TSTP Solution File: SWC095+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWC095+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n019.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 20:16:10 EDT 2022
% Result : Theorem 6.78s 2.16s
% Output : Proof 19.67s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC095+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n019.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 : Sat Jun 11 21:03:55 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.54/0.58 ____ _
% 0.54/0.58 ___ / __ \_____(_)___ ________ __________
% 0.54/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.54/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.54/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.54/0.58
% 0.54/0.58 A Theorem Prover for First-Order Logic
% 0.54/0.58 (ePrincess v.1.0)
% 0.54/0.58
% 0.54/0.58 (c) Philipp Rümmer, 2009-2015
% 0.54/0.58 (c) Peter Backeman, 2014-2015
% 0.54/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.54/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.54/0.58 Bug reports to peter@backeman.se
% 0.54/0.58
% 0.54/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.54/0.58
% 0.54/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.54/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.42/1.11 Prover 0: Preprocessing ...
% 4.71/1.70 Prover 0: Constructing countermodel ...
% 6.78/2.16 Prover 0: proved (1532ms)
% 6.78/2.16
% 6.78/2.16 No countermodel exists, formula is valid
% 6.78/2.16 % SZS status Theorem for theBenchmark
% 6.78/2.16
% 6.78/2.16 Generating proof ... found it (size 92)
% 18.81/6.11
% 18.81/6.11 % SZS output start Proof for theBenchmark
% 18.81/6.11 Assumed formulas after preprocessing and simplification:
% 18.81/6.11 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v6) & app(v4, v5) = v0 & app(v2, v5) = v1 & 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 = v1) | ~ (v12 = v0)))))) & ! [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)))
% 19.25/6.17 | 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:
% 19.25/6.17 | (1) ~ (all_0_0_0 = all_0_1_1) & app(all_0_3_3, all_0_2_2) = all_0_7_7 & app(all_0_5_5, all_0_2_2) = all_0_6_6 & 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_6_6) | ~ (v4 = all_0_7_7)))))) & ! [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))
% 19.25/6.20 |
% 19.25/6.20 | Applying alpha-rule on (1) yields:
% 19.25/6.20 | (2) ! [v0] : (v0 = nil | ~ segmentP(nil, v0) | ~ ssList(v0))
% 19.25/6.20 | (3) ! [v0] : ! [v1] : ( ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v1, v2) = v0 & ssList(v2)))
% 19.25/6.20 | (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)))
% 19.25/6.20 | (5) app(all_0_5_5, all_0_2_2) = all_0_6_6
% 19.25/6.20 | (6) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v1))
% 19.25/6.20 | (7) ! [v0] : ! [v1] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0))
% 19.25/6.20 | (8) ! [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)))
% 19.25/6.20 | (9) segmentP(nil, nil)
% 19.25/6.20 | (10) ! [v0] : ! [v1] : ( ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v1))
% 19.25/6.20 | (11) ! [v0] : ( ~ ssItem(v0) | geq(v0, v0))
% 19.25/6.20 | (12) ! [v0] : ! [v1] : ( ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v1, v0))
% 19.25/6.20 | (13) ssList(all_0_4_4)
% 19.25/6.20 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ~ ssList(v0) | ~ ssItem(v1) | cons(v1, v0) = v3)
% 19.25/6.20 | (15) ! [v0] : ! [v1] : ( ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v1, v0))
% 19.25/6.20 | (16) ! [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)))
% 19.25/6.20 | (17) ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v1))
% 19.25/6.20 | (18) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | duplicatefreeP(v1))
% 19.25/6.20 | (19) rearsegP(nil, nil)
% 19.25/6.20 | (20) ! [v0] : ! [v1] : ( ~ leq(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v1))
% 19.25/6.20 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ~ ssList(v0))
% 19.25/6.20 | (22) ! [v0] : ! [v1] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0))
% 19.25/6.21 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v0, v1) = v2) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2))
% 19.25/6.21 | (24) ! [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))
% 19.25/6.21 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | hd(v3) = v1)
% 19.25/6.21 | (26) app(all_0_5_5, all_0_4_4) = all_0_3_3
% 19.25/6.21 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v1, v3) = v4) | ~ (app(v2, v4) = v0) | ~ ssList(v3) | ~ ssList(v2) | ~ ssList(v0) | ~ ssItem(v1) | memberP(v0, v1))
% 19.25/6.21 | (28) ! [v0] : ! [v1] : (v1 = v0 | ~ ssList(v1) | ~ ssList(v0) | neq(v0, v1))
% 19.25/6.21 | (29) ! [v0] : ! [v1] : (v1 = v0 | ~ frontsegP(v1, v0) | ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0))
% 19.25/6.21 | (30) ! [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))
% 19.25/6.21 | (31) ssList(all_0_7_7)
% 19.25/6.21 | (32) ! [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))
% 19.25/6.21 | (33) ~ (all_0_0_0 = all_0_1_1)
% 19.25/6.21 | (34) ! [v0] : ( ~ ssItem(v0) | leq(v0, v0))
% 19.47/6.21 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0))
% 19.47/6.21 | (36) ! [v0] : ( ~ memberP(nil, v0) | ~ ssItem(v0))
% 19.47/6.21 | (37) ! [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))
% 19.47/6.21 | (38) ! [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))
% 19.47/6.21 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0))
% 19.47/6.21 | (40) ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v1, v0) | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0))
% 19.47/6.21 | (41) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ ssList(v0))
% 19.47/6.21 | (42) ! [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)))
% 19.47/6.21 | (43) ! [v0] : ! [v1] : ! [v2] : ( ~ segmentP(v1, v2) | ~ segmentP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v2))
% 19.47/6.21 | (44) ! [v0] : (v0 = nil | ~ frontsegP(nil, v0) | ~ ssList(v0))
% 19.47/6.21 | (45) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0))
% 19.47/6.21 | (46) ! [v0] : (v0 = nil | ~ ssList(v0) | ? [v1] : ? [v2] : (cons(v2, v1) = v0 & ssList(v1) & ssItem(v2)))
% 19.47/6.21 | (47) totalorderP(nil)
% 19.47/6.21 | (48) ! [v0] : ( ~ singletonP(v0) | ~ ssList(v0) | ? [v1] : (cons(v1, nil) = v0 & ssItem(v1)))
% 19.47/6.21 | (49) ! [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)))
% 19.47/6.21 | (50) ! [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)))
% 19.47/6.21 | (51) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderedP(v1))
% 19.47/6.21 | (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))
% 19.47/6.21 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 19.47/6.21 | (54) ! [v0] : ! [v1] : ( ~ (cons(v1, nil) = v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0))
% 19.47/6.21 | (55) ! [v0] : ! [v1] : ! [v2] : ( ~ geq(v1, v2) | ~ geq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v2))
% 19.47/6.21 | (56) ssList(all_0_6_6)
% 19.47/6.21 | (57) ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0))
% 19.47/6.21 | (58) ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = v0) | ~ ssList(v0) | ~ ssItem(v1))
% 19.47/6.22 | (59) ! [v0] : ( ~ ssList(v0) | rearsegP(v0, v0))
% 19.47/6.22 | (60) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderP(v1))
% 19.47/6.22 | (61) ! [v0] : ! [v1] : ! [v2] : ( ~ leq(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v2))
% 19.47/6.22 | (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)))
% 19.47/6.22 | (63) ! [v0] : ! [v1] : ( ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v2, v1) = v0 & ssList(v2)))
% 19.47/6.22 | (64) ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v1))
% 19.47/6.22 | (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))
% 19.47/6.22 | (66) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | cyclefreeP(v1))
% 19.47/6.22 | (67) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ ssList(v0))
% 19.47/6.22 | (68) totalorderedP(nil)
% 19.47/6.22 | (69) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderP(v1))
% 19.47/6.22 | (70) ssItem(all_0_1_1)
% 19.47/6.22 | (71) ! [v0] : ! [v1] : (v1 = v0 | ~ rearsegP(v1, v0) | ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0))
% 19.47/6.22 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v0, v2) = v3) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v3, v1))
% 19.47/6.22 | (73) ! [v0] : ( ~ ssList(v0) | frontsegP(v0, v0))
% 19.47/6.22 | (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))))
% 19.47/6.22 | (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))
% 19.47/6.22 | (76) ! [v0] : ( ~ ssList(v0) | ~ neq(v0, v0))
% 19.47/6.22 | (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)))
% 19.47/6.22 | (78) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 19.47/6.22 | (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)
% 19.47/6.22 | (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)))
% 19.47/6.22 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | hd(v2) = v1)
% 19.47/6.22 | (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))))))
% 19.47/6.22 | (83) ! [v0] : ( ~ ssList(v0) | segmentP(v0, nil))
% 19.47/6.22 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 19.47/6.22 | (85) ssList(all_0_2_2)
% 19.47/6.22 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2))
% 19.47/6.22 | (87) strictorderP(nil)
% 19.47/6.22 | (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))
% 19.47/6.22 | (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))))))
% 19.47/6.22 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0))
% 19.47/6.22 | (91) ! [v0] : (v0 = nil | ~ rearsegP(nil, v0) | ~ ssList(v0))
% 19.47/6.22 | (92) ! [v0] : ! [v1] : (v1 = v0 | ~ geq(v1, v0) | ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0))
% 19.47/6.22 | (93) ! [v0] : ( ~ neq(v0, v0) | ~ ssItem(v0))
% 19.47/6.22 | (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))
% 19.47/6.22 | (95) ! [v0] : ! [v1] : ! [v2] : ( ~ gt(v1, v2) | ~ gt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v2))
% 19.47/6.22 | (96) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v2, v0) = v3) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1))
% 19.47/6.22 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ rearsegP(v1, v2) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v2))
% 19.47/6.22 | (98) frontsegP(nil, nil)
% 19.47/6.22 | (99) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2))
% 19.47/6.22 | (100) ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = nil) | ~ ssList(v0) | ~ ssItem(v1))
% 19.47/6.22 | (101) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v2, v1) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v1))
% 19.47/6.22 | (102) ssItem(all_0_0_0)
% 19.47/6.22 | (103) strictorderedP(nil)
% 19.47/6.22 | (104) equalelemsP(nil)
% 19.47/6.23 | (105) ssList(all_0_5_5)
% 19.47/6.23 | (106) ! [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))))))
% 19.47/6.23 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | tl(v2) = v0)
% 19.47/6.23 | (108) ssList(nil)
% 19.47/6.23 | (109) ! [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))
% 19.47/6.23 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v2, v0))
% 19.47/6.23 | (111) ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2))
% 19.47/6.23 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2))
% 19.47/6.23 | (113) ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ lt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2))
% 19.47/6.23 | (114) ! [v0] : ! [v1] : (v1 = v0 | ~ ssItem(v1) | ~ ssItem(v0) | neq(v0, v1))
% 19.47/6.23 | (115) cyclefreeP(nil)
% 19.47/6.23 | (116) app(all_0_3_3, all_0_2_2) = all_0_7_7
% 19.47/6.23 | (117) duplicatefreeP(nil)
% 19.47/6.23 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0) | memberP(v1, v0))
% 19.47/6.23 | (119) ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0))
% 19.47/6.23 | (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))
% 19.47/6.23 | (121) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | equalelemsP(v1))
% 19.47/6.23 | (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)
% 19.47/6.23 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v1, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0))
% 19.47/6.23 | (124) ! [v0] : ! [v1] : ! [v2] : ( ~ frontsegP(v1, v2) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v2))
% 19.47/6.23 | (125) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ~ ssList(v0) | ssList(v1))
% 19.47/6.23 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0))
% 19.47/6.23 | (127) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | ? [v3] : (cons(v1, nil) = v3 & app(v3, v0) = v2))
% 19.47/6.23 | (128) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v1, v2) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v1))
% 19.47/6.23 | (129) ! [v0] : ( ~ ssList(v0) | frontsegP(v0, nil))
% 19.47/6.23 | (130) ! [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))))))
% 19.47/6.23 | (131) ! [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))
% 19.47/6.23 | (132) ! [v0] : ( ~ ssList(v0) | rearsegP(v0, nil))
% 19.47/6.23 | (133) ! [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))
% 19.47/6.23 | (134) ! [v0] : ! [v1] : (v1 = v0 | ~ segmentP(v1, v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0))
% 19.47/6.23 | (135) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ~ ssList(v0) | ssItem(v1))
% 19.47/6.23 | (136) ! [v0] : ( ~ lt(v0, v0) | ~ ssItem(v0))
% 19.47/6.23 | (137) ! [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))))
% 19.47/6.23 | (138) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v3, v0))
% 19.47/6.23 | (139) ! [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))
% 19.47/6.23 | (140) ! [v0] : ! [v1] : ( ~ gt(v1, v0) | ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0))
% 19.47/6.23 | (141) ! [v0] : ( ~ ssList(v0) | segmentP(v0, v0))
% 19.47/6.23 | (142) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderedP(v1))
% 19.47/6.23 | (143) ! [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_6_6) | ~ (v4 = all_0_7_7))))))
% 19.47/6.23 | (144) ~ singletonP(nil)
% 19.47/6.23 |
% 19.47/6.23 | Instantiating formula (143) with all_0_2_2, all_0_5_5 and discharging atoms ssList(all_0_2_2), ssList(all_0_5_5), yields:
% 19.47/6.23 | (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_6_6) | ~ (v2 = all_0_7_7)))))
% 19.47/6.23 |
% 19.47/6.23 | Instantiating formula (143) with all_0_4_4, all_0_5_5 and discharging atoms ssList(all_0_4_4), ssList(all_0_5_5), yields:
% 19.47/6.23 | (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_6_6) | ~ (v2 = all_0_7_7)))))
% 19.47/6.23 |
% 19.47/6.23 | Instantiating formula (143) with all_0_5_5, all_0_5_5 and discharging atoms ssList(all_0_5_5), yields:
% 19.47/6.23 | (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_6_6) | ~ (v2 = all_0_7_7)))))
% 19.47/6.23 |
% 19.47/6.23 | Instantiating formula (143) with all_0_6_6, all_0_5_5 and discharging atoms ssList(all_0_5_5), ssList(all_0_6_6), yields:
% 19.47/6.23 | (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_6_6) | ~ (v2 = all_0_7_7)))))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating formula (143) with all_0_7_7, all_0_5_5 and discharging atoms ssList(all_0_5_5), ssList(all_0_7_7), yields:
% 19.47/6.24 | (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_6_6) | ~ (v2 = all_0_7_7)))))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating formula (143) with nil, all_0_5_5 and discharging atoms ssList(all_0_5_5), ssList(nil), yields:
% 19.47/6.24 | (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_6_6) | ~ (v2 = all_0_7_7)))))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating (145) with all_24_0_13 yields:
% 19.47/6.24 | (151) app(all_0_5_5, all_0_2_2) = all_24_0_13 & ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_24_0_13, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_6_6) | ~ (v1 = all_0_7_7))))
% 19.47/6.24 |
% 19.47/6.24 | Applying alpha-rule on (151) yields:
% 19.47/6.24 | (152) app(all_0_5_5, all_0_2_2) = all_24_0_13
% 19.47/6.24 | (153) ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_24_0_13, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_6_6) | ~ (v1 = all_0_7_7))))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating formula (153) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields:
% 19.47/6.24 | (154) ? [v0] : ? [v1] : (app(all_24_0_13, all_0_4_4) = v0 & app(all_0_5_5, all_0_4_4) = v1 & ( ~ (v1 = all_0_6_6) | ~ (v0 = all_0_7_7)))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating (150) with all_39_0_18 yields:
% 19.47/6.24 | (155) app(all_0_5_5, nil) = all_39_0_18 & ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_39_0_18, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_6_6) | ~ (v1 = all_0_7_7))))
% 19.47/6.24 |
% 19.47/6.24 | Applying alpha-rule on (155) yields:
% 19.47/6.24 | (156) app(all_0_5_5, nil) = all_39_0_18
% 19.47/6.24 | (157) ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_39_0_18, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_6_6) | ~ (v1 = all_0_7_7))))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating formula (157) with all_0_2_2 and discharging atoms ssList(all_0_2_2), yields:
% 19.47/6.24 | (158) ? [v0] : ? [v1] : (app(all_39_0_18, all_0_2_2) = v0 & app(all_0_5_5, all_0_2_2) = v1 & ( ~ (v1 = all_0_6_6) | ~ (v0 = all_0_7_7)))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating formula (157) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields:
% 19.47/6.24 | (159) ? [v0] : ? [v1] : (app(all_39_0_18, all_0_4_4) = v0 & app(all_0_5_5, all_0_4_4) = v1 & ( ~ (v1 = all_0_6_6) | ~ (v0 = all_0_7_7)))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating (149) with all_62_0_26 yields:
% 19.47/6.24 | (160) app(all_0_5_5, all_0_7_7) = all_62_0_26 & ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_62_0_26, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_6_6) | ~ (v1 = all_0_7_7))))
% 19.47/6.24 |
% 19.47/6.24 | Applying alpha-rule on (160) yields:
% 19.47/6.24 | (161) app(all_0_5_5, all_0_7_7) = all_62_0_26
% 19.47/6.24 | (162) ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_62_0_26, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_6_6) | ~ (v1 = all_0_7_7))))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating formula (162) with all_0_2_2 and discharging atoms ssList(all_0_2_2), yields:
% 19.47/6.24 | (163) ? [v0] : ? [v1] : (app(all_62_0_26, all_0_2_2) = v0 & app(all_0_5_5, all_0_2_2) = v1 & ( ~ (v1 = all_0_6_6) | ~ (v0 = all_0_7_7)))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating formula (162) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields:
% 19.47/6.24 | (164) ? [v0] : ? [v1] : (app(all_62_0_26, all_0_4_4) = v0 & app(all_0_5_5, all_0_4_4) = v1 & ( ~ (v1 = all_0_6_6) | ~ (v0 = all_0_7_7)))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating (147) with all_71_0_29 yields:
% 19.47/6.24 | (165) app(all_0_5_5, all_0_5_5) = all_71_0_29 & ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_71_0_29, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_6_6) | ~ (v1 = all_0_7_7))))
% 19.47/6.24 |
% 19.47/6.24 | Applying alpha-rule on (165) yields:
% 19.47/6.24 | (166) app(all_0_5_5, all_0_5_5) = all_71_0_29
% 19.47/6.24 | (167) ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_71_0_29, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_6_6) | ~ (v1 = all_0_7_7))))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating formula (167) with all_0_2_2 and discharging atoms ssList(all_0_2_2), yields:
% 19.47/6.24 | (168) ? [v0] : ? [v1] : (app(all_71_0_29, all_0_2_2) = v0 & app(all_0_5_5, all_0_2_2) = v1 & ( ~ (v1 = all_0_6_6) | ~ (v0 = all_0_7_7)))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating formula (167) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields:
% 19.47/6.24 | (169) ? [v0] : ? [v1] : (app(all_71_0_29, all_0_4_4) = v0 & app(all_0_5_5, all_0_4_4) = v1 & ( ~ (v1 = all_0_6_6) | ~ (v0 = all_0_7_7)))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating (146) with all_74_0_30 yields:
% 19.47/6.24 | (170) app(all_0_5_5, all_0_4_4) = all_74_0_30 & ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_74_0_30, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_6_6) | ~ (v1 = all_0_7_7))))
% 19.47/6.24 |
% 19.47/6.24 | Applying alpha-rule on (170) yields:
% 19.47/6.24 | (171) app(all_0_5_5, all_0_4_4) = all_74_0_30
% 19.47/6.24 | (172) ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_74_0_30, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_6_6) | ~ (v1 = all_0_7_7))))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating formula (172) with all_0_2_2 and discharging atoms ssList(all_0_2_2), yields:
% 19.47/6.24 | (173) ? [v0] : ? [v1] : (app(all_74_0_30, all_0_2_2) = v0 & app(all_0_5_5, all_0_2_2) = v1 & ( ~ (v1 = all_0_6_6) | ~ (v0 = all_0_7_7)))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating formula (172) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields:
% 19.47/6.24 | (174) ? [v0] : ? [v1] : (app(all_74_0_30, all_0_4_4) = v0 & app(all_0_5_5, all_0_4_4) = v1 & ( ~ (v1 = all_0_6_6) | ~ (v0 = all_0_7_7)))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating (148) with all_99_0_39 yields:
% 19.47/6.24 | (175) app(all_0_5_5, all_0_6_6) = all_99_0_39 & ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_99_0_39, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_6_6) | ~ (v1 = all_0_7_7))))
% 19.47/6.24 |
% 19.47/6.24 | Applying alpha-rule on (175) yields:
% 19.47/6.24 | (176) app(all_0_5_5, all_0_6_6) = all_99_0_39
% 19.47/6.24 | (177) ! [v0] : ( ~ ssList(v0) | ? [v1] : ? [v2] : (app(all_99_0_39, v0) = v1 & app(all_0_5_5, v0) = v2 & ( ~ (v2 = all_0_6_6) | ~ (v1 = all_0_7_7))))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating formula (177) with all_0_2_2 and discharging atoms ssList(all_0_2_2), yields:
% 19.47/6.24 | (178) ? [v0] : ? [v1] : (app(all_99_0_39, all_0_2_2) = v0 & app(all_0_5_5, all_0_2_2) = v1 & ( ~ (v1 = all_0_6_6) | ~ (v0 = all_0_7_7)))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating formula (177) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields:
% 19.47/6.24 | (179) ? [v0] : ? [v1] : (app(all_99_0_39, all_0_4_4) = v0 & app(all_0_5_5, all_0_4_4) = v1 & ( ~ (v1 = all_0_6_6) | ~ (v0 = all_0_7_7)))
% 19.47/6.24 |
% 19.47/6.24 | Instantiating (154) with all_193_0_118, all_193_1_119 yields:
% 19.47/6.24 | (180) app(all_24_0_13, all_0_4_4) = all_193_1_119 & app(all_0_5_5, all_0_4_4) = all_193_0_118 & ( ~ (all_193_0_118 = all_0_6_6) | ~ (all_193_1_119 = all_0_7_7))
% 19.47/6.24 |
% 19.47/6.24 | Applying alpha-rule on (180) yields:
% 19.47/6.24 | (181) app(all_24_0_13, all_0_4_4) = all_193_1_119
% 19.47/6.24 | (182) app(all_0_5_5, all_0_4_4) = all_193_0_118
% 19.47/6.24 | (183) ~ (all_193_0_118 = all_0_6_6) | ~ (all_193_1_119 = all_0_7_7)
% 19.47/6.24 |
% 19.47/6.24 | Instantiating (159) with all_251_0_176, all_251_1_177 yields:
% 19.47/6.24 | (184) app(all_39_0_18, all_0_4_4) = all_251_1_177 & app(all_0_5_5, all_0_4_4) = all_251_0_176 & ( ~ (all_251_0_176 = all_0_6_6) | ~ (all_251_1_177 = all_0_7_7))
% 19.47/6.24 |
% 19.47/6.24 | Applying alpha-rule on (184) yields:
% 19.47/6.24 | (185) app(all_39_0_18, all_0_4_4) = all_251_1_177
% 19.47/6.24 | (186) app(all_0_5_5, all_0_4_4) = all_251_0_176
% 19.47/6.24 | (187) ~ (all_251_0_176 = all_0_6_6) | ~ (all_251_1_177 = all_0_7_7)
% 19.47/6.24 |
% 19.47/6.24 | Instantiating (158) with all_253_0_178, all_253_1_179 yields:
% 19.47/6.24 | (188) app(all_39_0_18, all_0_2_2) = all_253_1_179 & app(all_0_5_5, all_0_2_2) = all_253_0_178 & ( ~ (all_253_0_178 = all_0_6_6) | ~ (all_253_1_179 = all_0_7_7))
% 19.47/6.24 |
% 19.47/6.24 | Applying alpha-rule on (188) yields:
% 19.47/6.24 | (189) app(all_39_0_18, all_0_2_2) = all_253_1_179
% 19.47/6.24 | (190) app(all_0_5_5, all_0_2_2) = all_253_0_178
% 19.47/6.24 | (191) ~ (all_253_0_178 = all_0_6_6) | ~ (all_253_1_179 = all_0_7_7)
% 19.47/6.24 |
% 19.47/6.24 | Instantiating (164) with all_333_0_258, all_333_1_259 yields:
% 19.47/6.24 | (192) app(all_62_0_26, all_0_4_4) = all_333_1_259 & app(all_0_5_5, all_0_4_4) = all_333_0_258 & ( ~ (all_333_0_258 = all_0_6_6) | ~ (all_333_1_259 = all_0_7_7))
% 19.64/6.24 |
% 19.64/6.24 | Applying alpha-rule on (192) yields:
% 19.64/6.24 | (193) app(all_62_0_26, all_0_4_4) = all_333_1_259
% 19.64/6.24 | (194) app(all_0_5_5, all_0_4_4) = all_333_0_258
% 19.64/6.24 | (195) ~ (all_333_0_258 = all_0_6_6) | ~ (all_333_1_259 = all_0_7_7)
% 19.64/6.24 |
% 19.64/6.24 | Instantiating (163) with all_335_0_260, all_335_1_261 yields:
% 19.64/6.24 | (196) app(all_62_0_26, all_0_2_2) = all_335_1_261 & app(all_0_5_5, all_0_2_2) = all_335_0_260 & ( ~ (all_335_0_260 = all_0_6_6) | ~ (all_335_1_261 = all_0_7_7))
% 19.64/6.24 |
% 19.64/6.24 | Applying alpha-rule on (196) yields:
% 19.64/6.24 | (197) app(all_62_0_26, all_0_2_2) = all_335_1_261
% 19.64/6.24 | (198) app(all_0_5_5, all_0_2_2) = all_335_0_260
% 19.64/6.24 | (199) ~ (all_335_0_260 = all_0_6_6) | ~ (all_335_1_261 = all_0_7_7)
% 19.64/6.24 |
% 19.64/6.24 | Instantiating (169) with all_373_0_298, all_373_1_299 yields:
% 19.64/6.24 | (200) app(all_71_0_29, all_0_4_4) = all_373_1_299 & app(all_0_5_5, all_0_4_4) = all_373_0_298 & ( ~ (all_373_0_298 = all_0_6_6) | ~ (all_373_1_299 = all_0_7_7))
% 19.64/6.25 |
% 19.64/6.25 | Applying alpha-rule on (200) yields:
% 19.64/6.25 | (201) app(all_71_0_29, all_0_4_4) = all_373_1_299
% 19.64/6.25 | (202) app(all_0_5_5, all_0_4_4) = all_373_0_298
% 19.64/6.25 | (203) ~ (all_373_0_298 = all_0_6_6) | ~ (all_373_1_299 = all_0_7_7)
% 19.64/6.25 |
% 19.64/6.25 | Instantiating (168) with all_375_0_300, all_375_1_301 yields:
% 19.64/6.25 | (204) app(all_71_0_29, all_0_2_2) = all_375_1_301 & app(all_0_5_5, all_0_2_2) = all_375_0_300 & ( ~ (all_375_0_300 = all_0_6_6) | ~ (all_375_1_301 = all_0_7_7))
% 19.64/6.25 |
% 19.64/6.25 | Applying alpha-rule on (204) yields:
% 19.64/6.25 | (205) app(all_71_0_29, all_0_2_2) = all_375_1_301
% 19.64/6.25 | (206) app(all_0_5_5, all_0_2_2) = all_375_0_300
% 19.64/6.25 | (207) ~ (all_375_0_300 = all_0_6_6) | ~ (all_375_1_301 = all_0_7_7)
% 19.64/6.25 |
% 19.64/6.25 | Instantiating (174) with all_385_0_310, all_385_1_311 yields:
% 19.64/6.25 | (208) app(all_74_0_30, all_0_4_4) = all_385_1_311 & app(all_0_5_5, all_0_4_4) = all_385_0_310 & ( ~ (all_385_0_310 = all_0_6_6) | ~ (all_385_1_311 = all_0_7_7))
% 19.64/6.25 |
% 19.64/6.25 | Applying alpha-rule on (208) yields:
% 19.64/6.25 | (209) app(all_74_0_30, all_0_4_4) = all_385_1_311
% 19.64/6.25 | (210) app(all_0_5_5, all_0_4_4) = all_385_0_310
% 19.64/6.25 | (211) ~ (all_385_0_310 = all_0_6_6) | ~ (all_385_1_311 = all_0_7_7)
% 19.64/6.25 |
% 19.64/6.25 | Instantiating (173) with all_387_0_312, all_387_1_313 yields:
% 19.64/6.25 | (212) app(all_74_0_30, all_0_2_2) = all_387_1_313 & app(all_0_5_5, all_0_2_2) = all_387_0_312 & ( ~ (all_387_0_312 = all_0_6_6) | ~ (all_387_1_313 = all_0_7_7))
% 19.64/6.25 |
% 19.64/6.25 | Applying alpha-rule on (212) yields:
% 19.64/6.25 | (213) app(all_74_0_30, all_0_2_2) = all_387_1_313
% 19.64/6.25 | (214) app(all_0_5_5, all_0_2_2) = all_387_0_312
% 19.64/6.25 | (215) ~ (all_387_0_312 = all_0_6_6) | ~ (all_387_1_313 = all_0_7_7)
% 19.64/6.25 |
% 19.64/6.25 | Instantiating (179) with all_469_0_394, all_469_1_395 yields:
% 19.64/6.25 | (216) app(all_99_0_39, all_0_4_4) = all_469_1_395 & app(all_0_5_5, all_0_4_4) = all_469_0_394 & ( ~ (all_469_0_394 = all_0_6_6) | ~ (all_469_1_395 = all_0_7_7))
% 19.64/6.25 |
% 19.64/6.25 | Applying alpha-rule on (216) yields:
% 19.64/6.25 | (217) app(all_99_0_39, all_0_4_4) = all_469_1_395
% 19.64/6.25 | (218) app(all_0_5_5, all_0_4_4) = all_469_0_394
% 19.64/6.25 | (219) ~ (all_469_0_394 = all_0_6_6) | ~ (all_469_1_395 = all_0_7_7)
% 19.64/6.25 |
% 19.64/6.25 | Instantiating (178) with all_471_0_396, all_471_1_397 yields:
% 19.64/6.25 | (220) app(all_99_0_39, all_0_2_2) = all_471_1_397 & app(all_0_5_5, all_0_2_2) = all_471_0_396 & ( ~ (all_471_0_396 = all_0_6_6) | ~ (all_471_1_397 = all_0_7_7))
% 19.64/6.25 |
% 19.64/6.25 | Applying alpha-rule on (220) yields:
% 19.64/6.25 | (221) app(all_99_0_39, all_0_2_2) = all_471_1_397
% 19.64/6.25 | (222) app(all_0_5_5, all_0_2_2) = all_471_0_396
% 19.64/6.25 | (223) ~ (all_471_0_396 = all_0_6_6) | ~ (all_471_1_397 = all_0_7_7)
% 19.64/6.25 |
% 19.64/6.25 | Instantiating formula (84) with all_0_5_5, all_0_2_2, all_387_0_312, all_471_0_396 and discharging atoms app(all_0_5_5, all_0_2_2) = all_471_0_396, app(all_0_5_5, all_0_2_2) = all_387_0_312, yields:
% 19.64/6.25 | (224) all_471_0_396 = all_387_0_312
% 19.64/6.25 |
% 19.64/6.25 | Instantiating formula (84) with all_0_5_5, all_0_2_2, all_375_0_300, all_0_6_6 and discharging atoms app(all_0_5_5, all_0_2_2) = all_375_0_300, app(all_0_5_5, all_0_2_2) = all_0_6_6, yields:
% 19.64/6.25 | (225) all_375_0_300 = all_0_6_6
% 19.64/6.25 |
% 19.64/6.25 | Instantiating formula (84) with all_0_5_5, all_0_2_2, all_335_0_260, all_471_0_396 and discharging atoms app(all_0_5_5, all_0_2_2) = all_471_0_396, app(all_0_5_5, all_0_2_2) = all_335_0_260, yields:
% 19.64/6.25 | (226) all_471_0_396 = all_335_0_260
% 19.64/6.25 |
% 19.64/6.25 | Instantiating formula (84) with all_0_5_5, all_0_2_2, all_335_0_260, all_375_0_300 and discharging atoms app(all_0_5_5, all_0_2_2) = all_375_0_300, app(all_0_5_5, all_0_2_2) = all_335_0_260, yields:
% 19.64/6.25 | (227) all_375_0_300 = all_335_0_260
% 19.64/6.25 |
% 19.64/6.25 | Instantiating formula (84) with all_0_5_5, all_0_2_2, all_253_0_178, all_471_0_396 and discharging atoms app(all_0_5_5, all_0_2_2) = all_471_0_396, app(all_0_5_5, all_0_2_2) = all_253_0_178, yields:
% 19.64/6.25 | (228) all_471_0_396 = all_253_0_178
% 19.64/6.25 |
% 19.64/6.25 | Instantiating formula (84) with all_0_5_5, all_0_4_4, all_373_0_298, all_385_0_310 and discharging atoms app(all_0_5_5, all_0_4_4) = all_385_0_310, app(all_0_5_5, all_0_4_4) = all_373_0_298, yields:
% 19.64/6.25 | (229) all_385_0_310 = all_373_0_298
% 19.64/6.25 |
% 19.64/6.25 | Instantiating formula (84) with all_0_5_5, all_0_4_4, all_333_0_258, all_0_3_3 and discharging atoms app(all_0_5_5, all_0_4_4) = all_333_0_258, app(all_0_5_5, all_0_4_4) = all_0_3_3, yields:
% 19.64/6.25 | (230) all_333_0_258 = all_0_3_3
% 19.64/6.25 |
% 19.64/6.25 | Instantiating formula (84) with all_0_5_5, all_0_4_4, all_333_0_258, all_385_0_310 and discharging atoms app(all_0_5_5, all_0_4_4) = all_385_0_310, app(all_0_5_5, all_0_4_4) = all_333_0_258, yields:
% 19.64/6.25 | (231) all_385_0_310 = all_333_0_258
% 19.64/6.25 |
% 19.64/6.25 | Instantiating formula (84) with all_0_5_5, all_0_4_4, all_251_0_176, all_469_0_394 and discharging atoms app(all_0_5_5, all_0_4_4) = all_469_0_394, app(all_0_5_5, all_0_4_4) = all_251_0_176, yields:
% 19.64/6.25 | (232) all_469_0_394 = all_251_0_176
% 19.64/6.25 |
% 19.64/6.25 | Instantiating formula (84) with all_0_5_5, all_0_4_4, all_251_0_176, all_333_0_258 and discharging atoms app(all_0_5_5, all_0_4_4) = all_333_0_258, app(all_0_5_5, all_0_4_4) = all_251_0_176, yields:
% 19.67/6.25 | (233) all_333_0_258 = all_251_0_176
% 19.67/6.25 |
% 19.67/6.25 | Instantiating formula (84) with all_0_5_5, all_0_4_4, all_193_0_118, all_385_0_310 and discharging atoms app(all_0_5_5, all_0_4_4) = all_385_0_310, app(all_0_5_5, all_0_4_4) = all_193_0_118, yields:
% 19.67/6.25 | (234) all_385_0_310 = all_193_0_118
% 19.67/6.25 |
% 19.67/6.25 | Instantiating formula (84) with all_0_5_5, all_0_4_4, all_74_0_30, all_469_0_394 and discharging atoms app(all_0_5_5, all_0_4_4) = all_469_0_394, app(all_0_5_5, all_0_4_4) = all_74_0_30, yields:
% 19.67/6.25 | (235) all_469_0_394 = all_74_0_30
% 19.67/6.25 |
% 19.67/6.25 | Combining equations (226,224) yields a new equation:
% 19.67/6.25 | (236) all_387_0_312 = all_335_0_260
% 19.67/6.25 |
% 19.67/6.25 | Combining equations (228,224) yields a new equation:
% 19.67/6.25 | (237) all_387_0_312 = all_253_0_178
% 19.67/6.25 |
% 19.67/6.25 | Combining equations (232,235) yields a new equation:
% 19.67/6.25 | (238) all_251_0_176 = all_74_0_30
% 19.67/6.25 |
% 19.67/6.25 | Simplifying 238 yields:
% 19.67/6.25 | (239) all_251_0_176 = all_74_0_30
% 19.67/6.25 |
% 19.67/6.25 | Combining equations (236,237) yields a new equation:
% 19.67/6.25 | (240) all_335_0_260 = all_253_0_178
% 19.67/6.25 |
% 19.67/6.25 | Simplifying 240 yields:
% 19.67/6.25 | (241) all_335_0_260 = all_253_0_178
% 19.67/6.25 |
% 19.67/6.25 | Combining equations (231,229) yields a new equation:
% 19.67/6.25 | (242) all_373_0_298 = all_333_0_258
% 19.67/6.25 |
% 19.67/6.25 | Combining equations (234,229) yields a new equation:
% 19.67/6.25 | (243) all_373_0_298 = all_193_0_118
% 19.67/6.25 |
% 19.67/6.25 | Combining equations (227,225) yields a new equation:
% 19.67/6.25 | (244) all_335_0_260 = all_0_6_6
% 19.67/6.25 |
% 19.67/6.25 | Simplifying 244 yields:
% 19.67/6.25 | (245) all_335_0_260 = all_0_6_6
% 19.67/6.25 |
% 19.67/6.25 | Combining equations (242,243) yields a new equation:
% 19.67/6.25 | (246) all_333_0_258 = all_193_0_118
% 19.67/6.25 |
% 19.67/6.25 | Simplifying 246 yields:
% 19.67/6.25 | (247) all_333_0_258 = all_193_0_118
% 19.67/6.25 |
% 19.67/6.25 | Combining equations (245,241) yields a new equation:
% 19.67/6.25 | (248) all_253_0_178 = all_0_6_6
% 19.67/6.25 |
% 19.67/6.25 | Combining equations (230,247) yields a new equation:
% 19.67/6.25 | (249) all_193_0_118 = all_0_3_3
% 19.67/6.25 |
% 19.67/6.25 | Combining equations (233,247) yields a new equation:
% 19.67/6.25 | (250) all_251_0_176 = all_193_0_118
% 19.67/6.25 |
% 19.67/6.25 | Simplifying 250 yields:
% 19.67/6.25 | (251) all_251_0_176 = all_193_0_118
% 19.67/6.25 |
% 19.67/6.25 | Combining equations (251,239) yields a new equation:
% 19.67/6.25 | (252) all_193_0_118 = all_74_0_30
% 19.67/6.25 |
% 19.67/6.25 | Simplifying 252 yields:
% 19.67/6.25 | (253) all_193_0_118 = all_74_0_30
% 19.67/6.25 |
% 19.67/6.25 | Combining equations (249,253) yields a new equation:
% 19.67/6.25 | (254) all_74_0_30 = all_0_3_3
% 19.67/6.25 |
% 19.67/6.25 | Combining equations (248,237) yields a new equation:
% 19.67/6.25 | (255) all_387_0_312 = all_0_6_6
% 19.67/6.25 |
% 19.67/6.25 | From (254) and (213) follows:
% 19.67/6.25 | (256) app(all_0_3_3, all_0_2_2) = all_387_1_313
% 19.67/6.25 |
% 19.67/6.25 +-Applying beta-rule and splitting (215), into two cases.
% 19.67/6.25 |-Branch one:
% 19.67/6.25 | (257) ~ (all_387_0_312 = all_0_6_6)
% 19.67/6.25 |
% 19.67/6.25 | Equations (255) can reduce 257 to:
% 19.67/6.25 | (258) $false
% 19.67/6.25 |
% 19.67/6.25 |-The branch is then unsatisfiable
% 19.67/6.25 |-Branch two:
% 19.67/6.25 | (255) all_387_0_312 = all_0_6_6
% 19.67/6.25 | (260) ~ (all_387_1_313 = all_0_7_7)
% 19.67/6.25 |
% 19.67/6.25 | Instantiating formula (84) with all_0_3_3, all_0_2_2, all_387_1_313, all_0_7_7 and discharging atoms app(all_0_3_3, all_0_2_2) = all_387_1_313, app(all_0_3_3, all_0_2_2) = all_0_7_7, yields:
% 19.67/6.26 | (261) all_387_1_313 = all_0_7_7
% 19.67/6.26 |
% 19.67/6.26 | Equations (261) can reduce 260 to:
% 19.67/6.26 | (258) $false
% 19.67/6.26 |
% 19.67/6.26 |-The branch is then unsatisfiable
% 19.67/6.26 % SZS output end Proof for theBenchmark
% 19.67/6.26
% 19.67/6.26 5665ms
%------------------------------------------------------------------------------