TSTP Solution File: SWC204+1 by ePrincess---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% 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
%------------------------------------------------------------------------------