ? [v0: int] : ( ~ (v0 = 0) & ssList(all_101_0) = v0)
% 27.75/4.69 | |
% 27.75/4.69 | | DELTA: instantiating (19) with fresh symbol all_249_0 gives:
% 27.75/4.69 | | (20) ~ (all_249_0 = 0) & ssList(all_101_0) = all_249_0
% 27.75/4.69 | |
% 27.75/4.69 | | ALPHA: (20) implies:
% 27.75/4.69 | | (21) ~ (all_249_0 = 0)
% 27.75/4.70 | | (22) ssList(all_101_0) = all_249_0
% 27.75/4.70 | |
% 27.75/4.70 | | GROUND_INST: instantiating (3) with 0, all_249_0, all_101_0, simplifying
% 27.75/4.70 | | with (16), (22) gives:
% 27.75/4.70 | | (23) all_249_0 = 0
% 27.75/4.70 | |
% 27.75/4.70 | | REDUCE: (21), (23) imply:
% 27.75/4.70 | | (24) $false
% 27.75/4.70 | |
% 27.75/4.70 | | CLOSE: (24) is inconsistent.
% 27.75/4.70 | |
% 27.75/4.70 | Case 2:
% 27.75/4.70 | |
% 27.75/4.70 | | (25) all_101_0 = nil & all_93_0 = nil
% 27.75/4.70 | |
% 27.75/4.70 | | ALPHA: (25) implies:
% 27.75/4.70 | | (26) all_93_0 = nil
% 27.75/4.70 | |
% 27.75/4.70 | | REDUCE: (11), (26) imply:
% 27.75/4.70 | | (27) $false
% 27.75/4.70 | |
% 27.75/4.70 | | CLOSE: (27) is inconsistent.
% 27.75/4.70 | |
% 27.75/4.70 | End of split
% 27.75/4.70 |
% 27.75/4.70 End of proof
% 27.75/4.70 % SZS output end Proof for theBenchmark
% 27.75/4.70
% 27.75/4.70 4166ms
%------------------------------------------------------------------------------