TSTP Solution File: SWC006+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWC006+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n027.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 20:15:40 EDT 2022
% Result : Theorem 6.77s 2.20s
% Output : Proof 19.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC006+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n027.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 19:43:31 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.50/0.59 ____ _
% 0.50/0.59 ___ / __ \_____(_)___ ________ __________
% 0.50/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.50/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.50/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.50/0.59
% 0.50/0.59 A Theorem Prover for First-Order Logic
% 0.50/0.59 (ePrincess v.1.0)
% 0.50/0.59
% 0.50/0.59 (c) Philipp Rümmer, 2009-2015
% 0.50/0.59 (c) Peter Backeman, 2014-2015
% 0.50/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.50/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.50/0.59 Bug reports to peter@backeman.se
% 0.50/0.59
% 0.50/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.50/0.59
% 0.50/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.67/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.38/1.13 Prover 0: Preprocessing ...
% 4.75/1.73 Prover 0: Constructing countermodel ...
% 6.77/2.20 Prover 0: proved (1534ms)
% 6.77/2.20
% 6.77/2.20 No countermodel exists, formula is valid
% 6.77/2.20 % SZS status Theorem for theBenchmark
% 6.77/2.20
% 6.77/2.20 Generating proof ... found it (size 80)
% 18.42/5.88
% 18.42/5.88 % SZS output start Proof for theBenchmark
% 18.42/5.88 Assumed formulas after preprocessing and simplification:
% 18.42/5.88 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v6) & app(v4, v5) = v1 & app(v2, v5) = v0 & app(v2, v3) = v4 & equalelemsP(nil) & duplicatefreeP(nil) & strictorderedP(nil) & totalorderedP(nil) & strictorderP(nil) & totalorderP(nil) & cyclefreeP(nil) & segmentP(nil, nil) & rearsegP(nil, nil) & frontsegP(nil, nil) & ssList(v5) & ssList(v3) & ssList(v2) & ssList(v1) & ssList(v0) & ssList(nil) & ssItem(v7) & ssItem(v6) & ~ singletonP(nil) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cons(v10, v15) = v16) | ~ (cons(v9, v12) = v13) | ~ (app(v14, v16) = v8) | ~ (app(v11, v13) = v14) | ~ strictorderedP(v8) | ~ ssList(v15) | ~ ssList(v12) | ~ ssList(v11) | ~ ssList(v8) | ~ ssItem(v10) | ~ ssItem(v9) | lt(v9, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cons(v10, v15) = v16) | ~ (cons(v9, v12) = v13) | ~ (app(v14, v16) = v8) | ~ (app(v11, v13) = v14) | ~ totalorderedP(v8) | ~ ssList(v15) | ~ ssList(v12) | ~ ssList(v11) | ~ ssList(v8) | ~ ssItem(v10) | ~ ssItem(v9) | leq(v9, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cons(v10, v15) = v16) | ~ (cons(v9, v12) = v13) | ~ (app(v14, v16) = v8) | ~ (app(v11, v13) = v14) | ~ strictorderP(v8) | ~ ssList(v15) | ~ ssList(v12) | ~ ssList(v11) | ~ ssList(v8) | ~ ssItem(v10) | ~ ssItem(v9) | lt(v10, v9) | lt(v9, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cons(v10, v15) = v16) | ~ (cons(v9, v12) = v13) | ~ (app(v14, v16) = v8) | ~ (app(v11, v13) = v14) | ~ totalorderP(v8) | ~ ssList(v15) | ~ ssList(v12) | ~ ssList(v11) | ~ ssList(v8) | ~ ssItem(v10) | ~ ssItem(v9) | leq(v10, v9) | leq(v9, v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (cons(v10, v15) = v16) | ~ (cons(v9, v12) = v13) | ~ (app(v14, v16) = v8) | ~ (app(v11, v13) = v14) | ~ leq(v10, v9) | ~ leq(v9, v10) | ~ cyclefreeP(v8) | ~ ssList(v15) | ~ ssList(v12) | ~ ssList(v11) | ~ ssList(v8) | ~ ssItem(v10) | ~ ssItem(v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (cons(v9, v14) = v15) | ~ (cons(v9, v11) = v12) | ~ (app(v13, v15) = v8) | ~ (app(v10, v12) = v13) | ~ duplicatefreeP(v8) | ~ ssList(v14) | ~ ssList(v11) | ~ ssList(v10) | ~ ssList(v8) | ~ ssItem(v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (cons(v10, v12) = v13) | ~ (cons(v9, v13) = v14) | ~ (app(v11, v14) = v8) | ~ equalelemsP(v8) | ~ ssList(v12) | ~ ssList(v11) | ~ ssList(v8) | ~ ssItem(v10) | ~ ssItem(v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (cons(v9, v12) = v13) | ~ (cons(v8, v10) = v11) | ~ frontsegP(v11, v13) | ~ ssList(v12) | ~ ssList(v10) | ~ ssItem(v9) | ~ ssItem(v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cons(v11, v9) = v12) | ~ (app(v12, v8) = v13) | ~ (app(v9, v8) = v10) | ~ ssList(v9) | ~ ssList(v8) | ~ ssItem(v11) | cons(v11, v10) = v13) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cons(v9, v12) = v13) | ~ (cons(v8, v10) = v11) | ~ frontsegP(v11, v13) | ~ ssList(v12) | ~ ssList(v10) | ~ ssItem(v9) | ~ ssItem(v8) | frontsegP(v10, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (app(v11, v12) = v13) | ~ (app(v10, v8) = v11) | ~ segmentP(v8, v9) | ~ ssList(v12) | ~ ssList(v10) | ~ ssList(v9) | ~ ssList(v8) | segmentP(v13, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (app(v9, v11) = v12) | ~ (app(v8, v12) = v13) | ~ (app(v8, v9) = v10) | ~ ssList(v11) | ~ ssList(v9) | ~ ssList(v8) | app(v10, v11) = v13) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (cons(v12, v9) = v11) | ~ (cons(v10, v8) = v11) | ~ ssList(v9) | ~ ssList(v8) | ~ ssItem(v12) | ~ ssItem(v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (cons(v12, v9) = v11) | ~ (cons(v10, v8) = v11) | ~ ssList(v9) | ~ ssList(v8) | ~ ssItem(v12) | ~ ssItem(v10)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cons(v11, v10) = v12) | ~ (app(v9, v8) = v10) | ~ ssList(v9) | ~ ssList(v8) | ~ ssItem(v11) | ? [v13] : (cons(v11, v9) = v13 & app(v13, v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cons(v9, v11) = v12) | ~ (app(v10, v12) = v8) | ~ ssList(v11) | ~ ssList(v10) | ~ ssList(v8) | ~ ssItem(v9) | memberP(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cons(v8, v11) = v12) | ~ (cons(v8, v9) = v10) | ~ frontsegP(v9, v11) | ~ ssList(v11) | ~ ssList(v9) | ~ ssItem(v8) | frontsegP(v10, v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (app(v11, v12) = v8) | ~ (app(v10, v9) = v11) | ~ ssList(v12) | ~ ssList(v10) | ~ ssList(v9) | ~ ssList(v8) | segmentP(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (app(v10, v11) = v12) | ~ (app(v8, v9) = v10) | ~ ssList(v11) | ~ ssList(v9) | ~ ssList(v8) | ? [v13] : (app(v9, v11) = v13 & app(v8, v13) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | v8 = nil | ~ (tl(v8) = v10) | ~ (hd(v8) = v9) | ~ (cons(v9, v10) = v11) | ~ ssList(v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (app(v11, v9) = v10) | ~ (app(v8, v9) = v10) | ~ ssList(v11) | ~ ssList(v9) | ~ ssList(v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (app(v9, v11) = v10) | ~ (app(v9, v8) = v10) | ~ ssList(v11) | ~ ssList(v9) | ~ ssList(v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (cons(v11, v10) = v9) | ~ (cons(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (cons(v9, v10) = v11) | ~ memberP(v11, v8) | ~ ssList(v10) | ~ ssItem(v9) | ~ ssItem(v8) | memberP(v10, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (app(v11, v10) = v9) | ~ (app(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = nil | ~ (tl(v8) = v9) | ~ (app(v9, v10) = v11) | ~ ssList(v10) | ~ ssList(v8) | ? [v12] : (tl(v12) = v11 & app(v8, v10) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = nil | ~ (tl(v8) = v9) | ~ (app(v8, v10) = v11) | ~ ssList(v10) | ~ ssList(v8) | ? [v12] : (tl(v11) = v12 & app(v9, v10) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = nil | ~ (hd(v8) = v9) | ~ (app(v8, v10) = v11) | ~ ssList(v10) | ~ ssList(v8) | hd(v11) = v9) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (cons(v9, v10) = v11) | ~ memberP(v10, v8) | ~ ssList(v10) | ~ ssItem(v9) | ~ ssItem(v8) | memberP(v11, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (cons(v9, nil) = v10) | ~ (app(v10, v8) = v11) | ~ ssList(v8) | ~ ssItem(v9) | cons(v9, v8) = v11) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (app(v10, v8) = v11) | ~ rearsegP(v8, v9) | ~ ssList(v10) | ~ ssList(v9) | ~ ssList(v8) | rearsegP(v11, v9)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (app(v9, v10) = v11) | ~ memberP(v11, v8) | ~ ssList(v10) | ~ ssList(v9) | ~ ssItem(v8) | memberP(v10, v8) | memberP(v9, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (app(v9, v10) = v11) | ~ memberP(v10, v8) | ~ ssList(v10) | ~ ssList(v9) | ~ ssItem(v8) | memberP(v11, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (app(v9, v10) = v11) | ~ memberP(v9, v8) | ~ ssList(v10) | ~ ssList(v9) | ~ ssItem(v8) | memberP(v11, v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (app(v8, v10) = v11) | ~ frontsegP(v8, v9) | ~ ssList(v10) | ~ ssList(v9) | ~ ssList(v8) | frontsegP(v11, v9)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (tl(v10) = v9) | ~ (tl(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (hd(v10) = v9) | ~ (hd(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (hd(v9) = v10) | ~ ssList(v9) | ~ ssItem(v8) | ? [v11] : (cons(v8, v9) = v11 & (v9 = nil | ~ strictorderedP(v11) | (strictorderedP(v9) & lt(v8, v10))) & (strictorderedP(v11) | ( ~ (v9 = nil) & ( ~ strictorderedP(v9) | ~ lt(v8, v10)))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (hd(v9) = v10) | ~ ssList(v9) | ~ ssItem(v8) | ? [v11] : (cons(v8, v9) = v11 & (v9 = nil | ~ totalorderedP(v11) | (totalorderedP(v9) & leq(v8, v10))) & (totalorderedP(v11) | ( ~ (v9 = nil) & ( ~ totalorderedP(v9) | ~ leq(v8, v10)))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (cons(v9, v8) = v10) | ~ ssList(v8) | ~ ssItem(v9) | tl(v10) = v8) & ! [v8] : ! [v9] : ! [v10] : ( ~ (cons(v9, v8) = v10) | ~ ssList(v8) | ~ ssItem(v9) | hd(v10) = v9) & ! [v8] : ! [v9] : ! [v10] : ( ~ (cons(v9, v8) = v10) | ~ ssList(v8) | ~ ssItem(v9) | ssList(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (cons(v9, v8) = v10) | ~ ssList(v8) | ~ ssItem(v9) | ? [v11] : (cons(v9, nil) = v11 & app(v11, v8) = v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (cons(v8, v9) = v10) | ~ ssList(v9) | ~ ssItem(v8) | memberP(v10, v8)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (cons(v8, v9) = v10) | ~ ssList(v9) | ~ ssItem(v8) | ? [v11] : (hd(v9) = v11 & (v9 = nil | ~ strictorderedP(v10) | (strictorderedP(v9) & lt(v8, v11))) & (strictorderedP(v10) | ( ~ (v9 = nil) & ( ~ strictorderedP(v9) | ~ lt(v8, v11)))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (cons(v8, v9) = v10) | ~ ssList(v9) | ~ ssItem(v8) | ? [v11] : (hd(v9) = v11 & (v9 = nil | ~ totalorderedP(v10) | (totalorderedP(v9) & leq(v8, v11))) & (totalorderedP(v10) | ( ~ (v9 = nil) & ( ~ totalorderedP(v9) | ~ leq(v8, v11)))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (app(v10, v9) = v8) | ~ ssList(v10) | ~ ssList(v9) | ~ ssList(v8) | rearsegP(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (app(v9, v10) = v8) | ~ ssList(v10) | ~ ssList(v9) | ~ ssList(v8) | frontsegP(v8, v9)) & ! [v8] : ! [v9] : ! [v10] : ( ~ (app(v8, v9) = v10) | ~ ssList(v9) | ~ ssList(v8) | ssList(v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ gt(v9, v10) | ~ gt(v8, v9) | ~ ssItem(v10) | ~ ssItem(v9) | ~ ssItem(v8) | gt(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ geq(v9, v10) | ~ geq(v8, v9) | ~ ssItem(v10) | ~ ssItem(v9) | ~ ssItem(v8) | geq(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ lt(v9, v10) | ~ lt(v8, v9) | ~ ssItem(v10) | ~ ssItem(v9) | ~ ssItem(v8) | lt(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ lt(v9, v10) | ~ leq(v8, v9) | ~ ssItem(v10) | ~ ssItem(v9) | ~ ssItem(v8) | lt(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ leq(v9, v10) | ~ leq(v8, v9) | ~ ssItem(v10) | ~ ssItem(v9) | ~ ssItem(v8) | leq(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ segmentP(v9, v10) | ~ segmentP(v8, v9) | ~ ssList(v10) | ~ ssList(v9) | ~ ssList(v8) | segmentP(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ rearsegP(v9, v10) | ~ rearsegP(v8, v9) | ~ ssList(v10) | ~ ssList(v9) | ~ ssList(v8) | rearsegP(v8, v10)) & ! [v8] : ! [v9] : ! [v10] : ( ~ frontsegP(v9, v10) | ~ frontsegP(v8, v9) | ~ ssList(v10) | ~ ssList(v9) | ~ ssList(v8) | frontsegP(v8, v10)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (app(v8, nil) = v9) | ~ ssList(v8)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (app(nil, v8) = v9) | ~ ssList(v8)) & ! [v8] : ! [v9] : (v9 = v8 | ~ geq(v9, v8) | ~ geq(v8, v9) | ~ ssItem(v9) | ~ ssItem(v8)) & ! [v8] : ! [v9] : (v9 = v8 | ~ leq(v9, v8) | ~ leq(v8, v9) | ~ ssItem(v9) | ~ ssItem(v8)) & ! [v8] : ! [v9] : (v9 = v8 | ~ leq(v8, v9) | ~ ssItem(v9) | ~ ssItem(v8) | lt(v8, v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ segmentP(v9, v8) | ~ segmentP(v8, v9) | ~ ssList(v9) | ~ ssList(v8)) & ! [v8] : ! [v9] : (v9 = v8 | ~ rearsegP(v9, v8) | ~ rearsegP(v8, v9) | ~ ssList(v9) | ~ ssList(v8)) & ! [v8] : ! [v9] : (v9 = v8 | ~ frontsegP(v9, v8) | ~ frontsegP(v8, v9) | ~ ssList(v9) | ~ ssList(v8)) & ! [v8] : ! [v9] : (v9 = v8 | ~ ssList(v9) | ~ ssList(v8) | neq(v8, v9)) & ! [v8] : ! [v9] : (v9 = v8 | ~ ssItem(v9) | ~ ssItem(v8) | neq(v8, v9)) & ! [v8] : ! [v9] : (v9 = nil | ~ (app(v8, v9) = nil) | ~ ssList(v9) | ~ ssList(v8)) & ! [v8] : ! [v9] : (v8 = nil | ~ (tl(v8) = v9) | ~ ssList(v8) | ssList(v9)) & ! [v8] : ! [v9] : (v8 = nil | ~ (hd(v8) = v9) | ~ ssList(v8) | ssItem(v9)) & ! [v8] : ! [v9] : (v8 = nil | ~ (app(v8, v9) = nil) | ~ ssList(v9) | ~ ssList(v8)) & ! [v8] : ! [v9] : ( ~ (tl(v8) = v9) | ~ ssList(v8) | ? [v10] : (hd(v8) = v10 & ! [v11] : (v11 = v8 | v11 = nil | v8 = nil | ~ (tl(v11) = v9) | ~ ssList(v11) | ? [v12] : ( ~ (v12 = v10) & hd(v11) = v12)) & ! [v11] : (v11 = v8 | v11 = nil | v8 = nil | ~ (hd(v11) = v10) | ~ ssList(v11) | ? [v12] : ( ~ (v12 = v9) & tl(v11) = v12)))) & ! [v8] : ! [v9] : ( ~ (hd(v8) = v9) | ~ ssList(v8) | ? [v10] : (tl(v8) = v10 & ! [v11] : (v11 = v8 | v11 = nil | v8 = nil | ~ (tl(v11) = v10) | ~ ssList(v11) | ? [v12] : ( ~ (v12 = v9) & hd(v11) = v12)) & ! [v11] : (v11 = v8 | v11 = nil | v8 = nil | ~ (hd(v11) = v9) | ~ ssList(v11) | ? [v12] : ( ~ (v12 = v10) & tl(v11) = v12)))) & ! [v8] : ! [v9] : ( ~ (cons(v9, v8) = v8) | ~ ssList(v8) | ~ ssItem(v9)) & ! [v8] : ! [v9] : ( ~ (cons(v9, v8) = nil) | ~ ssList(v8) | ~ ssItem(v9)) & ! [v8] : ! [v9] : ( ~ (cons(v9, nil) = v8) | ~ ssList(v8) | ~ ssItem(v9) | singletonP(v8)) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ~ ssItem(v8) | equalelemsP(v9)) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ~ ssItem(v8) | duplicatefreeP(v9)) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ~ ssItem(v8) | strictorderedP(v9)) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ~ ssItem(v8) | totalorderedP(v9)) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ~ ssItem(v8) | strictorderP(v9)) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ~ ssItem(v8) | totalorderP(v9)) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ~ ssItem(v8) | cyclefreeP(v9)) & ! [v8] : ! [v9] : ( ~ gt(v9, v8) | ~ gt(v8, v9) | ~ ssItem(v9) | ~ ssItem(v8)) & ! [v8] : ! [v9] : ( ~ gt(v8, v9) | ~ ssItem(v9) | ~ ssItem(v8) | lt(v9, v8)) & ! [v8] : ! [v9] : ( ~ geq(v8, v9) | ~ ssItem(v9) | ~ ssItem(v8) | leq(v9, v8)) & ! [v8] : ! [v9] : ( ~ lt(v9, v8) | ~ lt(v8, v9) | ~ ssItem(v9) | ~ ssItem(v8)) & ! [v8] : ! [v9] : ( ~ lt(v9, v8) | ~ ssItem(v9) | ~ ssItem(v8) | gt(v8, v9)) & ! [v8] : ! [v9] : ( ~ lt(v8, v9) | ~ ssItem(v9) | ~ ssItem(v8) | leq(v8, v9)) & ! [v8] : ! [v9] : ( ~ leq(v9, v8) | ~ ssItem(v9) | ~ ssItem(v8) | geq(v8, v9)) & ! [v8] : ! [v9] : ( ~ segmentP(v8, v9) | ~ ssList(v9) | ~ ssList(v8) | ? [v10] : ? [v11] : ? [v12] : (app(v11, v12) = v8 & app(v10, v9) = v11 & ssList(v12) & ssList(v10))) & ! [v8] : ! [v9] : ( ~ rearsegP(v8, v9) | ~ ssList(v9) | ~ ssList(v8) | ? [v10] : (app(v10, v9) = v8 & ssList(v10))) & ! [v8] : ! [v9] : ( ~ frontsegP(v8, v9) | ~ ssList(v9) | ~ ssList(v8) | ? [v10] : (app(v9, v10) = v8 & ssList(v10))) & ! [v8] : ! [v9] : ( ~ memberP(v8, v9) | ~ ssList(v8) | ~ ssItem(v9) | ? [v10] : ? [v11] : ? [v12] : (cons(v9, v11) = v12 & app(v10, v12) = v8 & ssList(v11) & ssList(v10))) & ! [v8] : ! [v9] : ( ~ ssList(v9) | ~ ssList(v8) | ? [v10] : (app(v8, v9) = v10 & ! [v11] : ( ~ ssList(v11) | ? [v12] : ? [v13] : (app(v10, v11) = v12 & app(v8, v11) = v13 & ( ~ (v13 = v0) | ~ (v12 = v1)))))) & ! [v8] : (v8 = nil | ~ (app(nil, nil) = v8)) & ! [v8] : (v8 = nil | ~ segmentP(nil, v8) | ~ ssList(v8)) & ! [v8] : (v8 = nil | ~ rearsegP(nil, v8) | ~ ssList(v8)) & ! [v8] : (v8 = nil | ~ frontsegP(nil, v8) | ~ ssList(v8)) & ! [v8] : (v8 = nil | ~ ssList(v8) | ? [v9] : ? [v10] : (cons(v10, v9) = v8 & ssList(v9) & ssItem(v10))) & ! [v8] : ( ~ lt(v8, v8) | ~ ssItem(v8)) & ! [v8] : ( ~ singletonP(v8) | ~ ssList(v8) | ? [v9] : (cons(v9, nil) = v8 & ssItem(v9))) & ! [v8] : ( ~ memberP(nil, v8) | ~ ssItem(v8)) & ! [v8] : ( ~ ssList(v8) | ~ neq(v8, v8)) & ! [v8] : ( ~ ssList(v8) | equalelemsP(v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ( ~ (v10 = v9) & cons(v10, v12) = v13 & cons(v9, v13) = v14 & app(v11, v14) = v8 & ssList(v12) & ssList(v11) & ssItem(v10) & ssItem(v9))) & ! [v8] : ( ~ ssList(v8) | duplicatefreeP(v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : (cons(v9, v14) = v15 & cons(v9, v11) = v12 & app(v13, v15) = v8 & app(v10, v12) = v13 & ssList(v14) & ssList(v11) & ssList(v10) & ssItem(v9))) & ! [v8] : ( ~ ssList(v8) | strictorderedP(v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (cons(v10, v15) = v16 & cons(v9, v12) = v13 & app(v14, v16) = v8 & app(v11, v13) = v14 & ssList(v15) & ssList(v12) & ssList(v11) & ssItem(v10) & ssItem(v9) & ~ lt(v9, v10))) & ! [v8] : ( ~ ssList(v8) | totalorderedP(v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (cons(v10, v15) = v16 & cons(v9, v12) = v13 & app(v14, v16) = v8 & app(v11, v13) = v14 & ssList(v15) & ssList(v12) & ssList(v11) & ssItem(v10) & ssItem(v9) & ~ leq(v9, v10))) & ! [v8] : ( ~ ssList(v8) | strictorderP(v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (cons(v10, v15) = v16 & cons(v9, v12) = v13 & app(v14, v16) = v8 & app(v11, v13) = v14 & ssList(v15) & ssList(v12) & ssList(v11) & ssItem(v10) & ssItem(v9) & ~ lt(v10, v9) & ~ lt(v9, v10))) & ! [v8] : ( ~ ssList(v8) | totalorderP(v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (cons(v10, v15) = v16 & cons(v9, v12) = v13 & app(v14, v16) = v8 & app(v11, v13) = v14 & ssList(v15) & ssList(v12) & ssList(v11) & ssItem(v10) & ssItem(v9) & ~ leq(v10, v9) & ~ leq(v9, v10))) & ! [v8] : ( ~ ssList(v8) | cyclefreeP(v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : (cons(v10, v15) = v16 & cons(v9, v12) = v13 & app(v14, v16) = v8 & app(v11, v13) = v14 & leq(v10, v9) & leq(v9, v10) & ssList(v15) & ssList(v12) & ssList(v11) & ssItem(v10) & ssItem(v9))) & ! [v8] : ( ~ ssList(v8) | segmentP(v8, v8)) & ! [v8] : ( ~ ssList(v8) | segmentP(v8, nil)) & ! [v8] : ( ~ ssList(v8) | rearsegP(v8, v8)) & ! [v8] : ( ~ ssList(v8) | rearsegP(v8, nil)) & ! [v8] : ( ~ ssList(v8) | frontsegP(v8, v8)) & ! [v8] : ( ~ ssList(v8) | frontsegP(v8, nil)) & ! [v8] : ( ~ neq(v8, v8) | ~ ssItem(v8)) & ! [v8] : ( ~ ssItem(v8) | geq(v8, v8)) & ! [v8] : ( ~ ssItem(v8) | leq(v8, v8)))
% 18.87/5.97 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 18.87/5.97 | (1) ~ (all_0_0_0 = all_0_1_1) & app(all_0_3_3, all_0_2_2) = all_0_6_6 & app(all_0_5_5, all_0_2_2) = all_0_7_7 & app(all_0_5_5, all_0_4_4) = all_0_3_3 & 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_2_2) & ssList(all_0_4_4) & ssList(all_0_5_5) & ssList(all_0_6_6) & ssList(all_0_7_7) & ssList(nil) & ssItem(all_0_0_0) & ssItem(all_0_1_1) & ~ singletonP(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(v3, v1) = v4) | ~ (app(v4, v0) = v5) | ~ (app(v1, v0) = v2) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v3) | cons(v3, v2) = v5) & ! [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] : ! [v5] : ( ~ (app(v1, v3) = v4) | ~ (app(v0, v4) = v5) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | app(v2, v3) = v5) & ! [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 | ~ (tl(v0) = v1) | ~ (app(v0, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | ? [v4] : (tl(v3) = v4 & app(v1, 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] : (cons(v0, v1) = v3 & (v1 = nil | ~ strictorderedP(v3) | (strictorderedP(v1) & lt(v0, v2))) & (strictorderedP(v3) | ( ~ (v1 = nil) & ( ~ strictorderedP(v1) | ~ lt(v0, v2)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (hd(v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : (cons(v0, v1) = v3 & (v1 = nil | ~ totalorderedP(v3) | (totalorderedP(v1) & leq(v0, v2))) & (totalorderedP(v3) | ( ~ (v1 = nil) & ( ~ totalorderedP(v1) | ~ leq(v0, v2)))))) & ! [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(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | ? [v3] : (cons(v1, nil) = v3 & app(v3, v0) = v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : (hd(v1) = v3 & (v1 = nil | ~ strictorderedP(v2) | (strictorderedP(v1) & lt(v0, v3))) & (strictorderedP(v2) | ( ~ (v1 = nil) & ( ~ strictorderedP(v1) | ~ lt(v0, v3)))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : (hd(v1) = v3 & (v1 = nil | ~ totalorderedP(v2) | (totalorderedP(v1) & leq(v0, v3))) & (totalorderedP(v2) | ( ~ (v1 = nil) & ( ~ totalorderedP(v1) | ~ leq(v0, v3)))))) & ! [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)) & ! [v3] : (v3 = v0 | v3 = nil | v0 = nil | ~ (hd(v3) = v2) | ~ ssList(v3) | ? [v4] : ( ~ (v4 = v1) & tl(v3) = v4)))) & ! [v0] : ! [v1] : ( ~ (hd(v0) = v1) | ~ ssList(v0) | ? [v2] : (tl(v0) = v2 & ! [v3] : (v3 = v0 | v3 = nil | v0 = nil | ~ (tl(v3) = v2) | ~ ssList(v3) | ? [v4] : ( ~ (v4 = v1) & hd(v3) = v4)) & ! [v3] : (v3 = v0 | v3 = nil | v0 = nil | ~ (hd(v3) = v1) | ~ ssList(v3) | ? [v4] : ( ~ (v4 = v2) & tl(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] : ! [v1] : ( ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v0, v1) = v2 & ! [v3] : ( ~ ssList(v3) | ? [v4] : ? [v5] : (app(v2, v3) = v4 & app(v0, v3) = v5 & ( ~ (v5 = all_0_7_7) | ~ (v4 = all_0_6_6)))))) & ! [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))
% 18.87/6.00 |
% 18.87/6.00 | Applying alpha-rule on (1) yields:
% 18.87/6.00 | (2) ! [v0] : (v0 = nil | ~ segmentP(nil, v0) | ~ ssList(v0))
% 18.87/6.00 | (3) ! [v0] : ! [v1] : ( ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v1, v2) = v0 & ssList(v2)))
% 18.87/6.00 | (4) ! [v0] : ! [v1] : ( ~ memberP(v0, v1) | ~ ssList(v0) | ~ ssItem(v1) | ? [v2] : ? [v3] : ? [v4] : (cons(v1, v3) = v4 & app(v2, v4) = v0 & ssList(v3) & ssList(v2)))
% 18.87/6.00 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v1))
% 18.87/6.00 | (6) ! [v0] : ! [v1] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0))
% 18.87/6.00 | (7) ! [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)))
% 18.87/6.00 | (8) segmentP(nil, nil)
% 18.87/6.00 | (9) ! [v0] : ! [v1] : ( ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v1))
% 18.87/6.00 | (10) ! [v0] : ( ~ ssItem(v0) | geq(v0, v0))
% 18.87/6.00 | (11) ! [v0] : ! [v1] : ( ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v1, v0))
% 18.87/6.00 | (12) ssList(all_0_4_4)
% 18.87/6.00 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ~ ssList(v0) | ~ ssItem(v1) | cons(v1, v0) = v3)
% 18.87/6.00 | (14) ! [v0] : ! [v1] : ( ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v1, v0))
% 18.87/6.01 | (15) ! [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)))
% 18.87/6.01 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v1))
% 18.87/6.01 | (17) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | duplicatefreeP(v1))
% 18.87/6.01 | (18) rearsegP(nil, nil)
% 19.18/6.01 | (19) ! [v0] : ! [v1] : ( ~ leq(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v1))
% 19.18/6.01 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ~ ssList(v0))
% 19.18/6.01 | (21) ! [v0] : ! [v1] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0))
% 19.18/6.01 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v0, v1) = v2) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2))
% 19.18/6.01 | (23) ! [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))
% 19.18/6.01 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | hd(v3) = v1)
% 19.18/6.01 | (25) app(all_0_5_5, all_0_4_4) = all_0_3_3
% 19.18/6.01 | (26) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v1, v3) = v4) | ~ (app(v2, v4) = v0) | ~ ssList(v3) | ~ ssList(v2) | ~ ssList(v0) | ~ ssItem(v1) | memberP(v0, v1))
% 19.18/6.01 | (27) ! [v0] : ! [v1] : (v1 = v0 | ~ ssList(v1) | ~ ssList(v0) | neq(v0, v1))
% 19.18/6.01 | (28) ! [v0] : ! [v1] : (v1 = v0 | ~ frontsegP(v1, v0) | ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0))
% 19.18/6.01 | (29) ! [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))
% 19.18/6.01 | (30) ssList(all_0_7_7)
% 19.18/6.01 | (31) ! [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))
% 19.18/6.01 | (32) ~ (all_0_0_0 = all_0_1_1)
% 19.18/6.01 | (33) ! [v0] : ( ~ ssItem(v0) | leq(v0, v0))
% 19.18/6.01 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0))
% 19.18/6.01 | (35) ! [v0] : ( ~ memberP(nil, v0) | ~ ssItem(v0))
% 19.18/6.01 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (tl(v0) = v1) | ~ (app(v0, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | ? [v4] : (tl(v3) = v4 & app(v1, v2) = v4))
% 19.18/6.01 | (37) ! [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))
% 19.18/6.01 | (38) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0))
% 19.18/6.01 | (39) ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v1, v0) | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0))
% 19.18/6.01 | (40) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ ssList(v0))
% 19.18/6.01 | (41) ! [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)))
% 19.18/6.01 | (42) ! [v0] : ! [v1] : ! [v2] : ( ~ segmentP(v1, v2) | ~ segmentP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v2))
% 19.18/6.01 | (43) ! [v0] : (v0 = nil | ~ frontsegP(nil, v0) | ~ ssList(v0))
% 19.18/6.01 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0))
% 19.18/6.01 | (45) ! [v0] : (v0 = nil | ~ ssList(v0) | ? [v1] : ? [v2] : (cons(v2, v1) = v0 & ssList(v1) & ssItem(v2)))
% 19.18/6.02 | (46) totalorderP(nil)
% 19.18/6.02 | (47) ! [v0] : ( ~ singletonP(v0) | ~ ssList(v0) | ? [v1] : (cons(v1, nil) = v0 & ssItem(v1)))
% 19.18/6.02 | (48) ! [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)))
% 19.18/6.02 | (49) ! [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)))
% 19.18/6.02 | (50) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderedP(v1))
% 19.18/6.02 | (51) app(all_0_5_5, all_0_2_2) = all_0_7_7
% 19.18/6.02 | (52) ! [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))
% 19.18/6.02 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 19.18/6.02 | (54) ! [v0] : ! [v1] : ( ~ (cons(v1, nil) = v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0))
% 19.18/6.02 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ geq(v1, v2) | ~ geq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v2))
% 19.18/6.02 | (56) ssList(all_0_6_6)
% 19.18/6.02 | (57) ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0))
% 19.18/6.02 | (58) ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = v0) | ~ ssList(v0) | ~ ssItem(v1))
% 19.18/6.02 | (59) ! [v0] : ( ~ ssList(v0) | rearsegP(v0, v0))
% 19.18/6.02 | (60) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderP(v1))
% 19.18/6.02 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ leq(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v2))
% 19.18/6.02 | (62) ! [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)))
% 19.18/6.02 | (63) ! [v0] : ! [v1] : ( ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v2, v1) = v0 & ssList(v2)))
% 19.18/6.02 | (64) ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v1))
% 19.18/6.02 | (65) ! [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))
% 19.18/6.02 | (66) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | cyclefreeP(v1))
% 19.18/6.02 | (67) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ ssList(v0))
% 19.18/6.02 | (68) totalorderedP(nil)
% 19.18/6.02 | (69) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderP(v1))
% 19.18/6.02 | (70) ssItem(all_0_1_1)
% 19.18/6.02 | (71) ! [v0] : ! [v1] : (v1 = v0 | ~ rearsegP(v1, v0) | ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0))
% 19.18/6.02 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v0, v2) = v3) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v3, v1))
% 19.18/6.02 | (73) ! [v0] : ( ~ ssList(v0) | frontsegP(v0, v0))
% 19.18/6.02 | (74) ! [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)) & ! [v3] : (v3 = v0 | v3 = nil | v0 = nil | ~ (hd(v3) = v2) | ~ ssList(v3) | ? [v4] : ( ~ (v4 = v1) & tl(v3) = v4))))
% 19.18/6.02 | (75) ! [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))
% 19.18/6.02 | (76) ! [v0] : ( ~ ssList(v0) | ~ neq(v0, v0))
% 19.18/6.02 | (77) ! [v0] : ! [v1] : ( ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : ? [v3] : ? [v4] : (app(v3, v4) = v0 & app(v2, v1) = v3 & ssList(v4) & ssList(v2)))
% 19.18/6.03 | (78) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 19.18/6.03 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cons(v3, v1) = v4) | ~ (app(v4, v0) = v5) | ~ (app(v1, v0) = v2) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v3) | cons(v3, v2) = v5)
% 19.18/6.03 | (80) ! [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)))
% 19.18/6.03 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | hd(v2) = v1)
% 19.18/6.03 | (82) ! [v0] : ! [v1] : ! [v2] : ( ~ (hd(v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : (cons(v0, v1) = v3 & (v1 = nil | ~ totalorderedP(v3) | (totalorderedP(v1) & leq(v0, v2))) & (totalorderedP(v3) | ( ~ (v1 = nil) & ( ~ totalorderedP(v1) | ~ leq(v0, v2))))))
% 19.18/6.03 | (83) ! [v0] : ( ~ ssList(v0) | segmentP(v0, nil))
% 19.18/6.03 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 19.18/6.03 | (85) ssList(all_0_2_2)
% 19.18/6.03 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2))
% 19.18/6.03 | (87) strictorderP(nil)
% 19.18/6.03 | (88) ! [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))
% 19.18/6.03 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : (hd(v1) = v3 & (v1 = nil | ~ strictorderedP(v2) | (strictorderedP(v1) & lt(v0, v3))) & (strictorderedP(v2) | ( ~ (v1 = nil) & ( ~ strictorderedP(v1) | ~ lt(v0, v3))))))
% 19.18/6.03 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 19.18/6.03 | (91) ! [v0] : (v0 = nil | ~ rearsegP(nil, v0) | ~ ssList(v0))
% 19.18/6.03 | (92) ! [v0] : ! [v1] : (v1 = v0 | ~ geq(v1, v0) | ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0))
% 19.18/6.03 | (93) ! [v0] : ( ~ neq(v0, v0) | ~ ssItem(v0))
% 19.18/6.03 | (94) ! [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))
% 19.18/6.03 | (95) ! [v0] : ! [v1] : ! [v2] : ( ~ gt(v1, v2) | ~ gt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v2))
% 19.18/6.03 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v2, v0) = v3) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1))
% 19.18/6.03 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ rearsegP(v1, v2) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v2))
% 19.18/6.03 | (98) ! [v0] : ! [v1] : ( ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v0, v1) = v2 & ! [v3] : ( ~ ssList(v3) | ? [v4] : ? [v5] : (app(v2, v3) = v4 & app(v0, v3) = v5 & ( ~ (v5 = all_0_7_7) | ~ (v4 = all_0_6_6))))))
% 19.18/6.03 | (99) frontsegP(nil, nil)
% 19.18/6.03 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2))
% 19.18/6.03 | (101) ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = nil) | ~ ssList(v0) | ~ ssItem(v1))
% 19.18/6.03 | (102) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v2, v1) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v1))
% 19.18/6.03 | (103) ssItem(all_0_0_0)
% 19.18/6.03 | (104) strictorderedP(nil)
% 19.18/6.03 | (105) equalelemsP(nil)
% 19.18/6.03 | (106) ssList(all_0_5_5)
% 19.18/6.03 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : (hd(v1) = v3 & (v1 = nil | ~ totalorderedP(v2) | (totalorderedP(v1) & leq(v0, v3))) & (totalorderedP(v2) | ( ~ (v1 = nil) & ( ~ totalorderedP(v1) | ~ leq(v0, v3))))))
% 19.18/6.04 | (108) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | tl(v2) = v0)
% 19.18/6.04 | (109) ssList(nil)
% 19.18/6.04 | (110) ! [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))
% 19.18/6.04 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v2, v0))
% 19.18/6.04 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2))
% 19.18/6.04 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2))
% 19.18/6.04 | (114) ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ lt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2))
% 19.18/6.04 | (115) ! [v0] : ! [v1] : (v1 = v0 | ~ ssItem(v1) | ~ ssItem(v0) | neq(v0, v1))
% 19.18/6.04 | (116) cyclefreeP(nil)
% 19.18/6.04 | (117) duplicatefreeP(nil)
% 19.18/6.04 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0) | memberP(v1, v0))
% 19.18/6.04 | (119) ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0))
% 19.18/6.04 | (120) ! [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))
% 19.18/6.04 | (121) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | equalelemsP(v1))
% 19.18/6.04 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (app(v1, v3) = v4) | ~ (app(v0, v4) = v5) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | app(v2, v3) = v5)
% 19.18/6.04 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v1, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0))
% 19.18/6.04 | (124) ! [v0] : ! [v1] : ! [v2] : ( ~ frontsegP(v1, v2) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v2))
% 19.18/6.04 | (125) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ~ ssList(v0) | ssList(v1))
% 19.18/6.04 | (126) app(all_0_3_3, all_0_2_2) = all_0_6_6
% 19.18/6.04 | (127) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0))
% 19.18/6.04 | (128) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | ? [v3] : (cons(v1, nil) = v3 & app(v3, v0) = v2))
% 19.18/6.04 | (129) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v1, v2) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v1))
% 19.18/6.04 | (130) ! [v0] : ( ~ ssList(v0) | frontsegP(v0, nil))
% 19.18/6.04 | (131) ! [v0] : ! [v1] : ! [v2] : ( ~ (hd(v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : (cons(v0, v1) = v3 & (v1 = nil | ~ strictorderedP(v3) | (strictorderedP(v1) & lt(v0, v2))) & (strictorderedP(v3) | ( ~ (v1 = nil) & ( ~ strictorderedP(v1) | ~ lt(v0, v2))))))
% 19.18/6.04 | (132) ! [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))
% 19.18/6.04 | (133) ! [v0] : ( ~ ssList(v0) | rearsegP(v0, nil))
% 19.18/6.04 | (134) ! [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))
% 19.18/6.04 | (135) ! [v0] : ! [v1] : (v1 = v0 | ~ segmentP(v1, v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0))
% 19.18/6.04 | (136) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ~ ssList(v0) | ssItem(v1))
% 19.18/6.04 | (137) ! [v0] : ( ~ lt(v0, v0) | ~ ssItem(v0))
% 19.18/6.05 | (138) ! [v0] : ! [v1] : ( ~ (hd(v0) = v1) | ~ ssList(v0) | ? [v2] : (tl(v0) = v2 & ! [v3] : (v3 = v0 | v3 = nil | v0 = nil | ~ (tl(v3) = v2) | ~ ssList(v3) | ? [v4] : ( ~ (v4 = v1) & hd(v3) = v4)) & ! [v3] : (v3 = v0 | v3 = nil | v0 = nil | ~ (hd(v3) = v1) | ~ ssList(v3) | ? [v4] : ( ~ (v4 = v2) & tl(v3) = v4))))
% 19.18/6.05 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v3, v0))
% 19.18/6.05 | (140) ! [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))
% 19.18/6.05 | (141) ! [v0] : ! [v1] : ( ~ gt(v1, v0) | ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0))
% 19.18/6.05 | (142) ! [v0] : ( ~ ssList(v0) | segmentP(v0, v0))
% 19.18/6.05 | (143) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderedP(v1))
% 19.18/6.05 | (144) ~ singletonP(nil)
% 19.18/6.05 |
% 19.18/6.05 | Instantiating formula (98) with all_0_2_2, all_0_5_5 and discharging atoms ssList(all_0_2_2), ssList(all_0_5_5), yields:
% 19.18/6.05 | (145) ? [v0] : (app(all_0_5_5, all_0_2_2) = v0 & ! [v1] : ( ~ ssList(v1) | ? [v2] : ? [v3] : (app(v0, v1) = v2 & app(all_0_5_5, v1) = v3 & ( ~ (v3 = all_0_7_7) | ~ (v2 = all_0_6_6)))))
% 19.18/6.05 |
% 19.18/6.05 | Instantiating formula (98) with all_0_4_4, all_0_5_5 and discharging atoms ssList(all_0_4_4), ssList(all_0_5_5), yields:
% 19.18/6.05 | (146) ? [v0] : (app(all_0_5_5, all_0_4_4) = v0 & ! [v1] : ( ~ ssList(v1) | ? [v2] : ? [v3] : (app(v0, v1) = v2 & app(all_0_5_5, v1) = v3 & ( ~ (v3 = all_0_7_7) | ~ (v2 = all_0_6_6)))))
% 19.18/6.05 |
% 19.18/6.05 | Instantiating formula (98) with all_0_5_5, all_0_5_5 and discharging atoms ssList(all_0_5_5), yields:
% 19.18/6.05 | (147) ? [v0] : (app(all_0_5_5, all_0_5_5) = v0 & ! [v1] : ( ~ ssList(v1) | ? [v2] : ? [v3] : (app(v0, v1) = v2 & app(all_0_5_5, v1) = v3 & ( ~ (v3 = all_0_7_7) | ~ (v2 = all_0_6_6)))))
% 19.18/6.05 |
% 19.18/6.05 | Instantiating formula (98) with all_0_6_6, all_0_5_5 and discharging atoms ssList(all_0_5_5), ssList(all_0_6_6), yields:
% 19.18/6.05 | (148) ? [v0] : (app(all_0_5_5, all_0_6_6) = v0 & ! [v1] : ( ~ ssList(v1) | ? [v2] : ? [v3] : (app(v0, v1) = v2 & app(all_0_5_5, v1) = v3 & ( ~ (v3 = all_0_7_7) | ~ (v2 = all_0_6_6)))))
% 19.18/6.05 |
% 19.18/6.05 | Instantiating formula (98) with all_0_7_7, all_0_5_5 and discharging atoms ssList(all_0_5_5), ssList(all_0_7_7), yields:
% 19.18/6.05 | (149) ? [v0] : (app(all_0_5_5, all_0_7_7) = v0 & ! [v1] : ( ~ ssList(v1) | ? [v2] : ? [v3] : (app(v0, v1) = v2 & app(all_0_5_5, v1) = v3 & ( ~ (v3 = all_0_7_7) | ~ (v2 = all_0_6_6)))))
% 19.18/6.05 |
% 19.18/6.05 | Instantiating formula (98) with nil, all_0_5_5 and discharging atoms ssList(all_0_5_5), ssList(nil), yields:
% 19.18/6.05 | (150) ? [v0] : (app(all_0_5_5, nil) = v0 & ! [v1] : ( ~ ssList(v1) | ? [v2] : ? [v3] : (app(v0, v1) = v2 & app(all_0_5_5, v1) = v3 & ( ~ (v3 = all_0_7_7) | ~ (v2 = all_0_6_6)))))
% 19.18/6.05 |
% 19.18/6.05 | Instantiating (145) with all_12_0_9 yields:
% 19.18/6.05 | (151) app(all_0_5_5, all_0_2_2) = all_12_0_9 & ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_12_0_9, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_7_7) | ~ (v1 = all_0_6_6))))
% 19.18/6.05 |
% 19.18/6.05 | Applying alpha-rule on (151) yields:
% 19.18/6.05 | (152) app(all_0_5_5, all_0_2_2) = all_12_0_9
% 19.18/6.05 | (153) ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_12_0_9, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_7_7) | ~ (v1 = all_0_6_6))))
% 19.18/6.05 |
% 19.18/6.05 | Instantiating formula (153) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields:
% 19.18/6.05 | (154) ? [v0] : ? [v1] : (app(all_12_0_9, all_0_4_4) = v0 & app(all_0_5_5, all_0_4_4) = v1 & ( ~ (v1 = all_0_7_7) | ~ (v0 = all_0_6_6)))
% 19.18/6.05 |
% 19.18/6.05 | Instantiating (149) with all_21_0_12 yields:
% 19.18/6.05 | (155) app(all_0_5_5, all_0_7_7) = all_21_0_12 & ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_21_0_12, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_7_7) | ~ (v1 = all_0_6_6))))
% 19.18/6.05 |
% 19.18/6.05 | Applying alpha-rule on (155) yields:
% 19.18/6.05 | (156) app(all_0_5_5, all_0_7_7) = all_21_0_12
% 19.18/6.05 | (157) ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_21_0_12, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_7_7) | ~ (v1 = all_0_6_6))))
% 19.18/6.05 |
% 19.18/6.05 | Instantiating formula (157) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields:
% 19.18/6.05 | (158) ? [v0] : ? [v1] : (app(all_21_0_12, all_0_4_4) = v0 & app(all_0_5_5, all_0_4_4) = v1 & ( ~ (v1 = all_0_7_7) | ~ (v0 = all_0_6_6)))
% 19.18/6.05 |
% 19.18/6.05 | Instantiating (147) with all_54_0_26 yields:
% 19.18/6.05 | (159) app(all_0_5_5, all_0_5_5) = all_54_0_26 & ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_54_0_26, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_7_7) | ~ (v1 = all_0_6_6))))
% 19.18/6.05 |
% 19.18/6.06 | Applying alpha-rule on (159) yields:
% 19.18/6.06 | (160) app(all_0_5_5, all_0_5_5) = all_54_0_26
% 19.18/6.06 | (161) ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_54_0_26, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_7_7) | ~ (v1 = all_0_6_6))))
% 19.18/6.06 |
% 19.18/6.06 | Instantiating formula (161) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields:
% 19.18/6.06 | (162) ? [v0] : ? [v1] : (app(all_54_0_26, all_0_4_4) = v0 & app(all_0_5_5, all_0_4_4) = v1 & ( ~ (v1 = all_0_7_7) | ~ (v0 = all_0_6_6)))
% 19.18/6.06 |
% 19.18/6.06 | Instantiating (146) with all_57_0_27 yields:
% 19.18/6.06 | (163) app(all_0_5_5, all_0_4_4) = all_57_0_27 & ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_57_0_27, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_7_7) | ~ (v1 = all_0_6_6))))
% 19.18/6.06 |
% 19.18/6.06 | Applying alpha-rule on (163) yields:
% 19.18/6.06 | (164) app(all_0_5_5, all_0_4_4) = all_57_0_27
% 19.18/6.06 | (165) ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_57_0_27, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_7_7) | ~ (v1 = all_0_6_6))))
% 19.18/6.06 |
% 19.18/6.06 | Instantiating formula (165) with all_0_2_2 and discharging atoms ssList(all_0_2_2), yields:
% 19.18/6.06 | (166) ? [v0] : ? [v1] : (app(all_57_0_27, all_0_2_2) = v0 & app(all_0_5_5, all_0_2_2) = v1 & ( ~ (v1 = all_0_7_7) | ~ (v0 = all_0_6_6)))
% 19.18/6.06 |
% 19.18/6.06 | Instantiating formula (165) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields:
% 19.18/6.06 | (167) ? [v0] : ? [v1] : (app(all_57_0_27, all_0_4_4) = v0 & app(all_0_5_5, all_0_4_4) = v1 & ( ~ (v1 = all_0_7_7) | ~ (v0 = all_0_6_6)))
% 19.18/6.06 |
% 19.18/6.06 | Instantiating (150) with all_86_0_37 yields:
% 19.18/6.06 | (168) app(all_0_5_5, nil) = all_86_0_37 & ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_86_0_37, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_7_7) | ~ (v1 = all_0_6_6))))
% 19.18/6.06 |
% 19.18/6.06 | Applying alpha-rule on (168) yields:
% 19.18/6.06 | (169) app(all_0_5_5, nil) = all_86_0_37
% 19.18/6.06 | (170) ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_86_0_37, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_7_7) | ~ (v1 = all_0_6_6))))
% 19.18/6.06 |
% 19.18/6.06 | Instantiating formula (170) with all_0_2_2 and discharging atoms ssList(all_0_2_2), yields:
% 19.18/6.06 | (171) ? [v0] : ? [v1] : (app(all_86_0_37, all_0_2_2) = v0 & app(all_0_5_5, all_0_2_2) = v1 & ( ~ (v1 = all_0_7_7) | ~ (v0 = all_0_6_6)))
% 19.18/6.06 |
% 19.18/6.06 | Instantiating formula (170) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields:
% 19.18/6.06 | (172) ? [v0] : ? [v1] : (app(all_86_0_37, all_0_4_4) = v0 & app(all_0_5_5, all_0_4_4) = v1 & ( ~ (v1 = all_0_7_7) | ~ (v0 = all_0_6_6)))
% 19.44/6.06 |
% 19.44/6.06 | Instantiating (148) with all_116_0_47 yields:
% 19.44/6.06 | (173) app(all_0_5_5, all_0_6_6) = all_116_0_47 & ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_116_0_47, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_7_7) | ~ (v1 = all_0_6_6))))
% 19.44/6.06 |
% 19.44/6.06 | Applying alpha-rule on (173) yields:
% 19.44/6.06 | (174) app(all_0_5_5, all_0_6_6) = all_116_0_47
% 19.44/6.06 | (175) ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_116_0_47, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_7_7) | ~ (v1 = all_0_6_6))))
% 19.44/6.06 |
% 19.44/6.06 | Instantiating formula (175) with all_0_2_2 and discharging atoms ssList(all_0_2_2), yields:
% 19.44/6.06 | (176) ? [v0] : ? [v1] : (app(all_116_0_47, all_0_2_2) = v0 & app(all_0_5_5, all_0_2_2) = v1 & ( ~ (v1 = all_0_7_7) | ~ (v0 = all_0_6_6)))
% 19.44/6.06 |
% 19.44/6.06 | Instantiating formula (175) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields:
% 19.44/6.06 | (177) ? [v0] : ? [v1] : (app(all_116_0_47, all_0_4_4) = v0 & app(all_0_5_5, all_0_4_4) = v1 & ( ~ (v1 = all_0_7_7) | ~ (v0 = all_0_6_6)))
% 19.44/6.06 |
% 19.44/6.06 | Instantiating (154) with all_145_0_70, all_145_1_71 yields:
% 19.44/6.06 | (178) app(all_12_0_9, all_0_4_4) = all_145_1_71 & app(all_0_5_5, all_0_4_4) = all_145_0_70 & ( ~ (all_145_0_70 = all_0_7_7) | ~ (all_145_1_71 = all_0_6_6))
% 19.44/6.06 |
% 19.44/6.06 | Applying alpha-rule on (178) yields:
% 19.44/6.06 | (179) app(all_12_0_9, all_0_4_4) = all_145_1_71
% 19.44/6.06 | (180) app(all_0_5_5, all_0_4_4) = all_145_0_70
% 19.44/6.06 | (181) ~ (all_145_0_70 = all_0_7_7) | ~ (all_145_1_71 = all_0_6_6)
% 19.44/6.06 |
% 19.44/6.06 | Instantiating (158) with all_179_0_104, all_179_1_105 yields:
% 19.44/6.06 | (182) app(all_21_0_12, all_0_4_4) = all_179_1_105 & app(all_0_5_5, all_0_4_4) = all_179_0_104 & ( ~ (all_179_0_104 = all_0_7_7) | ~ (all_179_1_105 = all_0_6_6))
% 19.44/6.06 |
% 19.44/6.06 | Applying alpha-rule on (182) yields:
% 19.44/6.06 | (183) app(all_21_0_12, all_0_4_4) = all_179_1_105
% 19.44/6.06 | (184) app(all_0_5_5, all_0_4_4) = all_179_0_104
% 19.44/6.06 | (185) ~ (all_179_0_104 = all_0_7_7) | ~ (all_179_1_105 = all_0_6_6)
% 19.44/6.06 |
% 19.44/6.06 | Instantiating (162) with all_289_0_214, all_289_1_215 yields:
% 19.44/6.06 | (186) app(all_54_0_26, all_0_4_4) = all_289_1_215 & app(all_0_5_5, all_0_4_4) = all_289_0_214 & ( ~ (all_289_0_214 = all_0_7_7) | ~ (all_289_1_215 = all_0_6_6))
% 19.44/6.06 |
% 19.44/6.06 | Applying alpha-rule on (186) yields:
% 19.44/6.06 | (187) app(all_54_0_26, all_0_4_4) = all_289_1_215
% 19.44/6.06 | (188) app(all_0_5_5, all_0_4_4) = all_289_0_214
% 19.44/6.06 | (189) ~ (all_289_0_214 = all_0_7_7) | ~ (all_289_1_215 = all_0_6_6)
% 19.44/6.06 |
% 19.44/6.06 | Instantiating (167) with all_301_0_226, all_301_1_227 yields:
% 19.44/6.06 | (190) app(all_57_0_27, all_0_4_4) = all_301_1_227 & app(all_0_5_5, all_0_4_4) = all_301_0_226 & ( ~ (all_301_0_226 = all_0_7_7) | ~ (all_301_1_227 = all_0_6_6))
% 19.44/6.06 |
% 19.44/6.06 | Applying alpha-rule on (190) yields:
% 19.44/6.06 | (191) app(all_57_0_27, all_0_4_4) = all_301_1_227
% 19.44/6.06 | (192) app(all_0_5_5, all_0_4_4) = all_301_0_226
% 19.44/6.06 | (193) ~ (all_301_0_226 = all_0_7_7) | ~ (all_301_1_227 = all_0_6_6)
% 19.44/6.06 |
% 19.44/6.06 | Instantiating (166) with all_303_0_228, all_303_1_229 yields:
% 19.44/6.06 | (194) app(all_57_0_27, all_0_2_2) = all_303_1_229 & app(all_0_5_5, all_0_2_2) = all_303_0_228 & ( ~ (all_303_0_228 = all_0_7_7) | ~ (all_303_1_229 = all_0_6_6))
% 19.44/6.06 |
% 19.44/6.06 | Applying alpha-rule on (194) yields:
% 19.44/6.06 | (195) app(all_57_0_27, all_0_2_2) = all_303_1_229
% 19.44/6.06 | (196) app(all_0_5_5, all_0_2_2) = all_303_0_228
% 19.44/6.06 | (197) ~ (all_303_0_228 = all_0_7_7) | ~ (all_303_1_229 = all_0_6_6)
% 19.44/6.06 |
% 19.44/6.06 | Instantiating (172) with all_409_0_334, all_409_1_335 yields:
% 19.44/6.06 | (198) app(all_86_0_37, all_0_4_4) = all_409_1_335 & app(all_0_5_5, all_0_4_4) = all_409_0_334 & ( ~ (all_409_0_334 = all_0_7_7) | ~ (all_409_1_335 = all_0_6_6))
% 19.44/6.06 |
% 19.44/6.06 | Applying alpha-rule on (198) yields:
% 19.44/6.06 | (199) app(all_86_0_37, all_0_4_4) = all_409_1_335
% 19.44/6.06 | (200) app(all_0_5_5, all_0_4_4) = all_409_0_334
% 19.44/6.06 | (201) ~ (all_409_0_334 = all_0_7_7) | ~ (all_409_1_335 = all_0_6_6)
% 19.44/6.06 |
% 19.44/6.06 | Instantiating (171) with all_411_0_336, all_411_1_337 yields:
% 19.44/6.06 | (202) app(all_86_0_37, all_0_2_2) = all_411_1_337 & app(all_0_5_5, all_0_2_2) = all_411_0_336 & ( ~ (all_411_0_336 = all_0_7_7) | ~ (all_411_1_337 = all_0_6_6))
% 19.44/6.06 |
% 19.44/6.06 | Applying alpha-rule on (202) yields:
% 19.44/6.06 | (203) app(all_86_0_37, all_0_2_2) = all_411_1_337
% 19.44/6.06 | (204) app(all_0_5_5, all_0_2_2) = all_411_0_336
% 19.44/6.07 | (205) ~ (all_411_0_336 = all_0_7_7) | ~ (all_411_1_337 = all_0_6_6)
% 19.44/6.07 |
% 19.44/6.07 | Instantiating (177) with all_527_0_452, all_527_1_453 yields:
% 19.44/6.07 | (206) app(all_116_0_47, all_0_4_4) = all_527_1_453 & app(all_0_5_5, all_0_4_4) = all_527_0_452 & ( ~ (all_527_0_452 = all_0_7_7) | ~ (all_527_1_453 = all_0_6_6))
% 19.44/6.07 |
% 19.44/6.07 | Applying alpha-rule on (206) yields:
% 19.44/6.07 | (207) app(all_116_0_47, all_0_4_4) = all_527_1_453
% 19.44/6.07 | (208) app(all_0_5_5, all_0_4_4) = all_527_0_452
% 19.44/6.07 | (209) ~ (all_527_0_452 = all_0_7_7) | ~ (all_527_1_453 = all_0_6_6)
% 19.44/6.07 |
% 19.44/6.07 | Instantiating (176) with all_531_0_456, all_531_1_457 yields:
% 19.44/6.07 | (210) app(all_116_0_47, all_0_2_2) = all_531_1_457 & app(all_0_5_5, all_0_2_2) = all_531_0_456 & ( ~ (all_531_0_456 = all_0_7_7) | ~ (all_531_1_457 = all_0_6_6))
% 19.44/6.07 |
% 19.44/6.07 | Applying alpha-rule on (210) yields:
% 19.44/6.07 | (211) app(all_116_0_47, all_0_2_2) = all_531_1_457
% 19.44/6.07 | (212) app(all_0_5_5, all_0_2_2) = all_531_0_456
% 19.44/6.07 | (213) ~ (all_531_0_456 = all_0_7_7) | ~ (all_531_1_457 = all_0_6_6)
% 19.44/6.07 |
% 19.44/6.07 | Instantiating formula (84) with all_0_5_5, all_0_2_2, all_531_0_456, all_0_7_7 and discharging atoms app(all_0_5_5, all_0_2_2) = all_531_0_456, app(all_0_5_5, all_0_2_2) = all_0_7_7, yields:
% 19.44/6.07 | (214) all_531_0_456 = all_0_7_7
% 19.44/6.07 |
% 19.44/6.07 | Instantiating formula (84) with all_0_5_5, all_0_2_2, all_411_0_336, all_531_0_456 and discharging atoms app(all_0_5_5, all_0_2_2) = all_531_0_456, app(all_0_5_5, all_0_2_2) = all_411_0_336, yields:
% 19.44/6.07 | (215) all_531_0_456 = all_411_0_336
% 19.44/6.07 |
% 19.44/6.07 | Instantiating formula (84) with all_0_5_5, all_0_2_2, all_303_0_228, all_531_0_456 and discharging atoms app(all_0_5_5, all_0_2_2) = all_531_0_456, app(all_0_5_5, all_0_2_2) = all_303_0_228, yields:
% 19.44/6.07 | (216) all_531_0_456 = all_303_0_228
% 19.44/6.07 |
% 19.44/6.07 | Instantiating formula (84) with all_0_5_5, all_0_4_4, all_301_0_226, all_409_0_334 and discharging atoms app(all_0_5_5, all_0_4_4) = all_409_0_334, app(all_0_5_5, all_0_4_4) = all_301_0_226, yields:
% 19.44/6.07 | (217) all_409_0_334 = all_301_0_226
% 19.44/6.07 |
% 19.44/6.07 | Instantiating formula (84) with all_0_5_5, all_0_4_4, all_289_0_214, all_527_0_452 and discharging atoms app(all_0_5_5, all_0_4_4) = all_527_0_452, app(all_0_5_5, all_0_4_4) = all_289_0_214, yields:
% 19.44/6.07 | (218) all_527_0_452 = all_289_0_214
% 19.44/6.07 |
% 19.44/6.07 | Instantiating formula (84) with all_0_5_5, all_0_4_4, all_289_0_214, all_409_0_334 and discharging atoms app(all_0_5_5, all_0_4_4) = all_409_0_334, app(all_0_5_5, all_0_4_4) = all_289_0_214, yields:
% 19.44/6.07 | (219) all_409_0_334 = all_289_0_214
% 19.44/6.07 |
% 19.44/6.07 | Instantiating formula (84) with all_0_5_5, all_0_4_4, all_179_0_104, all_0_3_3 and discharging atoms app(all_0_5_5, all_0_4_4) = all_179_0_104, app(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 19.44/6.07 | (220) all_179_0_104 = all_0_3_3
% 19.44/6.07 |
% 19.44/6.07 | Instantiating formula (84) with all_0_5_5, all_0_4_4, all_179_0_104, all_289_0_214 and discharging atoms app(all_0_5_5, all_0_4_4) = all_289_0_214, app(all_0_5_5, all_0_4_4) = all_179_0_104, yields:
% 19.44/6.07 | (221) all_289_0_214 = all_179_0_104
% 19.44/6.07 |
% 19.44/6.07 | Instantiating formula (84) with all_0_5_5, all_0_4_4, all_145_0_70, all_409_0_334 and discharging atoms app(all_0_5_5, all_0_4_4) = all_409_0_334, app(all_0_5_5, all_0_4_4) = all_145_0_70, yields:
% 19.44/6.07 | (222) all_409_0_334 = all_145_0_70
% 19.44/6.07 |
% 19.44/6.07 | Instantiating formula (84) with all_0_5_5, all_0_4_4, all_57_0_27, all_527_0_452 and discharging atoms app(all_0_5_5, all_0_4_4) = all_527_0_452, app(all_0_5_5, all_0_4_4) = all_57_0_27, yields:
% 19.44/6.07 | (223) all_527_0_452 = all_57_0_27
% 19.44/6.07 |
% 19.44/6.07 | Combining equations (216,215) yields a new equation:
% 19.44/6.07 | (224) all_411_0_336 = all_303_0_228
% 19.44/6.07 |
% 19.44/6.07 | Combining equations (214,215) yields a new equation:
% 19.44/6.07 | (225) all_411_0_336 = all_0_7_7
% 19.44/6.07 |
% 19.44/6.07 | Combining equations (218,223) yields a new equation:
% 19.44/6.07 | (226) all_289_0_214 = all_57_0_27
% 19.44/6.07 |
% 19.44/6.07 | Simplifying 226 yields:
% 19.44/6.07 | (227) all_289_0_214 = all_57_0_27
% 19.44/6.07 |
% 19.44/6.07 | Combining equations (224,225) yields a new equation:
% 19.44/6.07 | (228) all_303_0_228 = all_0_7_7
% 19.44/6.07 |
% 19.44/6.07 | Simplifying 228 yields:
% 19.44/6.07 | (229) all_303_0_228 = all_0_7_7
% 19.44/6.07 |
% 19.44/6.07 | Combining equations (219,217) yields a new equation:
% 19.44/6.07 | (230) all_301_0_226 = all_289_0_214
% 19.44/6.07 |
% 19.44/6.07 | Combining equations (222,217) yields a new equation:
% 19.44/6.07 | (231) all_301_0_226 = all_145_0_70
% 19.44/6.07 |
% 19.44/6.07 | Combining equations (230,231) yields a new equation:
% 19.44/6.07 | (232) all_289_0_214 = all_145_0_70
% 19.44/6.07 |
% 19.44/6.07 | Simplifying 232 yields:
% 19.44/6.07 | (233) all_289_0_214 = all_145_0_70
% 19.44/6.07 |
% 19.44/6.07 | Combining equations (221,233) yields a new equation:
% 19.44/6.07 | (234) all_179_0_104 = all_145_0_70
% 19.44/6.07 |
% 19.44/6.07 | Simplifying 234 yields:
% 19.44/6.07 | (235) all_179_0_104 = all_145_0_70
% 19.44/6.07 |
% 19.44/6.07 | Combining equations (227,233) yields a new equation:
% 19.44/6.07 | (236) all_145_0_70 = all_57_0_27
% 19.44/6.07 |
% 19.44/6.07 | Combining equations (235,220) yields a new equation:
% 19.44/6.07 | (237) all_145_0_70 = all_0_3_3
% 19.44/6.07 |
% 19.44/6.07 | Simplifying 237 yields:
% 19.44/6.07 | (238) all_145_0_70 = all_0_3_3
% 19.44/6.07 |
% 19.44/6.07 | Combining equations (238,236) yields a new equation:
% 19.44/6.07 | (239) all_57_0_27 = all_0_3_3
% 19.44/6.07 |
% 19.44/6.07 | From (239) and (195) follows:
% 19.44/6.07 | (240) app(all_0_3_3, all_0_2_2) = all_303_1_229
% 19.44/6.07 |
% 19.44/6.07 +-Applying beta-rule and splitting (197), into two cases.
% 19.44/6.07 |-Branch one:
% 19.44/6.07 | (241) ~ (all_303_0_228 = all_0_7_7)
% 19.44/6.07 |
% 19.44/6.07 | Equations (229) can reduce 241 to:
% 19.44/6.07 | (242) $false
% 19.44/6.07 |
% 19.44/6.07 |-The branch is then unsatisfiable
% 19.44/6.07 |-Branch two:
% 19.44/6.07 | (229) all_303_0_228 = all_0_7_7
% 19.44/6.07 | (244) ~ (all_303_1_229 = all_0_6_6)
% 19.44/6.07 |
% 19.44/6.07 | Instantiating formula (84) with all_0_3_3, all_0_2_2, all_303_1_229, all_0_6_6 and discharging atoms app(all_0_3_3, all_0_2_2) = all_303_1_229, app(all_0_3_3, all_0_2_2) = all_0_6_6, yields:
% 19.44/6.07 | (245) all_303_1_229 = all_0_6_6
% 19.44/6.07 |
% 19.44/6.07 | Equations (245) can reduce 244 to:
% 19.44/6.07 | (242) $false
% 19.44/6.07 |
% 19.44/6.07 |-The branch is then unsatisfiable
% 19.44/6.07 % SZS output end Proof for theBenchmark
% 19.44/6.07
% 19.44/6.07 5463ms
%------------------------------------------------------------------------------