TSTP Solution File: SWC204+1 by ePrincess---1.0
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%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWC204+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 20:16:48 EDT 2022
% Result : Theorem 29.57s 8.78s
% Output : Proof 34.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC204+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n010.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 12 17:37:40 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.58 ____ _
% 0.18/0.58 ___ / __ \_____(_)___ ________ __________
% 0.18/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.18/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.18/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.18/0.58
% 0.18/0.58 A Theorem Prover for First-Order Logic
% 0.18/0.58 (ePrincess v.1.0)
% 0.18/0.58
% 0.18/0.58 (c) Philipp Rümmer, 2009-2015
% 0.18/0.58 (c) Peter Backeman, 2014-2015
% 0.18/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.18/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.18/0.58 Bug reports to peter@backeman.se
% 0.18/0.58
% 0.18/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.18/0.58
% 0.18/0.58 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.64/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.34/1.04 Prover 0: Preprocessing ...
% 4.72/1.64 Prover 0: Constructing countermodel ...
% 17.51/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 18.19/6.08 Prover 1: Preprocessing ...
% 19.35/6.32 Prover 1: Constructing countermodel ...
% 20.13/6.57 Prover 1: gave up
% 20.13/6.57 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 20.58/6.65 Prover 2: Preprocessing ...
% 22.75/7.17 Prover 2: Warning: ignoring some quantifiers
% 22.75/7.20 Prover 2: Constructing countermodel ...
% 27.59/8.28 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 28.03/8.39 Prover 3: Preprocessing ...
% 28.25/8.47 Prover 3: Constructing countermodel ...
% 29.57/8.78 Prover 3: proved (496ms)
% 29.57/8.78 Prover 2: stopped
% 29.57/8.78 Prover 0: stopped
% 29.57/8.78
% 29.57/8.78 No countermodel exists, formula is valid
% 29.57/8.78 % SZS status Theorem for theBenchmark
% 29.57/8.78
% 29.57/8.78 Generating proof ... found it (size 73)
% 33.38/9.64
% 33.38/9.64 % SZS output start Proof for theBenchmark
% 33.38/9.64 Assumed formulas after preprocessing and simplification:
% 33.38/9.64 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = v3) & tl(v1) = v2 & equalelemsP(nil) & duplicatefreeP(nil) & strictorderedP(nil) & totalorderedP(nil) & strictorderP(nil) & totalorderP(nil) & cyclefreeP(nil) & segmentP(nil, nil) & rearsegP(nil, nil) & frontsegP(nil, nil) & ssList(v1) & ssList(v0) & ssList(nil) & neq(v1, nil) & ssItem(v4) & ssItem(v3) & ~ singletonP(nil) & ~ neq(v0, nil) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cons(v7, v12) = v13) | ~ (cons(v6, v9) = v10) | ~ (app(v11, v13) = v5) | ~ (app(v8, v10) = v11) | ~ strictorderedP(v5) | ~ ssList(v12) | ~ ssList(v9) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v7) | ~ ssItem(v6) | lt(v6, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cons(v7, v12) = v13) | ~ (cons(v6, v9) = v10) | ~ (app(v11, v13) = v5) | ~ (app(v8, v10) = v11) | ~ totalorderedP(v5) | ~ ssList(v12) | ~ ssList(v9) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v7) | ~ ssItem(v6) | leq(v6, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cons(v7, v12) = v13) | ~ (cons(v6, v9) = v10) | ~ (app(v11, v13) = v5) | ~ (app(v8, v10) = v11) | ~ strictorderP(v5) | ~ ssList(v12) | ~ ssList(v9) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v7) | ~ ssItem(v6) | lt(v7, v6) | lt(v6, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cons(v7, v12) = v13) | ~ (cons(v6, v9) = v10) | ~ (app(v11, v13) = v5) | ~ (app(v8, v10) = v11) | ~ totalorderP(v5) | ~ ssList(v12) | ~ ssList(v9) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v7) | ~ ssItem(v6) | leq(v7, v6) | leq(v6, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cons(v7, v12) = v13) | ~ (cons(v6, v9) = v10) | ~ (app(v11, v13) = v5) | ~ (app(v8, v10) = v11) | ~ leq(v7, v6) | ~ leq(v6, v7) | ~ cyclefreeP(v5) | ~ ssList(v12) | ~ ssList(v9) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v7) | ~ ssItem(v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cons(v6, v11) = v12) | ~ (cons(v6, v8) = v9) | ~ (app(v10, v12) = v5) | ~ (app(v7, v9) = v10) | ~ duplicatefreeP(v5) | ~ ssList(v11) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v5) | ~ ssItem(v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = v6 | ~ (cons(v7, v9) = v10) | ~ (cons(v6, v10) = v11) | ~ (app(v8, v11) = v5) | ~ equalelemsP(v5) | ~ ssList(v9) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v7) | ~ ssItem(v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v6 = v5 | ~ (cons(v6, v9) = v10) | ~ (cons(v5, v7) = v8) | ~ frontsegP(v8, v10) | ~ ssList(v9) | ~ ssList(v7) | ~ ssItem(v6) | ~ ssItem(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (cons(v6, v9) = v10) | ~ (cons(v5, v7) = v8) | ~ frontsegP(v8, v10) | ~ ssList(v9) | ~ ssList(v7) | ~ ssItem(v6) | ~ ssItem(v5) | frontsegP(v7, v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (app(v8, v9) = v10) | ~ (app(v7, v5) = v8) | ~ segmentP(v5, v6) | ~ ssList(v9) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | segmentP(v10, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (cons(v9, v6) = v8) | ~ (cons(v7, v5) = v8) | ~ ssList(v6) | ~ ssList(v5) | ~ ssItem(v9) | ~ ssItem(v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (cons(v9, v6) = v8) | ~ (cons(v7, v5) = v8) | ~ ssList(v6) | ~ ssList(v5) | ~ ssItem(v9) | ~ ssItem(v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (cons(v8, v7) = v9) | ~ (app(v6, v5) = v7) | ~ ssList(v6) | ~ ssList(v5) | ~ ssItem(v8) | ? [v10] : (cons(v8, v6) = v10 & app(v10, v5) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (cons(v6, v8) = v9) | ~ (app(v7, v9) = v5) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v5) | ~ ssItem(v6) | memberP(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (cons(v5, v8) = v9) | ~ (cons(v5, v6) = v7) | ~ frontsegP(v6, v8) | ~ ssList(v8) | ~ ssList(v6) | ~ ssItem(v5) | frontsegP(v7, v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (app(v8, v9) = v5) | ~ (app(v7, v6) = v8) | ~ ssList(v9) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | segmentP(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (app(v7, v8) = v9) | ~ (app(v5, v6) = v7) | ~ ssList(v8) | ~ ssList(v6) | ~ ssList(v5) | ? [v10] : (app(v6, v8) = v10 & app(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v5 | v5 = nil | ~ (tl(v5) = v7) | ~ (hd(v5) = v6) | ~ (cons(v6, v7) = v8) | ~ ssList(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v5 | ~ (app(v8, v6) = v7) | ~ (app(v5, v6) = v7) | ~ ssList(v8) | ~ ssList(v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v5 | ~ (app(v6, v8) = v7) | ~ (app(v6, v5) = v7) | ~ ssList(v8) | ~ ssList(v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (cons(v8, v7) = v6) | ~ (cons(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (cons(v6, v7) = v8) | ~ memberP(v8, v5) | ~ ssList(v7) | ~ ssItem(v6) | ~ ssItem(v5) | memberP(v7, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (app(v8, v7) = v6) | ~ (app(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = nil | ~ (tl(v5) = v6) | ~ (app(v6, v7) = v8) | ~ ssList(v7) | ~ ssList(v5) | ? [v9] : (tl(v9) = v8 & app(v5, v7) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = nil | ~ (hd(v5) = v6) | ~ (app(v5, v7) = v8) | ~ ssList(v7) | ~ ssList(v5) | hd(v8) = v6) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v6, v7) = v8) | ~ memberP(v7, v5) | ~ ssList(v7) | ~ ssItem(v6) | ~ ssItem(v5) | memberP(v8, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v6, nil) = v7) | ~ (app(v7, v5) = v8) | ~ ssList(v5) | ~ ssItem(v6) | cons(v6, v5) = v8) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (app(v7, v5) = v8) | ~ rearsegP(v5, v6) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | rearsegP(v8, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (app(v6, v7) = v8) | ~ memberP(v8, v5) | ~ ssList(v7) | ~ ssList(v6) | ~ ssItem(v5) | memberP(v7, v5) | memberP(v6, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (app(v6, v7) = v8) | ~ memberP(v7, v5) | ~ ssList(v7) | ~ ssList(v6) | ~ ssItem(v5) | memberP(v8, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (app(v6, v7) = v8) | ~ memberP(v6, v5) | ~ ssList(v7) | ~ ssList(v6) | ~ ssItem(v5) | memberP(v8, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (app(v5, v7) = v8) | ~ frontsegP(v5, v6) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | frontsegP(v8, v6)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (tl(v7) = v6) | ~ (tl(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (hd(v7) = v6) | ~ (hd(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (hd(v6) = v7) | ~ ssList(v6) | ~ ssItem(v5) | ? [v8] : ((v6 = nil | (cons(v5, v6) = v8 & ~ strictorderedP(v8)) | (strictorderedP(v6) & lt(v5, v7))) & (( ~ (v6 = nil) & ( ~ strictorderedP(v6) | ~ lt(v5, v7))) | (cons(v5, v6) = v8 & strictorderedP(v8))))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (hd(v6) = v7) | ~ ssList(v6) | ~ ssItem(v5) | ? [v8] : ((v6 = nil | (cons(v5, v6) = v8 & ~ totalorderedP(v8)) | (totalorderedP(v6) & leq(v5, v7))) & (( ~ (v6 = nil) & ( ~ totalorderedP(v6) | ~ leq(v5, v7))) | (cons(v5, v6) = v8 & totalorderedP(v8))))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (cons(v6, v5) = v7) | ~ ssList(v5) | ~ ssItem(v6) | tl(v7) = v5) & ! [v5] : ! [v6] : ! [v7] : ( ~ (cons(v6, v5) = v7) | ~ ssList(v5) | ~ ssItem(v6) | hd(v7) = v6) & ! [v5] : ! [v6] : ! [v7] : ( ~ (cons(v6, v5) = v7) | ~ ssList(v5) | ~ ssItem(v6) | ssList(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (cons(v5, v6) = v7) | ~ ssList(v6) | ~ ssItem(v5) | memberP(v7, v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (app(v7, v6) = v5) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | rearsegP(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (app(v6, v7) = v5) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | frontsegP(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (app(v5, v6) = v7) | ~ ssList(v6) | ~ ssList(v5) | ssList(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ gt(v6, v7) | ~ gt(v5, v6) | ~ ssItem(v7) | ~ ssItem(v6) | ~ ssItem(v5) | gt(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ geq(v6, v7) | ~ geq(v5, v6) | ~ ssItem(v7) | ~ ssItem(v6) | ~ ssItem(v5) | geq(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ lt(v6, v7) | ~ lt(v5, v6) | ~ ssItem(v7) | ~ ssItem(v6) | ~ ssItem(v5) | lt(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ lt(v6, v7) | ~ leq(v5, v6) | ~ ssItem(v7) | ~ ssItem(v6) | ~ ssItem(v5) | lt(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ leq(v6, v7) | ~ leq(v5, v6) | ~ ssItem(v7) | ~ ssItem(v6) | ~ ssItem(v5) | leq(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ segmentP(v6, v7) | ~ segmentP(v5, v6) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | segmentP(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ rearsegP(v6, v7) | ~ rearsegP(v5, v6) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | rearsegP(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ frontsegP(v6, v7) | ~ frontsegP(v5, v6) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | frontsegP(v5, v7)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (app(v5, nil) = v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (app(nil, v5) = v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ geq(v6, v5) | ~ geq(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ leq(v6, v5) | ~ leq(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ leq(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5) | lt(v5, v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ segmentP(v6, v5) | ~ segmentP(v5, v6) | ~ ssList(v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ rearsegP(v6, v5) | ~ rearsegP(v5, v6) | ~ ssList(v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ frontsegP(v6, v5) | ~ frontsegP(v5, v6) | ~ ssList(v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ ssList(v6) | ~ ssList(v5) | neq(v5, v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ ssItem(v6) | ~ ssItem(v5) | neq(v5, v6)) & ! [v5] : ! [v6] : (v6 = nil | ~ (app(v5, v6) = nil) | ~ ssList(v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : (v5 = nil | ~ (tl(v5) = v6) | ~ ssList(v5) | ssList(v6)) & ! [v5] : ! [v6] : (v5 = nil | ~ (hd(v5) = v6) | ~ ssList(v5) | ssItem(v6)) & ! [v5] : ! [v6] : (v5 = nil | ~ (app(v5, v6) = nil) | ~ ssList(v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : ( ~ (tl(v5) = v6) | ~ ssList(v5) | ? [v7] : (hd(v5) = v7 & ! [v8] : (v8 = v5 | v8 = nil | v5 = nil | ~ (tl(v8) = v6) | ~ ssList(v8) | ? [v9] : ( ~ (v9 = v7) & hd(v8) = v9)))) & ! [v5] : ! [v6] : ( ~ (cons(v6, v5) = v5) | ~ ssList(v5) | ~ ssItem(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v6, v5) = nil) | ~ ssList(v5) | ~ ssItem(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v6, nil) = v5) | ~ ssList(v5) | ~ ssItem(v6) | singletonP(v5)) & ! [v5] : ! [v6] : ( ~ (cons(v5, nil) = v6) | ~ ssItem(v5) | equalelemsP(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v5, nil) = v6) | ~ ssItem(v5) | duplicatefreeP(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v5, nil) = v6) | ~ ssItem(v5) | strictorderedP(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v5, nil) = v6) | ~ ssItem(v5) | totalorderedP(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v5, nil) = v6) | ~ ssItem(v5) | strictorderP(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v5, nil) = v6) | ~ ssItem(v5) | totalorderP(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v5, nil) = v6) | ~ ssItem(v5) | cyclefreeP(v6)) & ! [v5] : ! [v6] : ( ~ gt(v6, v5) | ~ gt(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5)) & ! [v5] : ! [v6] : ( ~ gt(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5) | lt(v6, v5)) & ! [v5] : ! [v6] : ( ~ geq(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5) | leq(v6, v5)) & ! [v5] : ! [v6] : ( ~ lt(v6, v5) | ~ lt(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5)) & ! [v5] : ! [v6] : ( ~ lt(v6, v5) | ~ ssItem(v6) | ~ ssItem(v5) | gt(v5, v6)) & ! [v5] : ! [v6] : ( ~ lt(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5) | leq(v5, v6)) & ! [v5] : ! [v6] : ( ~ leq(v6, v5) | ~ ssItem(v6) | ~ ssItem(v5) | geq(v5, v6)) & ! [v5] : ! [v6] : ( ~ segmentP(v5, v6) | ~ ssList(v6) | ~ ssList(v5) | ? [v7] : ? [v8] : ? [v9] : (app(v8, v9) = v5 & app(v7, v6) = v8 & ssList(v9) & ssList(v7))) & ! [v5] : ! [v6] : ( ~ rearsegP(v5, v6) | ~ ssList(v6) | ~ ssList(v5) | ? [v7] : (app(v7, v6) = v5 & ssList(v7))) & ! [v5] : ! [v6] : ( ~ frontsegP(v5, v6) | ~ ssList(v6) | ~ ssList(v5) | ? [v7] : (app(v6, v7) = v5 & ssList(v7))) & ! [v5] : ! [v6] : ( ~ memberP(v5, v6) | ~ ssList(v5) | ~ ssItem(v6) | ? [v7] : ? [v8] : ? [v9] : (cons(v6, v8) = v9 & app(v7, v9) = v5 & ssList(v8) & ssList(v7))) & ! [v5] : (v5 = v1 | ~ ssList(v5) | ~ ssList(v2) | ~ neq(nil, v1) | ? [v6] : ( ~ (v6 = v5) & app(v0, v2) = v6)) & ! [v5] : (v5 = nil | ~ (app(nil, nil) = v5)) & ! [v5] : (v5 = nil | ~ segmentP(nil, v5) | ~ ssList(v5)) & ! [v5] : (v5 = nil | ~ rearsegP(nil, v5) | ~ ssList(v5)) & ! [v5] : (v5 = nil | ~ frontsegP(nil, v5) | ~ ssList(v5)) & ! [v5] : (v5 = nil | ~ ssList(v5) | ? [v6] : ? [v7] : (cons(v7, v6) = v5 & ssList(v6) & ssItem(v7))) & ! [v5] : ( ~ lt(v5, v5) | ~ ssItem(v5)) & ! [v5] : ( ~ singletonP(v5) | ~ ssList(v5) | ? [v6] : (cons(v6, nil) = v5 & ssItem(v6))) & ! [v5] : ( ~ memberP(nil, v5) | ~ ssItem(v5)) & ! [v5] : ( ~ ssList(v5) | ~ neq(v5, v5)) & ! [v5] : ( ~ ssList(v5) | equalelemsP(v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v7 = v6) & cons(v7, v9) = v10 & cons(v6, v10) = v11 & app(v8, v11) = v5 & ssList(v9) & ssList(v8) & ssItem(v7) & ssItem(v6))) & ! [v5] : ( ~ ssList(v5) | duplicatefreeP(v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (cons(v6, v11) = v12 & cons(v6, v8) = v9 & app(v10, v12) = v5 & app(v7, v9) = v10 & ssList(v11) & ssList(v8) & ssList(v7) & ssItem(v6))) & ! [v5] : ( ~ ssList(v5) | strictorderedP(v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (cons(v7, v12) = v13 & cons(v6, v9) = v10 & app(v11, v13) = v5 & app(v8, v10) = v11 & ssList(v12) & ssList(v9) & ssList(v8) & ssItem(v7) & ssItem(v6) & ~ lt(v6, v7))) & ! [v5] : ( ~ ssList(v5) | totalorderedP(v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (cons(v7, v12) = v13 & cons(v6, v9) = v10 & app(v11, v13) = v5 & app(v8, v10) = v11 & ssList(v12) & ssList(v9) & ssList(v8) & ssItem(v7) & ssItem(v6) & ~ leq(v6, v7))) & ! [v5] : ( ~ ssList(v5) | strictorderP(v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (cons(v7, v12) = v13 & cons(v6, v9) = v10 & app(v11, v13) = v5 & app(v8, v10) = v11 & ssList(v12) & ssList(v9) & ssList(v8) & ssItem(v7) & ssItem(v6) & ~ lt(v7, v6) & ~ lt(v6, v7))) & ! [v5] : ( ~ ssList(v5) | totalorderP(v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (cons(v7, v12) = v13 & cons(v6, v9) = v10 & app(v11, v13) = v5 & app(v8, v10) = v11 & ssList(v12) & ssList(v9) & ssList(v8) & ssItem(v7) & ssItem(v6) & ~ leq(v7, v6) & ~ leq(v6, v7))) & ! [v5] : ( ~ ssList(v5) | cyclefreeP(v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (cons(v7, v12) = v13 & cons(v6, v9) = v10 & app(v11, v13) = v5 & app(v8, v10) = v11 & leq(v7, v6) & leq(v6, v7) & ssList(v12) & ssList(v9) & ssList(v8) & ssItem(v7) & ssItem(v6))) & ! [v5] : ( ~ ssList(v5) | segmentP(v5, v5)) & ! [v5] : ( ~ ssList(v5) | segmentP(v5, nil)) & ! [v5] : ( ~ ssList(v5) | rearsegP(v5, v5)) & ! [v5] : ( ~ ssList(v5) | rearsegP(v5, nil)) & ! [v5] : ( ~ ssList(v5) | frontsegP(v5, v5)) & ! [v5] : ( ~ ssList(v5) | frontsegP(v5, nil)) & ! [v5] : ( ~ neq(v5, v5) | ~ ssItem(v5)) & ! [v5] : ( ~ ssItem(v5) | geq(v5, v5)) & ! [v5] : ( ~ ssItem(v5) | leq(v5, v5)))
% 33.38/9.71 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields:
% 33.38/9.71 | (1) ~ (all_0_0_0 = all_0_1_1) & tl(all_0_3_3) = all_0_2_2 & equalelemsP(nil) & duplicatefreeP(nil) & strictorderedP(nil) & totalorderedP(nil) & strictorderP(nil) & totalorderP(nil) & cyclefreeP(nil) & segmentP(nil, nil) & rearsegP(nil, nil) & frontsegP(nil, nil) & ssList(all_0_3_3) & ssList(all_0_4_4) & ssList(nil) & neq(all_0_3_3, nil) & ssItem(all_0_0_0) & ssItem(all_0_1_1) & ~ singletonP(nil) & ~ neq(all_0_4_4, nil) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v2, v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ strictorderedP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | lt(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v2, v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ totalorderedP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | leq(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v2, v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ strictorderP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | lt(v2, v1) | lt(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v2, v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ totalorderP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | leq(v2, v1) | leq(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v2, v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ leq(v2, v1) | ~ leq(v1, v2) | ~ cyclefreeP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (cons(v1, v6) = v7) | ~ (cons(v1, v3) = v4) | ~ (app(v5, v7) = v0) | ~ (app(v2, v4) = v5) | ~ duplicatefreeP(v0) | ~ ssList(v6) | ~ ssList(v3) | ~ ssList(v2) | ~ ssList(v0) | ~ ssItem(v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (cons(v2, v4) = v5) | ~ (cons(v1, v5) = v6) | ~ (app(v3, v6) = v0) | ~ equalelemsP(v0) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (cons(v1, v4) = v5) | ~ (cons(v0, v2) = v3) | ~ frontsegP(v3, v5) | ~ ssList(v4) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cons(v1, v4) = v5) | ~ (cons(v0, v2) = v3) | ~ frontsegP(v3, v5) | ~ ssList(v4) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | frontsegP(v2, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (app(v3, v4) = v5) | ~ (app(v2, v0) = v3) | ~ segmentP(v0, v1) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v5, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v3, v2) = v4) | ~ (app(v1, v0) = v2) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v3) | ? [v5] : (cons(v3, v1) = v5 & app(v5, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v1, v3) = v4) | ~ (app(v2, v4) = v0) | ~ ssList(v3) | ~ ssList(v2) | ~ ssList(v0) | ~ ssItem(v1) | memberP(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v0, v3) = v4) | ~ (cons(v0, v1) = v2) | ~ frontsegP(v1, v3) | ~ ssList(v3) | ~ ssList(v1) | ~ ssItem(v0) | frontsegP(v2, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5] : (app(v1, v3) = v5 & app(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ~ ssList(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | ? [v4] : (tl(v4) = v3 & app(v0, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | hd(v3) = v1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ~ ssList(v0) | ~ ssItem(v1) | cons(v1, v0) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v2, v0) = v3) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0) | memberP(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v1, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v0, v2) = v3) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (hd(v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : ((v1 = nil | (cons(v0, v1) = v3 & ~ strictorderedP(v3)) | (strictorderedP(v1) & lt(v0, v2))) & (( ~ (v1 = nil) & ( ~ strictorderedP(v1) | ~ lt(v0, v2))) | (cons(v0, v1) = v3 & strictorderedP(v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (hd(v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : ((v1 = nil | (cons(v0, v1) = v3 & ~ totalorderedP(v3)) | (totalorderedP(v1) & leq(v0, v2))) & (( ~ (v1 = nil) & ( ~ totalorderedP(v1) | ~ leq(v0, v2))) | (cons(v0, v1) = v3 & totalorderedP(v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | tl(v2) = v0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | hd(v2) = v1) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v2, v1) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v1, v2) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v0, v1) = v2) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ gt(v1, v2) | ~ gt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ geq(v1, v2) | ~ geq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ lt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ leq(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ segmentP(v1, v2) | ~ segmentP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ rearsegP(v1, v2) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ frontsegP(v1, v2) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ geq(v1, v0) | ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v1, v0) | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ segmentP(v1, v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ rearsegP(v1, v0) | ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ frontsegP(v1, v0) | ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ ssList(v1) | ~ ssList(v0) | neq(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ ssItem(v1) | ~ ssItem(v0) | neq(v0, v1)) & ! [v0] : ! [v1] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ~ ssList(v0) | ssList(v1)) & ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ~ ssList(v0) | ssItem(v1)) & ! [v0] : ! [v1] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : ( ~ (tl(v0) = v1) | ~ ssList(v0) | ? [v2] : (hd(v0) = v2 & ! [v3] : (v3 = v0 | v3 = nil | v0 = nil | ~ (tl(v3) = v1) | ~ ssList(v3) | ? [v4] : ( ~ (v4 = v2) & hd(v3) = v4)))) & ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = v0) | ~ ssList(v0) | ~ ssItem(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = nil) | ~ ssList(v0) | ~ ssItem(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v1, nil) = v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | equalelemsP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | duplicatefreeP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderedP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderedP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | cyclefreeP(v1)) & ! [v0] : ! [v1] : ( ~ gt(v1, v0) | ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0] : ! [v1] : ( ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v1, v0)) & ! [v0] : ! [v1] : ( ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v1, v0)) & ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v1)) & ! [v0] : ! [v1] : ( ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v1)) & ! [v0] : ! [v1] : ( ~ leq(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v1)) & ! [v0] : ! [v1] : ( ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : ? [v3] : ? [v4] : (app(v3, v4) = v0 & app(v2, v1) = v3 & ssList(v4) & ssList(v2))) & ! [v0] : ! [v1] : ( ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v2, v1) = v0 & ssList(v2))) & ! [v0] : ! [v1] : ( ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v1, v2) = v0 & ssList(v2))) & ! [v0] : ! [v1] : ( ~ memberP(v0, v1) | ~ ssList(v0) | ~ ssItem(v1) | ? [v2] : ? [v3] : ? [v4] : (cons(v1, v3) = v4 & app(v2, v4) = v0 & ssList(v3) & ssList(v2))) & ! [v0] : (v0 = all_0_3_3 | ~ ssList(v0) | ~ ssList(all_0_2_2) | ~ neq(nil, all_0_3_3) | ? [v1] : ( ~ (v1 = v0) & app(all_0_4_4, all_0_2_2) = v1)) & ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0)) & ! [v0] : (v0 = nil | ~ segmentP(nil, v0) | ~ ssList(v0)) & ! [v0] : (v0 = nil | ~ rearsegP(nil, v0) | ~ ssList(v0)) & ! [v0] : (v0 = nil | ~ frontsegP(nil, v0) | ~ ssList(v0)) & ! [v0] : (v0 = nil | ~ ssList(v0) | ? [v1] : ? [v2] : (cons(v2, v1) = v0 & ssList(v1) & ssItem(v2))) & ! [v0] : ( ~ lt(v0, v0) | ~ ssItem(v0)) & ! [v0] : ( ~ singletonP(v0) | ~ ssList(v0) | ? [v1] : (cons(v1, nil) = v0 & ssItem(v1))) & ! [v0] : ( ~ memberP(nil, v0) | ~ ssItem(v0)) & ! [v0] : ( ~ ssList(v0) | ~ neq(v0, v0)) & ! [v0] : ( ~ ssList(v0) | equalelemsP(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v2 = v1) & cons(v2, v4) = v5 & cons(v1, v5) = v6 & app(v3, v6) = v0 & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1))) & ! [v0] : ( ~ ssList(v0) | duplicatefreeP(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (cons(v1, v6) = v7 & cons(v1, v3) = v4 & app(v5, v7) = v0 & app(v2, v4) = v5 & ssList(v6) & ssList(v3) & ssList(v2) & ssItem(v1))) & ! [v0] : ( ~ ssList(v0) | strictorderedP(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3, v5) = v6 & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1) & ~ lt(v1, v2))) & ! [v0] : ( ~ ssList(v0) | totalorderedP(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3, v5) = v6 & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1) & ~ leq(v1, v2))) & ! [v0] : ( ~ ssList(v0) | strictorderP(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3, v5) = v6 & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1) & ~ lt(v2, v1) & ~ lt(v1, v2))) & ! [v0] : ( ~ ssList(v0) | totalorderP(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3, v5) = v6 & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1) & ~ leq(v2, v1) & ~ leq(v1, v2))) & ! [v0] : ( ~ ssList(v0) | cyclefreeP(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3, v5) = v6 & leq(v2, v1) & leq(v1, v2) & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1))) & ! [v0] : ( ~ ssList(v0) | segmentP(v0, v0)) & ! [v0] : ( ~ ssList(v0) | segmentP(v0, nil)) & ! [v0] : ( ~ ssList(v0) | rearsegP(v0, v0)) & ! [v0] : ( ~ ssList(v0) | rearsegP(v0, nil)) & ! [v0] : ( ~ ssList(v0) | frontsegP(v0, v0)) & ! [v0] : ( ~ ssList(v0) | frontsegP(v0, nil)) & ! [v0] : ( ~ neq(v0, v0) | ~ ssItem(v0)) & ! [v0] : ( ~ ssItem(v0) | geq(v0, v0)) & ! [v0] : ( ~ ssItem(v0) | leq(v0, v0))
% 33.79/9.73 |
% 33.79/9.73 | Applying alpha-rule on (1) yields:
% 33.79/9.73 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5] : (app(v1, v3) = v5 & app(v0, v5) = v4))
% 33.79/9.73 | (3) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderP(v1))
% 33.79/9.73 | (4) ! [v0] : ( ~ ssList(v0) | rearsegP(v0, nil))
% 33.79/9.73 | (5) ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = v0) | ~ ssList(v0) | ~ ssItem(v1))
% 33.79/9.73 | (6) ssItem(all_0_1_1)
% 33.79/9.73 | (7) ! [v0] : ( ~ ssList(v0) | segmentP(v0, nil))
% 33.79/9.73 | (8) ssList(nil)
% 33.79/9.73 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v2, v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ leq(v2, v1) | ~ leq(v1, v2) | ~ cyclefreeP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1))
% 33.79/9.73 | (10) ! [v0] : ( ~ neq(v0, v0) | ~ ssItem(v0))
% 33.79/9.73 | (11) ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = nil) | ~ ssList(v0) | ~ ssItem(v1))
% 33.79/9.74 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (cons(v1, v4) = v5) | ~ (cons(v0, v2) = v3) | ~ frontsegP(v3, v5) | ~ ssList(v4) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0))
% 33.79/9.74 | (13) ! [v0] : ! [v1] : ( ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v1, v0))
% 33.79/9.74 | (14) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0))
% 33.79/9.74 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cons(v1, v4) = v5) | ~ (cons(v0, v2) = v3) | ~ frontsegP(v3, v5) | ~ ssList(v4) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | frontsegP(v2, v4))
% 33.79/9.74 | (16) segmentP(nil, nil)
% 33.79/9.74 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v0, v3) = v4) | ~ (cons(v0, v1) = v2) | ~ frontsegP(v1, v3) | ~ ssList(v3) | ~ ssList(v1) | ~ ssItem(v0) | frontsegP(v2, v4))
% 33.79/9.74 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v1, v0) | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0))
% 33.79/9.74 | (19) ~ neq(all_0_4_4, nil)
% 33.79/9.74 | (20) ! [v0] : ( ~ ssList(v0) | rearsegP(v0, v0))
% 33.79/9.74 | (21) ! [v0] : (v0 = nil | ~ frontsegP(nil, v0) | ~ ssList(v0))
% 33.79/9.74 | (22) ! [v0] : ( ~ lt(v0, v0) | ~ ssItem(v0))
% 33.79/9.74 | (23) ssList(all_0_3_3)
% 33.79/9.74 | (24) ! [v0] : ( ~ ssList(v0) | cyclefreeP(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3, v5) = v6 & leq(v2, v1) & leq(v1, v2) & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1)))
% 33.79/9.74 | (25) ! [v0] : ! [v1] : ( ~ (cons(v1, nil) = v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0))
% 33.79/9.74 | (26) ssList(all_0_4_4)
% 33.79/9.74 | (27) ! [v0] : ! [v1] : (v1 = v0 | ~ geq(v1, v0) | ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0))
% 33.79/9.74 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v2, v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ strictorderedP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | lt(v1, v2))
% 33.79/9.74 | (29) strictorderP(nil)
% 33.79/9.74 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0))
% 33.79/9.74 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v3, v0))
% 33.79/9.74 | (32) ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0))
% 33.79/9.74 | (33) ~ (all_0_0_0 = all_0_1_1)
% 33.79/9.74 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ gt(v1, v2) | ~ gt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v2))
% 33.79/9.74 | (35) ~ singletonP(nil)
% 33.79/9.74 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2))
% 33.79/9.74 | (37) ! [v0] : ! [v1] : ( ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v1, v2) = v0 & ssList(v2)))
% 33.79/9.74 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0) | memberP(v1, v0))
% 33.79/9.74 | (39) strictorderedP(nil)
% 33.79/9.74 | (40) ! [v0] : ( ~ ssList(v0) | totalorderP(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3, v5) = v6 & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1) & ~ leq(v2, v1) & ~ leq(v1, v2)))
% 33.79/9.74 | (41) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ~ ssList(v0) | ssList(v1))
% 33.79/9.74 | (42) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ ssList(v0))
% 33.79/9.74 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0))
% 33.79/9.74 | (44) ! [v0] : ! [v1] : ( ~ gt(v1, v0) | ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0))
% 33.79/9.74 | (45) ! [v0] : ! [v1] : ( ~ (tl(v0) = v1) | ~ ssList(v0) | ? [v2] : (hd(v0) = v2 & ! [v3] : (v3 = v0 | v3 = nil | v0 = nil | ~ (tl(v3) = v1) | ~ ssList(v3) | ? [v4] : ( ~ (v4 = v2) & hd(v3) = v4))))
% 33.79/9.74 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v1, v3) = v4) | ~ (app(v2, v4) = v0) | ~ ssList(v3) | ~ ssList(v2) | ~ ssList(v0) | ~ ssItem(v1) | memberP(v0, v1))
% 33.79/9.75 | (47) ! [v0] : ! [v1] : (v1 = v0 | ~ segmentP(v1, v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0))
% 33.79/9.75 | (48) ! [v0] : (v0 = nil | ~ segmentP(nil, v0) | ~ ssList(v0))
% 33.79/9.75 | (49) ! [v0] : ! [v1] : ! [v2] : ( ~ (hd(v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : ((v1 = nil | (cons(v0, v1) = v3 & ~ totalorderedP(v3)) | (totalorderedP(v1) & leq(v0, v2))) & (( ~ (v1 = nil) & ( ~ totalorderedP(v1) | ~ leq(v0, v2))) | (cons(v0, v1) = v3 & totalorderedP(v3)))))
% 33.79/9.75 | (50) ! [v0] : ( ~ ssItem(v0) | geq(v0, v0))
% 33.79/9.75 | (51) ! [v0] : ( ~ ssList(v0) | strictorderedP(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3, v5) = v6 & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1) & ~ lt(v1, v2)))
% 33.79/9.75 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | ? [v4] : (tl(v4) = v3 & app(v0, v2) = v4))
% 33.79/9.75 | (53) ! [v0] : ( ~ ssList(v0) | equalelemsP(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v2 = v1) & cons(v2, v4) = v5 & cons(v1, v5) = v6 & app(v3, v6) = v0 & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1)))
% 33.79/9.75 | (54) ! [v0] : ( ~ ssList(v0) | frontsegP(v0, v0))
% 33.79/9.75 | (55) duplicatefreeP(nil)
% 33.79/9.75 | (56) ! [v0] : ( ~ ssItem(v0) | leq(v0, v0))
% 33.79/9.75 | (57) ! [v0] : ! [v1] : ! [v2] : ( ~ geq(v1, v2) | ~ geq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v2))
% 33.79/9.75 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ segmentP(v1, v2) | ~ segmentP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v2))
% 33.79/9.75 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ~ ssList(v0))
% 33.79/9.75 | (60) ! [v0] : ! [v1] : (v1 = v0 | ~ ssList(v1) | ~ ssList(v0) | neq(v0, v1))
% 33.79/9.75 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (cons(v1, v6) = v7) | ~ (cons(v1, v3) = v4) | ~ (app(v5, v7) = v0) | ~ (app(v2, v4) = v5) | ~ duplicatefreeP(v0) | ~ ssList(v6) | ~ ssList(v3) | ~ ssList(v2) | ~ ssList(v0) | ~ ssItem(v1))
% 33.79/9.75 | (62) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v2, v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ totalorderedP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | leq(v1, v2))
% 33.79/9.75 | (63) ! [v0] : ( ~ ssList(v0) | frontsegP(v0, nil))
% 33.79/9.75 | (64) frontsegP(nil, nil)
% 33.79/9.75 | (65) ! [v0] : (v0 = nil | ~ ssList(v0) | ? [v1] : ? [v2] : (cons(v2, v1) = v0 & ssList(v1) & ssItem(v2)))
% 33.79/9.75 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v0, v1) = v2) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2))
% 33.79/9.75 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v3, v2) = v4) | ~ (app(v1, v0) = v2) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v3) | ? [v5] : (cons(v3, v1) = v5 & app(v5, v0) = v4))
% 33.79/9.75 | (68) ! [v0] : ( ~ ssList(v0) | ~ neq(v0, v0))
% 33.79/9.75 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (cons(v2, v4) = v5) | ~ (cons(v1, v5) = v6) | ~ (app(v3, v6) = v0) | ~ equalelemsP(v0) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1))
% 33.79/9.75 | (70) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | duplicatefreeP(v1))
% 33.79/9.75 | (71) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 33.79/9.75 | (72) ! [v0] : ( ~ ssList(v0) | duplicatefreeP(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : (cons(v1, v6) = v7 & cons(v1, v3) = v4 & app(v5, v7) = v0 & app(v2, v4) = v5 & ssList(v6) & ssList(v3) & ssList(v2) & ssItem(v1)))
% 33.79/9.75 | (73) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderedP(v1))
% 33.79/9.75 | (74) ! [v0] : ! [v1] : (v1 = v0 | ~ rearsegP(v1, v0) | ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0))
% 33.79/9.75 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 33.79/9.75 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 33.79/9.76 | (77) ! [v0] : ( ~ ssList(v0) | strictorderP(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3, v5) = v6 & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1) & ~ lt(v2, v1) & ~ lt(v1, v2)))
% 33.79/9.76 | (78) cyclefreeP(nil)
% 33.79/9.76 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | hd(v3) = v1)
% 33.79/9.76 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v1, v2) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v1))
% 33.79/9.76 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | tl(v2) = v0)
% 33.79/9.76 | (82) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v2, v0))
% 33.79/9.76 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (app(v3, v4) = v5) | ~ (app(v2, v0) = v3) | ~ segmentP(v0, v1) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v5, v1))
% 33.79/9.76 | (84) ! [v0] : ! [v1] : (v1 = v0 | ~ frontsegP(v1, v0) | ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0))
% 33.79/9.76 | (85) ! [v0] : ! [v1] : ( ~ memberP(v0, v1) | ~ ssList(v0) | ~ ssItem(v1) | ? [v2] : ? [v3] : ? [v4] : (cons(v1, v3) = v4 & app(v2, v4) = v0 & ssList(v3) & ssList(v2)))
% 33.79/9.76 | (86) ! [v0] : ! [v1] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0))
% 33.79/9.76 | (87) ! [v0] : ( ~ singletonP(v0) | ~ ssList(v0) | ? [v1] : (cons(v1, nil) = v0 & ssItem(v1)))
% 33.79/9.76 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ leq(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v2))
% 33.79/9.76 | (89) ! [v0] : ( ~ ssList(v0) | totalorderedP(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3, v5) = v6 & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1) & ~ leq(v1, v2)))
% 33.79/9.76 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | hd(v2) = v1)
% 33.79/9.76 | (91) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v2, v1) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v1))
% 33.79/9.76 | (92) ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ lt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2))
% 33.79/9.76 | (93) ! [v0] : ! [v1] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0))
% 33.79/9.76 | (94) ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2))
% 33.79/9.76 | (95) ! [v0] : ! [v1] : (v1 = v0 | ~ ssItem(v1) | ~ ssItem(v0) | neq(v0, v1))
% 33.79/9.76 | (96) tl(all_0_3_3) = all_0_2_2
% 33.79/9.76 | (97) neq(all_0_3_3, nil)
% 33.79/9.76 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 33.79/9.76 | (99) ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v1))
% 33.79/9.76 | (100) ! [v0] : ! [v1] : ( ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v2, v1) = v0 & ssList(v2)))
% 33.79/9.76 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ~ ssList(v0) | ~ ssItem(v1) | cons(v1, v0) = v3)
% 33.79/9.76 | (102) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderP(v1))
% 33.79/9.76 | (103) ! [v0] : (v0 = nil | ~ rearsegP(nil, v0) | ~ ssList(v0))
% 33.79/9.76 | (104) ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v1))
% 33.79/9.76 | (105) ! [v0] : ! [v1] : ( ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v1))
% 33.79/9.76 | (106) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderedP(v1))
% 33.79/9.76 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2))
% 33.79/9.76 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v2, v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ totalorderP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | leq(v2, v1) | leq(v1, v2))
% 33.79/9.76 | (109) ! [v0] : ( ~ ssList(v0) | segmentP(v0, v0))
% 33.79/9.76 | (110) ! [v0] : (v0 = all_0_3_3 | ~ ssList(v0) | ~ ssList(all_0_2_2) | ~ neq(nil, all_0_3_3) | ? [v1] : ( ~ (v1 = v0) & app(all_0_4_4, all_0_2_2) = v1))
% 33.79/9.76 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v1))
% 33.79/9.76 | (112) rearsegP(nil, nil)
% 33.79/9.76 | (113) ! [v0] : ! [v1] : ( ~ leq(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v1))
% 33.79/9.76 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v2, v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ strictorderP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | lt(v2, v1) | lt(v1, v2))
% 33.79/9.76 | (115) ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0))
% 33.79/9.76 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ frontsegP(v1, v2) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v2))
% 33.79/9.76 | (117) ssItem(all_0_0_0)
% 33.79/9.76 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2))
% 33.79/9.76 | (119) ! [v0] : ! [v1] : ( ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v1, v0))
% 33.79/9.76 | (120) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | equalelemsP(v1))
% 33.79/9.76 | (121) ! [v0] : ! [v1] : ( ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : ? [v3] : ? [v4] : (app(v3, v4) = v0 & app(v2, v1) = v3 & ssList(v4) & ssList(v2)))
% 33.79/9.76 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0))
% 33.79/9.76 | (123) equalelemsP(nil)
% 33.79/9.76 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v2, v0) = v3) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1))
% 33.79/9.77 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v1, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0))
% 33.79/9.77 | (126) ! [v0] : ! [v1] : ! [v2] : ( ~ rearsegP(v1, v2) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v2))
% 33.79/9.77 | (127) totalorderP(nil)
% 33.79/9.77 | (128) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | cyclefreeP(v1))
% 33.79/9.77 | (129) ! [v0] : ! [v1] : ! [v2] : ( ~ (hd(v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : ((v1 = nil | (cons(v0, v1) = v3 & ~ strictorderedP(v3)) | (strictorderedP(v1) & lt(v0, v2))) & (( ~ (v1 = nil) & ( ~ strictorderedP(v1) | ~ lt(v0, v2))) | (cons(v0, v1) = v3 & strictorderedP(v3)))))
% 33.79/9.77 | (130) totalorderedP(nil)
% 33.79/9.77 | (131) ! [v0] : ( ~ memberP(nil, v0) | ~ ssItem(v0))
% 33.79/9.77 | (132) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ ssList(v0))
% 33.79/9.77 | (133) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v0, v2) = v3) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v3, v1))
% 33.79/9.77 | (134) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ~ ssList(v0) | ssItem(v1))
% 33.79/9.77 |
% 33.79/9.77 | Using (97) and (19) yields:
% 33.79/9.77 | (135) ~ (all_0_3_3 = all_0_4_4)
% 33.79/9.77 |
% 33.79/9.77 | Instantiating formula (41) with all_0_2_2, all_0_3_3 and discharging atoms tl(all_0_3_3) = all_0_2_2, ssList(all_0_3_3), yields:
% 33.79/9.77 | (136) all_0_3_3 = nil | ssList(all_0_2_2)
% 33.79/9.77 |
% 33.79/9.77 | Instantiating formula (45) with all_0_2_2, all_0_3_3 and discharging atoms tl(all_0_3_3) = all_0_2_2, ssList(all_0_3_3), yields:
% 33.79/9.77 | (137) ? [v0] : (hd(all_0_3_3) = v0 & ! [v1] : (v1 = all_0_3_3 | v1 = nil | all_0_3_3 = nil | ~ (tl(v1) = all_0_2_2) | ~ ssList(v1) | ? [v2] : ( ~ (v2 = v0) & hd(v1) = v2)))
% 33.79/9.77 |
% 33.79/9.77 | Instantiating formula (65) with all_0_3_3 and discharging atoms ssList(all_0_3_3), yields:
% 33.79/9.77 | (138) all_0_3_3 = nil | ? [v0] : ? [v1] : (cons(v1, v0) = all_0_3_3 & ssList(v0) & ssItem(v1))
% 33.79/9.77 |
% 33.79/9.77 | Instantiating formula (121) with nil, nil and discharging atoms segmentP(nil, nil), ssList(nil), yields:
% 33.79/9.77 | (139) ? [v0] : ? [v1] : ? [v2] : (app(v1, v2) = nil & app(v0, nil) = v1 & ssList(v2) & ssList(v0))
% 33.79/9.77 |
% 33.79/9.77 | Instantiating formula (100) with nil, nil and discharging atoms rearsegP(nil, nil), ssList(nil), yields:
% 33.79/9.77 | (140) ? [v0] : (app(v0, nil) = nil & ssList(v0))
% 33.79/9.77 |
% 33.79/9.77 | Instantiating formula (60) with all_0_3_3, nil and discharging atoms ssList(all_0_3_3), ssList(nil), yields:
% 33.79/9.77 | (141) all_0_3_3 = nil | neq(nil, all_0_3_3)
% 33.79/9.77 |
% 33.79/9.77 | Instantiating formula (60) with nil, all_0_4_4 and discharging atoms ssList(all_0_4_4), ssList(nil), ~ neq(all_0_4_4, nil), yields:
% 33.79/9.77 | (142) all_0_4_4 = nil
% 33.79/9.77 |
% 33.79/9.77 | Instantiating (137) with all_13_0_5 yields:
% 33.79/9.77 | (143) hd(all_0_3_3) = all_13_0_5 & ! [v0] : (v0 = all_0_3_3 | v0 = nil | all_0_3_3 = nil | ~ (tl(v0) = all_0_2_2) | ~ ssList(v0) | ? [v1] : ( ~ (v1 = all_13_0_5) & hd(v0) = v1))
% 33.79/9.77 |
% 33.79/9.77 | Applying alpha-rule on (143) yields:
% 33.79/9.77 | (144) hd(all_0_3_3) = all_13_0_5
% 33.79/9.77 | (145) ! [v0] : (v0 = all_0_3_3 | v0 = nil | all_0_3_3 = nil | ~ (tl(v0) = all_0_2_2) | ~ ssList(v0) | ? [v1] : ( ~ (v1 = all_13_0_5) & hd(v0) = v1))
% 33.79/9.77 |
% 33.79/9.77 | Instantiating (140) with all_18_0_7 yields:
% 33.79/9.77 | (146) app(all_18_0_7, nil) = nil & ssList(all_18_0_7)
% 33.79/9.77 |
% 33.79/9.77 | Applying alpha-rule on (146) yields:
% 33.79/9.77 | (147) app(all_18_0_7, nil) = nil
% 33.79/9.77 | (148) ssList(all_18_0_7)
% 33.79/9.77 |
% 33.79/9.77 | Instantiating (139) with all_20_0_8, all_20_1_9, all_20_2_10 yields:
% 33.79/9.77 | (149) app(all_20_1_9, all_20_0_8) = nil & app(all_20_2_10, nil) = all_20_1_9 & ssList(all_20_0_8) & ssList(all_20_2_10)
% 33.79/9.77 |
% 33.79/9.77 | Applying alpha-rule on (149) yields:
% 33.79/9.77 | (150) app(all_20_1_9, all_20_0_8) = nil
% 33.79/9.77 | (151) app(all_20_2_10, nil) = all_20_1_9
% 33.79/9.77 | (152) ssList(all_20_0_8)
% 33.79/9.77 | (153) ssList(all_20_2_10)
% 33.79/9.77 |
% 33.79/9.77 | Equations (142) can reduce 135 to:
% 33.79/9.77 | (154) ~ (all_0_3_3 = nil)
% 33.79/9.77 |
% 33.79/9.77 +-Applying beta-rule and splitting (138), into two cases.
% 33.79/9.77 |-Branch one:
% 33.79/9.77 | (155) all_0_3_3 = nil
% 33.79/9.77 |
% 33.79/9.77 | Equations (155) can reduce 154 to:
% 33.79/9.77 | (156) $false
% 33.79/9.77 |
% 33.79/9.77 |-The branch is then unsatisfiable
% 33.79/9.77 |-Branch two:
% 33.79/9.77 | (154) ~ (all_0_3_3 = nil)
% 33.79/9.77 | (158) ? [v0] : ? [v1] : (cons(v1, v0) = all_0_3_3 & ssList(v0) & ssItem(v1))
% 33.79/9.77 |
% 33.79/9.77 | Instantiating (158) with all_29_0_11, all_29_1_12 yields:
% 33.79/9.77 | (159) cons(all_29_0_11, all_29_1_12) = all_0_3_3 & ssList(all_29_1_12) & ssItem(all_29_0_11)
% 33.79/9.77 |
% 33.79/9.77 | Applying alpha-rule on (159) yields:
% 33.79/9.77 | (160) cons(all_29_0_11, all_29_1_12) = all_0_3_3
% 33.79/9.77 | (161) ssList(all_29_1_12)
% 33.79/9.77 | (162) ssItem(all_29_0_11)
% 33.79/9.77 |
% 33.79/9.77 +-Applying beta-rule and splitting (136), into two cases.
% 33.79/9.77 |-Branch one:
% 33.79/9.77 | (163) ssList(all_0_2_2)
% 33.79/9.77 |
% 33.79/9.77 +-Applying beta-rule and splitting (141), into two cases.
% 33.79/9.77 |-Branch one:
% 33.79/9.77 | (164) neq(nil, all_0_3_3)
% 33.79/9.77 |
% 33.79/9.77 | Instantiating formula (132) with all_20_1_9, all_20_2_10 and discharging atoms app(all_20_2_10, nil) = all_20_1_9, ssList(all_20_2_10), yields:
% 33.79/9.77 | (165) all_20_1_9 = all_20_2_10
% 33.79/9.77 |
% 33.79/9.77 | Instantiating formula (132) with nil, all_18_0_7 and discharging atoms app(all_18_0_7, nil) = nil, ssList(all_18_0_7), yields:
% 33.79/9.77 | (166) all_18_0_7 = nil
% 33.79/9.77 |
% 33.79/9.77 | Instantiating formula (86) with all_20_0_8, all_20_2_10 and discharging atoms ssList(all_20_0_8), ssList(all_20_2_10), yields:
% 33.79/9.77 | (167) all_20_2_10 = nil | ~ (app(all_20_2_10, all_20_0_8) = nil)
% 33.79/9.77 |
% 33.79/9.77 | Instantiating formula (93) with all_20_0_8, all_18_0_7 and discharging atoms ssList(all_20_0_8), ssList(all_18_0_7), yields:
% 33.79/9.77 | (168) all_20_0_8 = nil | ~ (app(all_18_0_7, all_20_0_8) = nil)
% 33.79/9.77 |
% 33.79/9.77 | From (165) and (150) follows:
% 33.79/9.77 | (169) app(all_20_2_10, all_20_0_8) = nil
% 33.79/9.77 |
% 33.79/9.77 +-Applying beta-rule and splitting (167), into two cases.
% 33.79/9.77 |-Branch one:
% 33.79/9.77 | (170) ~ (app(all_20_2_10, all_20_0_8) = nil)
% 33.79/9.77 |
% 33.79/9.77 | Using (169) and (170) yields:
% 33.79/9.77 | (171) $false
% 33.79/9.77 |
% 33.79/9.77 |-The branch is then unsatisfiable
% 33.79/9.77 |-Branch two:
% 33.79/9.77 | (169) app(all_20_2_10, all_20_0_8) = nil
% 33.79/9.77 | (173) all_20_2_10 = nil
% 33.79/9.78 |
% 33.79/9.78 | From (173) and (169) follows:
% 33.79/9.78 | (174) app(nil, all_20_0_8) = nil
% 33.79/9.78 |
% 33.79/9.78 +-Applying beta-rule and splitting (168), into two cases.
% 33.79/9.78 |-Branch one:
% 33.79/9.78 | (175) ~ (app(all_18_0_7, all_20_0_8) = nil)
% 33.79/9.78 |
% 33.79/9.78 | From (166) and (175) follows:
% 33.79/9.78 | (176) ~ (app(nil, all_20_0_8) = nil)
% 33.79/9.78 |
% 33.79/9.78 | Using (174) and (176) yields:
% 33.79/9.78 | (171) $false
% 33.79/9.78 |
% 33.79/9.78 |-The branch is then unsatisfiable
% 33.79/9.78 |-Branch two:
% 33.79/9.78 | (178) app(all_18_0_7, all_20_0_8) = nil
% 33.79/9.78 | (179) all_20_0_8 = nil
% 33.79/9.78 |
% 33.79/9.78 | From (179) and (152) follows:
% 33.79/9.78 | (8) ssList(nil)
% 33.79/9.78 |
% 33.79/9.78 | Instantiating formula (110) with nil and discharging atoms ssList(all_0_2_2), ssList(nil), neq(nil, all_0_3_3), yields:
% 33.79/9.78 | (181) all_0_3_3 = nil | ? [v0] : ( ~ (v0 = nil) & app(all_0_4_4, all_0_2_2) = v0)
% 33.79/9.78 |
% 33.79/9.78 | Instantiating formula (110) with all_29_1_12 and discharging atoms ssList(all_29_1_12), ssList(all_0_2_2), neq(nil, all_0_3_3), yields:
% 33.79/9.78 | (182) all_29_1_12 = all_0_3_3 | ? [v0] : ( ~ (v0 = all_29_1_12) & app(all_0_4_4, all_0_2_2) = v0)
% 33.79/9.78 |
% 33.79/9.78 | Instantiating formula (81) with all_0_3_3, all_29_0_11, all_29_1_12 and discharging atoms cons(all_29_0_11, all_29_1_12) = all_0_3_3, ssList(all_29_1_12), ssItem(all_29_0_11), yields:
% 33.79/9.78 | (183) tl(all_0_3_3) = all_29_1_12
% 33.79/9.78 |
% 33.79/9.78 | Instantiating formula (90) with all_0_3_3, all_29_0_11, all_29_1_12 and discharging atoms cons(all_29_0_11, all_29_1_12) = all_0_3_3, ssList(all_29_1_12), ssItem(all_29_0_11), yields:
% 33.79/9.78 | (184) hd(all_0_3_3) = all_29_0_11
% 33.79/9.78 |
% 33.79/9.78 +-Applying beta-rule and splitting (181), into two cases.
% 33.79/9.78 |-Branch one:
% 33.79/9.78 | (155) all_0_3_3 = nil
% 33.79/9.78 |
% 33.79/9.78 | Equations (155) can reduce 154 to:
% 33.79/9.78 | (156) $false
% 33.79/9.78 |
% 33.79/9.78 |-The branch is then unsatisfiable
% 33.79/9.78 |-Branch two:
% 33.79/9.78 | (154) ~ (all_0_3_3 = nil)
% 33.79/9.78 | (188) ? [v0] : ( ~ (v0 = nil) & app(all_0_4_4, all_0_2_2) = v0)
% 33.79/9.78 |
% 33.79/9.78 | Instantiating (188) with all_94_0_29 yields:
% 33.79/9.78 | (189) ~ (all_94_0_29 = nil) & app(all_0_4_4, all_0_2_2) = all_94_0_29
% 33.79/9.78 |
% 33.79/9.78 | Applying alpha-rule on (189) yields:
% 33.79/9.78 | (190) ~ (all_94_0_29 = nil)
% 33.79/9.78 | (191) app(all_0_4_4, all_0_2_2) = all_94_0_29
% 33.79/9.78 |
% 33.79/9.78 | From (142) and (191) follows:
% 33.79/9.78 | (192) app(nil, all_0_2_2) = all_94_0_29
% 33.79/9.78 |
% 33.79/9.78 | Instantiating formula (30) with all_0_3_3, all_29_1_12, all_0_2_2 and discharging atoms tl(all_0_3_3) = all_29_1_12, tl(all_0_3_3) = all_0_2_2, yields:
% 33.79/9.78 | (193) all_29_1_12 = all_0_2_2
% 33.79/9.78 |
% 33.79/9.78 | Instantiating formula (71) with all_0_3_3, all_29_0_11, all_13_0_5 and discharging atoms hd(all_0_3_3) = all_29_0_11, hd(all_0_3_3) = all_13_0_5, yields:
% 33.79/9.78 | (194) all_29_0_11 = all_13_0_5
% 33.79/9.78 |
% 33.79/9.78 | Instantiating formula (42) with all_94_0_29, all_0_2_2 and discharging atoms app(nil, all_0_2_2) = all_94_0_29, ssList(all_0_2_2), yields:
% 33.79/9.78 | (195) all_94_0_29 = all_0_2_2
% 33.79/9.78 |
% 33.79/9.78 | From (194)(193) and (160) follows:
% 33.79/9.78 | (196) cons(all_13_0_5, all_0_2_2) = all_0_3_3
% 33.79/9.78 |
% 33.79/9.78 | From (195) and (192) follows:
% 33.79/9.78 | (197) app(nil, all_0_2_2) = all_0_2_2
% 33.79/9.78 |
% 33.79/9.78 | From (193) and (161) follows:
% 33.79/9.78 | (163) ssList(all_0_2_2)
% 33.79/9.78 |
% 33.79/9.78 | From (194) and (162) follows:
% 33.79/9.78 | (199) ssItem(all_13_0_5)
% 33.79/9.78 |
% 33.79/9.78 +-Applying beta-rule and splitting (182), into two cases.
% 33.79/9.78 |-Branch one:
% 33.79/9.78 | (200) all_29_1_12 = all_0_3_3
% 33.79/9.78 |
% 33.79/9.78 | Combining equations (193,200) yields a new equation:
% 33.79/9.78 | (201) all_0_2_2 = all_0_3_3
% 33.79/9.78 |
% 33.79/9.78 | Simplifying 201 yields:
% 33.79/9.78 | (202) all_0_2_2 = all_0_3_3
% 33.79/9.78 |
% 33.79/9.78 | From (202) and (196) follows:
% 33.79/9.78 | (203) cons(all_13_0_5, all_0_3_3) = all_0_3_3
% 33.79/9.78 |
% 33.79/9.78 | From (202) and (163) follows:
% 33.79/9.78 | (23) ssList(all_0_3_3)
% 33.79/9.78 |
% 33.79/9.78 | Instantiating formula (5) with all_13_0_5, all_0_3_3 and discharging atoms cons(all_13_0_5, all_0_3_3) = all_0_3_3, ssList(all_0_3_3), ssItem(all_13_0_5), yields:
% 33.79/9.78 | (171) $false
% 33.79/9.78 |
% 33.79/9.78 |-The branch is then unsatisfiable
% 33.79/9.78 |-Branch two:
% 33.79/9.78 | (206) ~ (all_29_1_12 = all_0_3_3)
% 33.79/9.78 | (207) ? [v0] : ( ~ (v0 = all_29_1_12) & app(all_0_4_4, all_0_2_2) = v0)
% 33.79/9.78 |
% 33.79/9.78 | Instantiating (207) with all_112_0_35 yields:
% 33.79/9.78 | (208) ~ (all_112_0_35 = all_29_1_12) & app(all_0_4_4, all_0_2_2) = all_112_0_35
% 33.79/9.78 |
% 33.79/9.78 | Applying alpha-rule on (208) yields:
% 33.79/9.78 | (209) ~ (all_112_0_35 = all_29_1_12)
% 33.79/9.78 | (210) app(all_0_4_4, all_0_2_2) = all_112_0_35
% 34.14/9.78 |
% 34.14/9.78 | Equations (193) can reduce 209 to:
% 34.14/9.78 | (211) ~ (all_112_0_35 = all_0_2_2)
% 34.14/9.78 |
% 34.14/9.78 | From (142) and (210) follows:
% 34.14/9.78 | (212) app(nil, all_0_2_2) = all_112_0_35
% 34.14/9.78 |
% 34.14/9.78 | Instantiating formula (75) with nil, all_0_2_2, all_0_2_2, all_112_0_35 and discharging atoms app(nil, all_0_2_2) = all_112_0_35, app(nil, all_0_2_2) = all_0_2_2, yields:
% 34.14/9.78 | (213) all_112_0_35 = all_0_2_2
% 34.14/9.78 |
% 34.14/9.78 | Equations (213) can reduce 211 to:
% 34.14/9.78 | (156) $false
% 34.14/9.78 |
% 34.14/9.78 |-The branch is then unsatisfiable
% 34.14/9.78 |-Branch two:
% 34.14/9.78 | (215) ~ neq(nil, all_0_3_3)
% 34.14/9.78 | (155) all_0_3_3 = nil
% 34.14/9.78 |
% 34.14/9.78 | Equations (155) can reduce 154 to:
% 34.14/9.78 | (156) $false
% 34.14/9.78 |
% 34.14/9.78 |-The branch is then unsatisfiable
% 34.14/9.78 |-Branch two:
% 34.14/9.78 | (218) ~ ssList(all_0_2_2)
% 34.14/9.78 | (155) all_0_3_3 = nil
% 34.14/9.78 |
% 34.14/9.78 | Equations (155) can reduce 154 to:
% 34.14/9.78 | (156) $false
% 34.14/9.78 |
% 34.14/9.78 |-The branch is then unsatisfiable
% 34.14/9.78 % SZS output end Proof for theBenchmark
% 34.14/9.78
% 34.14/9.78 9191ms
%------------------------------------------------------------------------------