%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWC380+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n021.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 20:17:49 EDT 2022 % Result : Theorem 8.21s 2.43s % Output : Proof 15.06s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWC380+1 : TPTP v8.1.0. Released v2.4.0. % 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n021.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 23:26:10 EDT 2022 % 0.12/0.33 % CPUTime : % 0.58/0.58 ____ _ % 0.58/0.58 ___ / __ \_____(_)___ ________ __________ % 0.58/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.58/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.58/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.58/0.58 % 0.58/0.58 A Theorem Prover for First-Order Logic % 0.58/0.58 (ePrincess v.1.0) % 0.58/0.58 % 0.58/0.58 (c) Philipp Rümmer, 2009-2015 % 0.58/0.58 (c) Peter Backeman, 2014-2015 % 0.58/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.58/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.58/0.58 Bug reports to peter@backeman.se % 0.58/0.58 % 0.58/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.58/0.58 % 0.58/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.58/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.07/1.02 Prover 0: Preprocessing ... % 4.68/1.59 Prover 0: Constructing countermodel ... % 8.21/2.43 Prover 0: proved (1798ms) % 8.21/2.43 % 8.21/2.43 No countermodel exists, formula is valid % 8.21/2.43 % SZS status Theorem for theBenchmark % 8.21/2.43 % 8.21/2.43 Generating proof ... found it (size 96) % 14.34/3.89 % 14.34/3.89 % SZS output start Proof for theBenchmark % 14.34/3.89 Assumed formulas after preprocessing and simplification: % 14.34/3.89 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ( ~ (v5 = v4) & cons(v2, nil) = v0 & app(v0, v3) = v1 & equalelemsP(nil) & duplicatefreeP(nil) & strictorderedP(nil) & totalorderedP(nil) & strictorderP(nil) & totalorderP(nil) & cyclefreeP(nil) & segmentP(nil, nil) & rearsegP(nil, nil) & frontsegP(nil, nil) & ssList(v3) & ssList(v1) & ssList(v0) & ssList(nil) & neq(v1, nil) & ssItem(v5) & ssItem(v4) & ssItem(v2) & ~ singletonP(nil) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cons(v8, v13) = v14) | ~ (cons(v7, v10) = v11) | ~ (app(v12, v14) = v6) | ~ (app(v9, v11) = v12) | ~ strictorderedP(v6) | ~ ssList(v13) | ~ ssList(v10) | ~ ssList(v9) | ~ ssList(v6) | ~ ssItem(v8) | ~ ssItem(v7) | lt(v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cons(v8, v13) = v14) | ~ (cons(v7, v10) = v11) | ~ (app(v12, v14) = v6) | ~ (app(v9, v11) = v12) | ~ totalorderedP(v6) | ~ ssList(v13) | ~ ssList(v10) | ~ ssList(v9) | ~ ssList(v6) | ~ ssItem(v8) | ~ ssItem(v7) | leq(v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cons(v8, v13) = v14) | ~ (cons(v7, v10) = v11) | ~ (app(v12, v14) = v6) | ~ (app(v9, v11) = v12) | ~ strictorderP(v6) | ~ ssList(v13) | ~ ssList(v10) | ~ ssList(v9) | ~ ssList(v6) | ~ ssItem(v8) | ~ ssItem(v7) | lt(v8, v7) | lt(v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cons(v8, v13) = v14) | ~ (cons(v7, v10) = v11) | ~ (app(v12, v14) = v6) | ~ (app(v9, v11) = v12) | ~ totalorderP(v6) | ~ ssList(v13) | ~ ssList(v10) | ~ ssList(v9) | ~ ssList(v6) | ~ ssItem(v8) | ~ ssItem(v7) | leq(v8, v7) | leq(v7, v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cons(v8, v13) = v14) | ~ (cons(v7, v10) = v11) | ~ (app(v12, v14) = v6) | ~ (app(v9, v11) = v12) | ~ leq(v8, v7) | ~ leq(v7, v8) | ~ cyclefreeP(v6) | ~ ssList(v13) | ~ ssList(v10) | ~ ssList(v9) | ~ ssList(v6) | ~ ssItem(v8) | ~ ssItem(v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cons(v7, v12) = v13) | ~ (cons(v7, v9) = v10) | ~ (app(v11, v13) = v6) | ~ (app(v8, v10) = v11) | ~ duplicatefreeP(v6) | ~ ssList(v12) | ~ ssList(v9) | ~ ssList(v8) | ~ ssList(v6) | ~ ssItem(v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v8 = v7 | ~ (cons(v8, v10) = v11) | ~ (cons(v7, v11) = v12) | ~ (app(v9, v12) = v6) | ~ equalelemsP(v6) | ~ ssList(v10) | ~ ssList(v9) | ~ ssList(v6) | ~ ssItem(v8) | ~ ssItem(v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = v6 | ~ (cons(v7, v10) = v11) | ~ (cons(v6, v8) = v9) | ~ frontsegP(v9, v11) | ~ ssList(v10) | ~ ssList(v8) | ~ ssItem(v7) | ~ ssItem(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (cons(v9, v7) = v10) | ~ (app(v10, v6) = v11) | ~ (app(v7, v6) = v8) | ~ ssList(v7) | ~ ssList(v6) | ~ ssItem(v9) | cons(v9, v8) = v11) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (cons(v7, v10) = v11) | ~ (cons(v6, v8) = v9) | ~ frontsegP(v9, v11) | ~ ssList(v10) | ~ ssList(v8) | ~ ssItem(v7) | ~ ssItem(v6) | frontsegP(v8, v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (app(v9, v10) = v11) | ~ (app(v8, v6) = v9) | ~ segmentP(v6, v7) | ~ ssList(v10) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v6) | segmentP(v11, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (app(v7, v9) = v10) | ~ (app(v6, v10) = v11) | ~ (app(v6, v7) = v8) | ~ ssList(v9) | ~ ssList(v7) | ~ ssList(v6) | app(v8, v9) = v11) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v8 | ~ (cons(v10, v7) = v9) | ~ (cons(v8, v6) = v9) | ~ ssList(v7) | ~ ssList(v6) | ~ ssItem(v10) | ~ ssItem(v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = v6 | ~ (cons(v10, v7) = v9) | ~ (cons(v8, v6) = v9) | ~ ssList(v7) | ~ ssList(v6) | ~ ssItem(v10) | ~ ssItem(v8)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (cons(v9, v8) = v10) | ~ (app(v7, v6) = v8) | ~ ssList(v7) | ~ ssList(v6) | ~ ssItem(v9) | ? [v11] : (cons(v9, v7) = v11 & app(v11, v6) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (cons(v7, v9) = v10) | ~ (app(v8, v10) = v6) | ~ ssList(v9) | ~ ssList(v8) | ~ ssList(v6) | ~ ssItem(v7) | memberP(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (cons(v6, v9) = v10) | ~ (cons(v6, v7) = v8) | ~ frontsegP(v7, v9) | ~ ssList(v9) | ~ ssList(v7) | ~ ssItem(v6) | frontsegP(v8, v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (app(v9, v10) = v6) | ~ (app(v8, v7) = v9) | ~ ssList(v10) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v6) | segmentP(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (app(v8, v9) = v10) | ~ (app(v6, v7) = v8) | ~ ssList(v9) | ~ ssList(v7) | ~ ssList(v6) | ? [v11] : (app(v7, v9) = v11 & app(v6, v11) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v6 | v6 = nil | ~ (tl(v6) = v8) | ~ (hd(v6) = v7) | ~ (cons(v7, v8) = v9) | ~ ssList(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v6 | ~ (app(v9, v7) = v8) | ~ (app(v6, v7) = v8) | ~ ssList(v9) | ~ ssList(v7) | ~ ssList(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v6 | ~ (app(v7, v9) = v8) | ~ (app(v7, v6) = v8) | ~ ssList(v9) | ~ ssList(v7) | ~ ssList(v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (cons(v9, v8) = v7) | ~ (cons(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (cons(v7, v8) = v9) | ~ memberP(v9, v6) | ~ ssList(v8) | ~ ssItem(v7) | ~ ssItem(v6) | memberP(v8, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v7 = v6 | ~ (app(v9, v8) = v7) | ~ (app(v9, v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = nil | ~ (tl(v6) = v7) | ~ (app(v7, v8) = v9) | ~ ssList(v8) | ~ ssList(v6) | ? [v10] : (tl(v10) = v9 & app(v6, v8) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = nil | ~ (tl(v6) = v7) | ~ (app(v6, v8) = v9) | ~ ssList(v8) | ~ ssList(v6) | ? [v10] : (tl(v9) = v10 & app(v7, v8) = v10)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = nil | ~ (hd(v6) = v7) | ~ (app(v6, v8) = v9) | ~ ssList(v8) | ~ ssList(v6) | hd(v9) = v7) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (cons(v7, v8) = v9) | ~ memberP(v8, v6) | ~ ssList(v8) | ~ ssItem(v7) | ~ ssItem(v6) | memberP(v9, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (cons(v7, nil) = v8) | ~ (app(v8, v6) = v9) | ~ ssList(v6) | ~ ssItem(v7) | cons(v7, v6) = v9) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (app(v8, v6) = v9) | ~ rearsegP(v6, v7) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v6) | rearsegP(v9, v7)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (app(v7, v8) = v9) | ~ memberP(v9, v6) | ~ ssList(v8) | ~ ssList(v7) | ~ ssItem(v6) | memberP(v8, v6) | memberP(v7, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (app(v7, v8) = v9) | ~ memberP(v8, v6) | ~ ssList(v8) | ~ ssList(v7) | ~ ssItem(v6) | memberP(v9, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (app(v7, v8) = v9) | ~ memberP(v7, v6) | ~ ssList(v8) | ~ ssList(v7) | ~ ssItem(v6) | memberP(v9, v6)) & ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (app(v6, v8) = v9) | ~ frontsegP(v6, v7) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v6) | frontsegP(v9, v7)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (tl(v8) = v7) | ~ (tl(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : (v7 = v6 | ~ (hd(v8) = v7) | ~ (hd(v8) = v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (hd(v7) = v8) | ~ ssList(v7) | ~ ssItem(v6) | ? [v9] : (cons(v6, v7) = v9 & (v7 = nil | ~ strictorderedP(v9) | (strictorderedP(v7) & lt(v6, v8))) & (strictorderedP(v9) | ( ~ (v7 = nil) & ( ~ strictorderedP(v7) | ~ lt(v6, v8)))))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (hd(v7) = v8) | ~ ssList(v7) | ~ ssItem(v6) | ? [v9] : (cons(v6, v7) = v9 & (v7 = nil | ~ totalorderedP(v9) | (totalorderedP(v7) & leq(v6, v8))) & (totalorderedP(v9) | ( ~ (v7 = nil) & ( ~ totalorderedP(v7) | ~ leq(v6, v8)))))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v7, v6) = v8) | ~ ssList(v6) | ~ ssItem(v7) | tl(v8) = v6) & ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v7, v6) = v8) | ~ ssList(v6) | ~ ssItem(v7) | hd(v8) = v7) & ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v7, v6) = v8) | ~ ssList(v6) | ~ ssItem(v7) | ssList(v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v7, v6) = v8) | ~ ssList(v6) | ~ ssItem(v7) | ? [v9] : (cons(v7, nil) = v9 & app(v9, v6) = v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v6, v7) = v8) | ~ ssList(v7) | ~ ssItem(v6) | memberP(v8, v6)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v6, v7) = v8) | ~ ssList(v7) | ~ ssItem(v6) | ? [v9] : (hd(v7) = v9 & (v7 = nil | ~ strictorderedP(v8) | (strictorderedP(v7) & lt(v6, v9))) & (strictorderedP(v8) | ( ~ (v7 = nil) & ( ~ strictorderedP(v7) | ~ lt(v6, v9)))))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v6, v7) = v8) | ~ ssList(v7) | ~ ssItem(v6) | ? [v9] : (hd(v7) = v9 & (v7 = nil | ~ totalorderedP(v8) | (totalorderedP(v7) & leq(v6, v9))) & (totalorderedP(v8) | ( ~ (v7 = nil) & ( ~ totalorderedP(v7) | ~ leq(v6, v9)))))) & ! [v6] : ! [v7] : ! [v8] : ( ~ (app(v8, v7) = v6) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v6) | rearsegP(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (app(v7, v8) = v6) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v6) | frontsegP(v6, v7)) & ! [v6] : ! [v7] : ! [v8] : ( ~ (app(v6, v7) = v8) | ~ ssList(v7) | ~ ssList(v6) | ssList(v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ gt(v7, v8) | ~ gt(v6, v7) | ~ ssItem(v8) | ~ ssItem(v7) | ~ ssItem(v6) | gt(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ geq(v7, v8) | ~ geq(v6, v7) | ~ ssItem(v8) | ~ ssItem(v7) | ~ ssItem(v6) | geq(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ lt(v7, v8) | ~ lt(v6, v7) | ~ ssItem(v8) | ~ ssItem(v7) | ~ ssItem(v6) | lt(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ lt(v7, v8) | ~ leq(v6, v7) | ~ ssItem(v8) | ~ ssItem(v7) | ~ ssItem(v6) | lt(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ leq(v7, v8) | ~ leq(v6, v7) | ~ ssItem(v8) | ~ ssItem(v7) | ~ ssItem(v6) | leq(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ segmentP(v7, v8) | ~ segmentP(v6, v7) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v6) | segmentP(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ rearsegP(v7, v8) | ~ rearsegP(v6, v7) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v6) | rearsegP(v6, v8)) & ! [v6] : ! [v7] : ! [v8] : ( ~ frontsegP(v7, v8) | ~ frontsegP(v6, v7) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v6) | frontsegP(v6, v8)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (app(v6, nil) = v7) | ~ ssList(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ (app(nil, v6) = v7) | ~ ssList(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ geq(v7, v6) | ~ geq(v6, v7) | ~ ssItem(v7) | ~ ssItem(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ leq(v7, v6) | ~ leq(v6, v7) | ~ ssItem(v7) | ~ ssItem(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ leq(v6, v7) | ~ ssItem(v7) | ~ ssItem(v6) | lt(v6, v7)) & ! [v6] : ! [v7] : (v7 = v6 | ~ segmentP(v7, v6) | ~ segmentP(v6, v7) | ~ ssList(v7) | ~ ssList(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ rearsegP(v7, v6) | ~ rearsegP(v6, v7) | ~ ssList(v7) | ~ ssList(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ frontsegP(v7, v6) | ~ frontsegP(v6, v7) | ~ ssList(v7) | ~ ssList(v6)) & ! [v6] : ! [v7] : (v7 = v6 | ~ ssList(v7) | ~ ssList(v6) | neq(v6, v7)) & ! [v6] : ! [v7] : (v7 = v6 | ~ ssItem(v7) | ~ ssItem(v6) | neq(v6, v7)) & ! [v6] : ! [v7] : (v7 = nil | ~ (app(v6, v7) = nil) | ~ ssList(v7) | ~ ssList(v6)) & ! [v6] : ! [v7] : (v6 = nil | ~ (tl(v6) = v7) | ~ ssList(v6) | ssList(v7)) & ! [v6] : ! [v7] : (v6 = nil | ~ (hd(v6) = v7) | ~ ssList(v6) | ssItem(v7)) & ! [v6] : ! [v7] : (v6 = nil | ~ (app(v6, v7) = nil) | ~ ssList(v7) | ~ ssList(v6)) & ! [v6] : ! [v7] : ( ~ (tl(v6) = v7) | ~ ssList(v6) | ? [v8] : (hd(v6) = v8 & ! [v9] : (v9 = v6 | v9 = nil | v6 = nil | ~ (tl(v9) = v7) | ~ ssList(v9) | ? [v10] : ( ~ (v10 = v8) & hd(v9) = v10)) & ! [v9] : (v9 = v6 | v9 = nil | v6 = nil | ~ (hd(v9) = v8) | ~ ssList(v9) | ? [v10] : ( ~ (v10 = v7) & tl(v9) = v10)))) & ! [v6] : ! [v7] : ( ~ (hd(v6) = v7) | ~ ssList(v6) | ? [v8] : (tl(v6) = v8 & ! [v9] : (v9 = v6 | v9 = nil | v6 = nil | ~ (tl(v9) = v8) | ~ ssList(v9) | ? [v10] : ( ~ (v10 = v7) & hd(v9) = v10)) & ! [v9] : (v9 = v6 | v9 = nil | v6 = nil | ~ (hd(v9) = v7) | ~ ssList(v9) | ? [v10] : ( ~ (v10 = v8) & tl(v9) = v10)))) & ! [v6] : ! [v7] : ( ~ (cons(v7, v6) = v6) | ~ ssList(v6) | ~ ssItem(v7)) & ! [v6] : ! [v7] : ( ~ (cons(v7, v6) = nil) | ~ ssList(v6) | ~ ssItem(v7)) & ! [v6] : ! [v7] : ( ~ (cons(v7, nil) = v6) | ~ ssList(v6) | ~ ssItem(v7) | singletonP(v6)) & ! [v6] : ! [v7] : ( ~ (cons(v6, nil) = v7) | ~ ssItem(v6) | equalelemsP(v7)) & ! [v6] : ! [v7] : ( ~ (cons(v6, nil) = v7) | ~ ssItem(v6) | duplicatefreeP(v7)) & ! [v6] : ! [v7] : ( ~ (cons(v6, nil) = v7) | ~ ssItem(v6) | strictorderedP(v7)) & ! [v6] : ! [v7] : ( ~ (cons(v6, nil) = v7) | ~ ssItem(v6) | totalorderedP(v7)) & ! [v6] : ! [v7] : ( ~ (cons(v6, nil) = v7) | ~ ssItem(v6) | strictorderP(v7)) & ! [v6] : ! [v7] : ( ~ (cons(v6, nil) = v7) | ~ ssItem(v6) | totalorderP(v7)) & ! [v6] : ! [v7] : ( ~ (cons(v6, nil) = v7) | ~ ssItem(v6) | cyclefreeP(v7)) & ! [v6] : ! [v7] : ( ~ gt(v7, v6) | ~ gt(v6, v7) | ~ ssItem(v7) | ~ ssItem(v6)) & ! [v6] : ! [v7] : ( ~ gt(v6, v7) | ~ ssItem(v7) | ~ ssItem(v6) | lt(v7, v6)) & ! [v6] : ! [v7] : ( ~ geq(v6, v7) | ~ ssItem(v7) | ~ ssItem(v6) | leq(v7, v6)) & ! [v6] : ! [v7] : ( ~ lt(v7, v6) | ~ lt(v6, v7) | ~ ssItem(v7) | ~ ssItem(v6)) & ! [v6] : ! [v7] : ( ~ lt(v7, v6) | ~ ssItem(v7) | ~ ssItem(v6) | gt(v6, v7)) & ! [v6] : ! [v7] : ( ~ lt(v6, v7) | ~ ssItem(v7) | ~ ssItem(v6) | leq(v6, v7)) & ! [v6] : ! [v7] : ( ~ leq(v7, v6) | ~ ssItem(v7) | ~ ssItem(v6) | geq(v6, v7)) & ! [v6] : ! [v7] : ( ~ segmentP(v6, v7) | ~ ssList(v7) | ~ ssList(v6) | ? [v8] : ? [v9] : ? [v10] : (app(v9, v10) = v6 & app(v8, v7) = v9 & ssList(v10) & ssList(v8))) & ! [v6] : ! [v7] : ( ~ rearsegP(v6, v7) | ~ ssList(v7) | ~ ssList(v6) | ? [v8] : (app(v8, v7) = v6 & ssList(v8))) & ! [v6] : ! [v7] : ( ~ frontsegP(v6, v7) | ~ ssList(v7) | ~ ssList(v6) | ? [v8] : (app(v7, v8) = v6 & ssList(v8))) & ! [v6] : ! [v7] : ( ~ memberP(v6, v7) | ~ ssList(v6) | ~ ssItem(v7) | ? [v8] : ? [v9] : ? [v10] : (cons(v7, v9) = v10 & app(v8, v10) = v6 & ssList(v9) & ssList(v8))) & ! [v6] : (v6 = nil | ~ (app(nil, nil) = v6)) & ! [v6] : (v6 = nil | ~ segmentP(nil, v6) | ~ ssList(v6)) & ! [v6] : (v6 = nil | ~ rearsegP(nil, v6) | ~ ssList(v6)) & ! [v6] : (v6 = nil | ~ frontsegP(nil, v6) | ~ ssList(v6)) & ! [v6] : (v6 = nil | ~ ssList(v6) | ? [v7] : ? [v8] : (cons(v8, v7) = v6 & ssList(v7) & ssItem(v8))) & ! [v6] : ( ~ lt(v6, v6) | ~ ssItem(v6)) & ! [v6] : ( ~ singletonP(v6) | ~ ssList(v6) | ? [v7] : (cons(v7, nil) = v6 & ssItem(v7))) & ! [v6] : ( ~ memberP(v1, v6) | ~ ssItem(v6) | ? [v7] : ( ~ (v7 = v0) & cons(v6, nil) = v7)) & ! [v6] : ( ~ memberP(nil, v6) | ~ ssItem(v6)) & ! [v6] : ( ~ ssList(v6) | ~ neq(v6, v6)) & ! [v6] : ( ~ ssList(v6) | equalelemsP(v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ( ~ (v8 = v7) & cons(v8, v10) = v11 & cons(v7, v11) = v12 & app(v9, v12) = v6 & ssList(v10) & ssList(v9) & ssItem(v8) & ssItem(v7))) & ! [v6] : ( ~ ssList(v6) | duplicatefreeP(v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (cons(v7, v12) = v13 & cons(v7, v9) = v10 & app(v11, v13) = v6 & app(v8, v10) = v11 & ssList(v12) & ssList(v9) & ssList(v8) & ssItem(v7))) & ! [v6] : ( ~ ssList(v6) | strictorderedP(v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (cons(v8, v13) = v14 & cons(v7, v10) = v11 & app(v12, v14) = v6 & app(v9, v11) = v12 & ssList(v13) & ssList(v10) & ssList(v9) & ssItem(v8) & ssItem(v7) & ~ lt(v7, v8))) & ! [v6] : ( ~ ssList(v6) | totalorderedP(v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (cons(v8, v13) = v14 & cons(v7, v10) = v11 & app(v12, v14) = v6 & app(v9, v11) = v12 & ssList(v13) & ssList(v10) & ssList(v9) & ssItem(v8) & ssItem(v7) & ~ leq(v7, v8))) & ! [v6] : ( ~ ssList(v6) | strictorderP(v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (cons(v8, v13) = v14 & cons(v7, v10) = v11 & app(v12, v14) = v6 & app(v9, v11) = v12 & ssList(v13) & ssList(v10) & ssList(v9) & ssItem(v8) & ssItem(v7) & ~ lt(v8, v7) & ~ lt(v7, v8))) & ! [v6] : ( ~ ssList(v6) | totalorderP(v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (cons(v8, v13) = v14 & cons(v7, v10) = v11 & app(v12, v14) = v6 & app(v9, v11) = v12 & ssList(v13) & ssList(v10) & ssList(v9) & ssItem(v8) & ssItem(v7) & ~ leq(v8, v7) & ~ leq(v7, v8))) & ! [v6] : ( ~ ssList(v6) | cyclefreeP(v6) | ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : (cons(v8, v13) = v14 & cons(v7, v10) = v11 & app(v12, v14) = v6 & app(v9, v11) = v12 & leq(v8, v7) & leq(v7, v8) & ssList(v13) & ssList(v10) & ssList(v9) & ssItem(v8) & ssItem(v7))) & ! [v6] : ( ~ ssList(v6) | segmentP(v6, v6)) & ! [v6] : ( ~ ssList(v6) | segmentP(v6, nil)) & ! [v6] : ( ~ ssList(v6) | rearsegP(v6, v6)) & ! [v6] : ( ~ ssList(v6) | rearsegP(v6, nil)) & ! [v6] : ( ~ ssList(v6) | frontsegP(v6, v6)) & ! [v6] : ( ~ ssList(v6) | frontsegP(v6, nil)) & ! [v6] : ( ~ neq(v6, v6) | ~ ssItem(v6)) & ! [v6] : ( ~ ssItem(v6) | geq(v6, v6)) & ! [v6] : ( ~ ssItem(v6) | leq(v6, v6))) % 14.75/3.97 | 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 yields: % 14.75/3.97 | (1) ~ (all_0_0_0 = all_0_1_1) & cons(all_0_3_3, nil) = all_0_5_5 & app(all_0_5_5, all_0_2_2) = all_0_4_4 & 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(nil) & neq(all_0_4_4, nil) & ssItem(all_0_0_0) & ssItem(all_0_1_1) & ssItem(all_0_3_3) & ~ 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] : (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(all_0_4_4, v0) | ~ ssItem(v0) | ? [v1] : ( ~ (v1 = all_0_5_5) & cons(v0, nil) = 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)) % 14.75/4.00 | % 14.75/4.00 | Applying alpha-rule on (1) yields: % 14.75/4.00 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2)) % 14.75/4.00 | (3) ssList(all_0_5_5) % 14.75/4.00 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ frontsegP(v1, v2) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v2)) % 14.75/4.00 | (5) segmentP(nil, nil) % 14.75/4.00 | (6) ! [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)))))) % 14.75/4.00 | (7) ! [v0] : ( ~ memberP(all_0_4_4, v0) | ~ ssItem(v0) | ? [v1] : ( ~ (v1 = all_0_5_5) & cons(v0, nil) = v1)) % 14.75/4.00 | (8) ! [v0] : ( ~ ssList(v0) | ~ neq(v0, v0)) % 14.75/4.00 | (9) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 14.75/4.00 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v1)) % 14.75/4.00 | (11) ! [v0] : ( ~ neq(v0, v0) | ~ ssItem(v0)) % 14.75/4.00 | (12) ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = v0) | ~ ssList(v0) | ~ ssItem(v1)) % 14.75/4.00 | (13) ssList(all_0_2_2) % 14.75/4.00 | (14) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2)) % 14.75/4.00 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | tl(v2) = v0) % 14.75/4.00 | (16) ! [v0] : (v0 = nil | ~ frontsegP(nil, v0) | ~ ssList(v0)) % 14.75/4.00 | (17) ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0)) % 14.75/4.00 | (18) ! [v0] : ! [v1] : ( ~ gt(v1, v0) | ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 14.75/4.00 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v2, v0) = v3) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1)) % 14.75/4.00 | (20) ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = nil) | ~ ssList(v0) | ~ ssItem(v1)) % 14.75/4.00 | (21) ! [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)) % 14.75/4.00 | (22) ssList(nil) % 14.75/4.00 | (23) frontsegP(nil, nil) % 14.75/4.00 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 14.75/4.00 | (25) ! [v0] : (v0 = nil | ~ rearsegP(nil, v0) | ~ ssList(v0)) % 14.75/4.00 | (26) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2)) % 14.75/4.00 | (27) ! [v0] : (v0 = nil | ~ segmentP(nil, v0) | ~ ssList(v0)) % 14.75/4.00 | (28) ! [v0] : ! [v1] : (v1 = v0 | ~ rearsegP(v1, v0) | ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) % 14.75/4.00 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2)) % 14.75/4.00 | (30) ! [v0] : ! [v1] : ( ~ leq(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v1)) % 14.75/4.00 | (31) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) % 14.75/4.00 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ ssList(v0)) % 14.75/4.00 | (33) ! [v0] : ( ~ ssItem(v0) | geq(v0, v0)) % 14.75/4.00 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ segmentP(v1, v2) | ~ segmentP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v2)) % 14.75/4.00 | (35) ! [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)) % 14.75/4.00 | (36) ! [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)) % 14.75/4.00 | (37) cyclefreeP(nil) % 14.75/4.00 | (38) duplicatefreeP(nil) % 14.75/4.00 | (39) rearsegP(nil, nil) % 14.75/4.00 | (40) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v0, v1) = v2) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2)) % 14.75/4.01 | (41) ! [v0] : ! [v1] : ( ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : ? [v3] : ? [v4] : (app(v3, v4) = v0 & app(v2, v1) = v3 & ssList(v4) & ssList(v2))) % 14.75/4.01 | (42) ! [v0] : ! [v1] : ( ~ memberP(v0, v1) | ~ ssList(v0) | ~ ssItem(v1) | ? [v2] : ? [v3] : ? [v4] : (cons(v1, v3) = v4 & app(v2, v4) = v0 & ssList(v3) & ssList(v2))) % 14.75/4.01 | (43) ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v1)) % 14.75/4.01 | (44) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderP(v1)) % 14.75/4.01 | (45) ! [v0] : ( ~ memberP(nil, v0) | ~ ssItem(v0)) % 14.75/4.01 | (46) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ~ ssList(v0) | ssItem(v1)) % 14.75/4.01 | (47) ssList(all_0_4_4) % 14.75/4.01 | (48) ! [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)) % 14.75/4.01 | (49) ! [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)) % 14.75/4.01 | (50) ! [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)) % 14.75/4.01 | (51) ! [v0] : ( ~ ssList(v0) | frontsegP(v0, v0)) % 14.75/4.01 | (52) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v2, v1) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v1)) % 14.75/4.01 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ~ ssList(v0)) % 14.75/4.01 | (54) app(all_0_5_5, all_0_2_2) = all_0_4_4 % 14.75/4.01 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v0, v2) = v3) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v3, v1)) % 14.75/4.01 | (56) ! [v0] : ! [v1] : ( ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v1, v0)) % 14.75/4.01 | (57) ! [v0] : ! [v1] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0)) % 14.75/4.01 | (58) ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v1, v0) | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 14.75/4.01 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v2, v0)) % 14.75/4.01 | (60) ! [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)) % 14.75/4.01 | (61) ! [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)) % 14.75/4.01 | (62) totalorderedP(nil) % 14.75/4.01 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ gt(v1, v2) | ~ gt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v2)) % 14.75/4.01 | (64) strictorderedP(nil) % 14.75/4.01 | (65) ! [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)) % 14.75/4.01 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v1, v3) = v4) | ~ (app(v2, v4) = v0) | ~ ssList(v3) | ~ ssList(v2) | ~ ssList(v0) | ~ ssItem(v1) | memberP(v0, v1)) % 14.75/4.01 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) % 14.75/4.01 | (68) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ~ ssList(v0) | ssList(v1)) % 14.75/4.01 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) % 14.75/4.01 | (70) ! [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))) % 14.75/4.01 | (71) ! [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))) % 14.75/4.02 | (72) ! [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)))) % 14.75/4.02 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v3, v0)) % 14.75/4.02 | (74) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderedP(v1)) % 14.75/4.02 | (75) ! [v0] : ! [v1] : (v1 = v0 | ~ segmentP(v1, v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) % 14.75/4.02 | (76) equalelemsP(nil) % 14.75/4.02 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | hd(v2) = v1) % 14.75/4.02 | (78) ! [v0] : ( ~ ssList(v0) | segmentP(v0, v0)) % 14.75/4.02 | (79) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | duplicatefreeP(v1)) % 14.75/4.02 | (80) ! [v0] : ! [v1] : ! [v2] : ( ~ leq(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v2)) % 14.75/4.02 | (81) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0)) % 14.75/4.02 | (82) ! [v0] : ! [v1] : ( ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v2, v1) = v0 & ssList(v2))) % 14.75/4.02 | (83) cons(all_0_3_3, nil) = all_0_5_5 % 14.75/4.02 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v1, v2) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v1)) % 14.75/4.02 | (85) ! [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)) % 14.75/4.02 | (86) ssItem(all_0_0_0) % 14.75/4.02 | (87) ~ singletonP(nil) % 14.75/4.02 | (88) ! [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))) % 14.75/4.02 | (89) ! [v0] : ( ~ ssList(v0) | rearsegP(v0, nil)) % 14.75/4.02 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | ? [v3] : (cons(v1, nil) = v3 & app(v3, v0) = v2)) % 14.75/4.02 | (91) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ ssList(v0)) % 14.75/4.02 | (92) ! [v0] : ! [v1] : ( ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v1, v0)) % 14.75/4.02 | (93) ! [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))) % 14.75/4.02 | (94) ! [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) % 14.75/4.02 | (95) ! [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)) % 14.75/4.02 | (96) ! [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) % 14.75/4.02 | (97) neq(all_0_4_4, nil) % 14.75/4.02 | (98) ! [v0] : ( ~ lt(v0, v0) | ~ ssItem(v0)) % 14.75/4.02 | (99) ! [v0] : ( ~ ssList(v0) | frontsegP(v0, nil)) % 14.75/4.02 | (100) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderedP(v1)) % 14.75/4.02 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | hd(v3) = v1) % 14.75/4.02 | (102) ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ lt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2)) % 14.75/4.02 | (103) ! [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)) % 14.75/4.03 | (104) ! [v0] : ! [v1] : ! [v2] : ( ~ geq(v1, v2) | ~ geq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v2)) % 14.75/4.03 | (105) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderP(v1)) % 14.75/4.03 | (106) ! [v0] : ! [v1] : ! [v2] : ( ~ rearsegP(v1, v2) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v2)) % 14.75/4.03 | (107) ! [v0] : ! [v1] : (v1 = v0 | ~ frontsegP(v1, v0) | ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) % 14.75/4.03 | (108) ! [v0] : ! [v1] : (v1 = v0 | ~ ssList(v1) | ~ ssList(v0) | neq(v0, v1)) % 14.75/4.03 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) % 14.75/4.03 | (110) ! [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))) % 14.75/4.03 | (111) ! [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)))))) % 14.75/4.03 | (112) ! [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)) % 14.75/4.03 | (113) ! [v0] : (v0 = nil | ~ ssList(v0) | ? [v1] : ? [v2] : (cons(v2, v1) = v0 & ssList(v1) & ssItem(v2))) % 14.75/4.03 | (114) ssItem(all_0_3_3) % 14.75/4.03 | (115) ssItem(all_0_1_1) % 14.75/4.03 | (116) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ~ ssList(v0) | ~ ssItem(v1) | cons(v1, v0) = v3) % 14.75/4.03 | (117) ! [v0] : ( ~ singletonP(v0) | ~ ssList(v0) | ? [v1] : (cons(v1, nil) = v0 & ssItem(v1))) % 15.06/4.03 | (118) ! [v0] : ( ~ ssItem(v0) | leq(v0, v0)) % 15.06/4.03 | (119) ! [v0] : ! [v1] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0)) % 15.06/4.03 | (120) ! [v0] : ! [v1] : ( ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v1, v2) = v0 & ssList(v2))) % 15.06/4.03 | (121) ! [v0] : ( ~ ssList(v0) | rearsegP(v0, v0)) % 15.06/4.03 | (122) ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 15.06/4.03 | (123) ! [v0] : ! [v1] : (v1 = v0 | ~ ssItem(v1) | ~ ssItem(v0) | neq(v0, v1)) % 15.06/4.03 | (124) totalorderP(nil) % 15.06/4.03 | (125) ~ (all_0_0_0 = all_0_1_1) % 15.06/4.03 | (126) ! [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)) % 15.06/4.03 | (127) ! [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)))))) % 15.06/4.03 | (128) ! [v0] : ! [v1] : (v1 = v0 | ~ geq(v1, v0) | ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 15.06/4.03 | (129) ! [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)))))) % 15.06/4.03 | (130) ! [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)) % 15.06/4.03 | (131) ! [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))) % 15.06/4.03 | (132) ! [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))) % 15.06/4.04 | (133) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | equalelemsP(v1)) % 15.06/4.04 | (134) ! [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)))) % 15.06/4.04 | (135) ! [v0] : ! [v1] : ( ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v1)) % 15.06/4.04 | (136) ! [v0] : ( ~ ssList(v0) | segmentP(v0, nil)) % 15.06/4.04 | (137) ! [v0] : ! [v1] : ( ~ (cons(v1, nil) = v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) % 15.06/4.04 | (138) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | cyclefreeP(v1)) % 15.06/4.04 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0) | memberP(v1, v0)) % 15.06/4.04 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) % 15.06/4.04 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v1, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) % 15.06/4.04 | (142) strictorderP(nil) % 15.06/4.04 | (143) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0)) % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (89) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields: % 15.06/4.04 | (144) rearsegP(all_0_4_4, nil) % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (51) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields: % 15.06/4.04 | (145) frontsegP(all_0_4_4, all_0_4_4) % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (99) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields: % 15.06/4.04 | (146) frontsegP(all_0_4_4, nil) % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (84) with all_0_2_2, all_0_5_5, all_0_4_4 and discharging atoms app(all_0_5_5, all_0_2_2) = all_0_4_4, ssList(all_0_2_2), ssList(all_0_4_4), ssList(all_0_5_5), yields: % 15.06/4.04 | (147) frontsegP(all_0_4_4, all_0_5_5) % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (121) with all_0_5_5 and discharging atoms ssList(all_0_5_5), yields: % 15.06/4.04 | (148) rearsegP(all_0_5_5, all_0_5_5) % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (89) with all_0_5_5 and discharging atoms ssList(all_0_5_5), yields: % 15.06/4.04 | (149) rearsegP(all_0_5_5, nil) % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (99) with all_0_5_5 and discharging atoms ssList(all_0_5_5), yields: % 15.06/4.04 | (150) frontsegP(all_0_5_5, nil) % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (41) with nil, nil and discharging atoms segmentP(nil, nil), ssList(nil), yields: % 15.06/4.04 | (151) ? [v0] : ? [v1] : ? [v2] : (app(v1, v2) = nil & app(v0, nil) = v1 & ssList(v2) & ssList(v0)) % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (35) with all_0_5_5, nil, all_0_5_5, nil, all_0_3_3 and discharging atoms cons(all_0_3_3, nil) = all_0_5_5, frontsegP(nil, nil), ssList(nil), ssItem(all_0_3_3), yields: % 15.06/4.04 | (152) frontsegP(all_0_5_5, all_0_5_5) % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (77) with all_0_5_5, all_0_3_3, nil and discharging atoms cons(all_0_3_3, nil) = all_0_5_5, ssList(nil), ssItem(all_0_3_3), yields: % 15.06/4.04 | (153) hd(all_0_5_5) = all_0_3_3 % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (90) with all_0_5_5, all_0_3_3, nil and discharging atoms cons(all_0_3_3, nil) = all_0_5_5, ssList(nil), ssItem(all_0_3_3), yields: % 15.06/4.04 | (154) ? [v0] : (cons(all_0_3_3, nil) = v0 & app(v0, nil) = all_0_5_5) % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (143) with all_0_5_5, nil, all_0_3_3 and discharging atoms cons(all_0_3_3, nil) = all_0_5_5, ssList(nil), ssItem(all_0_3_3), yields: % 15.06/4.04 | (155) memberP(all_0_5_5, all_0_3_3) % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (116) with all_0_4_4, all_0_5_5, all_0_3_3, all_0_2_2 and discharging atoms cons(all_0_3_3, nil) = all_0_5_5, app(all_0_5_5, all_0_2_2) = all_0_4_4, ssList(all_0_2_2), ssItem(all_0_3_3), yields: % 15.06/4.04 | (156) cons(all_0_3_3, all_0_2_2) = all_0_4_4 % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (137) with all_0_3_3, all_0_5_5 and discharging atoms cons(all_0_3_3, nil) = all_0_5_5, ssList(all_0_5_5), ssItem(all_0_3_3), yields: % 15.06/4.04 | (157) singletonP(all_0_5_5) % 15.06/4.04 | % 15.06/4.04 | Instantiating (151) with all_15_0_9, all_15_1_10, all_15_2_11 yields: % 15.06/4.04 | (158) app(all_15_1_10, all_15_0_9) = nil & app(all_15_2_11, nil) = all_15_1_10 & ssList(all_15_0_9) & ssList(all_15_2_11) % 15.06/4.04 | % 15.06/4.04 | Applying alpha-rule on (158) yields: % 15.06/4.04 | (159) app(all_15_1_10, all_15_0_9) = nil % 15.06/4.04 | (160) app(all_15_2_11, nil) = all_15_1_10 % 15.06/4.04 | (161) ssList(all_15_0_9) % 15.06/4.04 | (162) ssList(all_15_2_11) % 15.06/4.04 | % 15.06/4.04 | Instantiating (154) with all_19_0_13 yields: % 15.06/4.04 | (163) cons(all_0_3_3, nil) = all_19_0_13 & app(all_19_0_13, nil) = all_0_5_5 % 15.06/4.04 | % 15.06/4.04 | Applying alpha-rule on (163) yields: % 15.06/4.04 | (164) cons(all_0_3_3, nil) = all_19_0_13 % 15.06/4.04 | (165) app(all_19_0_13, nil) = all_0_5_5 % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (109) with all_0_3_3, nil, all_19_0_13, all_0_5_5 and discharging atoms cons(all_0_3_3, nil) = all_19_0_13, cons(all_0_3_3, nil) = all_0_5_5, yields: % 15.06/4.04 | (166) all_19_0_13 = all_0_5_5 % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (32) with all_15_1_10, all_15_2_11 and discharging atoms app(all_15_2_11, nil) = all_15_1_10, ssList(all_15_2_11), yields: % 15.06/4.04 | (167) all_15_1_10 = all_15_2_11 % 15.06/4.04 | % 15.06/4.04 | From (166) and (165) follows: % 15.06/4.04 | (168) app(all_0_5_5, nil) = all_0_5_5 % 15.06/4.04 | % 15.06/4.04 | From (167) and (159) follows: % 15.06/4.04 | (169) app(all_15_2_11, all_15_0_9) = nil % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (119) with all_15_0_9, all_15_2_11 and discharging atoms app(all_15_2_11, all_15_0_9) = nil, ssList(all_15_0_9), ssList(all_15_2_11), yields: % 15.06/4.04 | (170) all_15_2_11 = nil % 15.06/4.04 | % 15.06/4.04 | From (170) and (162) follows: % 15.06/4.04 | (22) ssList(nil) % 15.06/4.04 | % 15.06/4.04 | Instantiating formula (111) with all_0_3_3, all_0_5_5, all_0_3_3 and discharging atoms hd(all_0_5_5) = all_0_3_3, ssList(all_0_5_5), ssItem(all_0_3_3), yields: % 15.06/4.05 | (172) ? [v0] : (cons(all_0_3_3, all_0_5_5) = v0 & (all_0_5_5 = nil | ~ strictorderedP(v0) | (strictorderedP(all_0_5_5) & lt(all_0_3_3, all_0_3_3))) & (strictorderedP(v0) | ( ~ (all_0_5_5 = nil) & ( ~ strictorderedP(all_0_5_5) | ~ lt(all_0_3_3, all_0_3_3))))) % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (129) with all_0_3_3, all_0_5_5, all_0_3_3 and discharging atoms hd(all_0_5_5) = all_0_3_3, ssList(all_0_5_5), ssItem(all_0_3_3), yields: % 15.06/4.05 | (173) ? [v0] : (cons(all_0_3_3, all_0_5_5) = v0 & (all_0_5_5 = nil | ~ totalorderedP(v0) | (totalorderedP(all_0_5_5) & leq(all_0_3_3, all_0_3_3))) & (totalorderedP(v0) | ( ~ (all_0_5_5 = nil) & ( ~ totalorderedP(all_0_5_5) | ~ leq(all_0_3_3, all_0_3_3))))) % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (82) with nil, all_0_4_4 and discharging atoms rearsegP(all_0_4_4, nil), ssList(all_0_4_4), ssList(nil), yields: % 15.06/4.05 | (174) ? [v0] : (app(v0, nil) = all_0_4_4 & ssList(v0)) % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (82) with all_0_5_5, all_0_5_5 and discharging atoms rearsegP(all_0_5_5, all_0_5_5), ssList(all_0_5_5), yields: % 15.06/4.05 | (175) ? [v0] : (app(v0, all_0_5_5) = all_0_5_5 & ssList(v0)) % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (82) with nil, all_0_5_5 and discharging atoms rearsegP(all_0_5_5, nil), ssList(all_0_5_5), ssList(nil), yields: % 15.06/4.05 | (176) ? [v0] : (app(v0, nil) = all_0_5_5 & ssList(v0)) % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (120) with all_0_4_4, all_0_4_4 and discharging atoms frontsegP(all_0_4_4, all_0_4_4), ssList(all_0_4_4), yields: % 15.06/4.05 | (177) ? [v0] : (app(all_0_4_4, v0) = all_0_4_4 & ssList(v0)) % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (120) with nil, all_0_4_4 and discharging atoms frontsegP(all_0_4_4, nil), ssList(all_0_4_4), ssList(nil), yields: % 15.06/4.05 | (178) ? [v0] : (app(nil, v0) = all_0_4_4 & ssList(v0)) % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (120) with all_0_5_5, all_0_5_5 and discharging atoms frontsegP(all_0_5_5, all_0_5_5), ssList(all_0_5_5), yields: % 15.06/4.05 | (179) ? [v0] : (app(all_0_5_5, v0) = all_0_5_5 & ssList(v0)) % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (120) with nil, all_0_5_5 and discharging atoms frontsegP(all_0_5_5, nil), ssList(all_0_5_5), ssList(nil), yields: % 15.06/4.05 | (180) ? [v0] : (app(nil, v0) = all_0_5_5 & ssList(v0)) % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (117) with all_0_5_5 and discharging atoms singletonP(all_0_5_5), ssList(all_0_5_5), yields: % 15.06/4.05 | (181) ? [v0] : (cons(v0, nil) = all_0_5_5 & ssItem(v0)) % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (141) with all_0_4_4, all_0_2_2, all_0_5_5, all_0_3_3 and discharging atoms app(all_0_5_5, all_0_2_2) = all_0_4_4, memberP(all_0_5_5, all_0_3_3), ssList(all_0_2_2), ssList(all_0_5_5), ssItem(all_0_3_3), yields: % 15.06/4.05 | (182) memberP(all_0_4_4, all_0_3_3) % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (42) with all_0_3_3, all_0_5_5 and discharging atoms memberP(all_0_5_5, all_0_3_3), ssList(all_0_5_5), ssItem(all_0_3_3), yields: % 15.06/4.05 | (183) ? [v0] : ? [v1] : ? [v2] : (cons(all_0_3_3, v1) = v2 & app(v0, v2) = all_0_5_5 & ssList(v1) & ssList(v0)) % 15.06/4.05 | % 15.06/4.05 | Instantiating (177) with all_43_0_14 yields: % 15.06/4.05 | (184) app(all_0_4_4, all_43_0_14) = all_0_4_4 & ssList(all_43_0_14) % 15.06/4.05 | % 15.06/4.05 | Applying alpha-rule on (184) yields: % 15.06/4.05 | (185) app(all_0_4_4, all_43_0_14) = all_0_4_4 % 15.06/4.05 | (186) ssList(all_43_0_14) % 15.06/4.05 | % 15.06/4.05 | Instantiating (176) with all_55_0_24 yields: % 15.06/4.05 | (187) app(all_55_0_24, nil) = all_0_5_5 & ssList(all_55_0_24) % 15.06/4.05 | % 15.06/4.05 | Applying alpha-rule on (187) yields: % 15.06/4.05 | (188) app(all_55_0_24, nil) = all_0_5_5 % 15.06/4.05 | (189) ssList(all_55_0_24) % 15.06/4.05 | % 15.06/4.05 | Instantiating (175) with all_67_0_36 yields: % 15.06/4.05 | (190) app(all_67_0_36, all_0_5_5) = all_0_5_5 & ssList(all_67_0_36) % 15.06/4.05 | % 15.06/4.05 | Applying alpha-rule on (190) yields: % 15.06/4.05 | (191) app(all_67_0_36, all_0_5_5) = all_0_5_5 % 15.06/4.05 | (192) ssList(all_67_0_36) % 15.06/4.05 | % 15.06/4.05 | Instantiating (183) with all_74_0_39, all_74_1_40, all_74_2_41 yields: % 15.06/4.05 | (193) cons(all_0_3_3, all_74_1_40) = all_74_0_39 & app(all_74_2_41, all_74_0_39) = all_0_5_5 & ssList(all_74_1_40) & ssList(all_74_2_41) % 15.06/4.05 | % 15.06/4.05 | Applying alpha-rule on (193) yields: % 15.06/4.05 | (194) cons(all_0_3_3, all_74_1_40) = all_74_0_39 % 15.06/4.05 | (195) app(all_74_2_41, all_74_0_39) = all_0_5_5 % 15.06/4.05 | (196) ssList(all_74_1_40) % 15.06/4.05 | (197) ssList(all_74_2_41) % 15.06/4.05 | % 15.06/4.05 | Instantiating (180) with all_76_0_42 yields: % 15.06/4.05 | (198) app(nil, all_76_0_42) = all_0_5_5 & ssList(all_76_0_42) % 15.06/4.05 | % 15.06/4.05 | Applying alpha-rule on (198) yields: % 15.06/4.05 | (199) app(nil, all_76_0_42) = all_0_5_5 % 15.06/4.05 | (200) ssList(all_76_0_42) % 15.06/4.05 | % 15.06/4.05 | Instantiating (179) with all_78_0_43 yields: % 15.06/4.05 | (201) app(all_0_5_5, all_78_0_43) = all_0_5_5 & ssList(all_78_0_43) % 15.06/4.05 | % 15.06/4.05 | Applying alpha-rule on (201) yields: % 15.06/4.05 | (202) app(all_0_5_5, all_78_0_43) = all_0_5_5 % 15.06/4.05 | (203) ssList(all_78_0_43) % 15.06/4.05 | % 15.06/4.05 | Instantiating (178) with all_80_0_44 yields: % 15.06/4.05 | (204) app(nil, all_80_0_44) = all_0_4_4 & ssList(all_80_0_44) % 15.06/4.05 | % 15.06/4.05 | Applying alpha-rule on (204) yields: % 15.06/4.05 | (205) app(nil, all_80_0_44) = all_0_4_4 % 15.06/4.05 | (206) ssList(all_80_0_44) % 15.06/4.05 | % 15.06/4.05 | Instantiating (181) with all_82_0_45 yields: % 15.06/4.05 | (207) cons(all_82_0_45, nil) = all_0_5_5 & ssItem(all_82_0_45) % 15.06/4.05 | % 15.06/4.05 | Applying alpha-rule on (207) yields: % 15.06/4.05 | (208) cons(all_82_0_45, nil) = all_0_5_5 % 15.06/4.05 | (209) ssItem(all_82_0_45) % 15.06/4.05 | % 15.06/4.05 | Instantiating (173) with all_86_0_47 yields: % 15.06/4.05 | (210) cons(all_0_3_3, all_0_5_5) = all_86_0_47 & (all_0_5_5 = nil | ~ totalorderedP(all_86_0_47) | (totalorderedP(all_0_5_5) & leq(all_0_3_3, all_0_3_3))) & (totalorderedP(all_86_0_47) | ( ~ (all_0_5_5 = nil) & ( ~ totalorderedP(all_0_5_5) | ~ leq(all_0_3_3, all_0_3_3)))) % 15.06/4.05 | % 15.06/4.05 | Applying alpha-rule on (210) yields: % 15.06/4.05 | (211) cons(all_0_3_3, all_0_5_5) = all_86_0_47 % 15.06/4.05 | (212) all_0_5_5 = nil | ~ totalorderedP(all_86_0_47) | (totalorderedP(all_0_5_5) & leq(all_0_3_3, all_0_3_3)) % 15.06/4.05 | (213) totalorderedP(all_86_0_47) | ( ~ (all_0_5_5 = nil) & ( ~ totalorderedP(all_0_5_5) | ~ leq(all_0_3_3, all_0_3_3))) % 15.06/4.05 | % 15.06/4.05 | Instantiating (174) with all_90_0_49 yields: % 15.06/4.05 | (214) app(all_90_0_49, nil) = all_0_4_4 & ssList(all_90_0_49) % 15.06/4.05 | % 15.06/4.05 | Applying alpha-rule on (214) yields: % 15.06/4.05 | (215) app(all_90_0_49, nil) = all_0_4_4 % 15.06/4.05 | (216) ssList(all_90_0_49) % 15.06/4.05 | % 15.06/4.05 | Instantiating (172) with all_98_0_55 yields: % 15.06/4.05 | (217) cons(all_0_3_3, all_0_5_5) = all_98_0_55 & (all_0_5_5 = nil | ~ strictorderedP(all_98_0_55) | (strictorderedP(all_0_5_5) & lt(all_0_3_3, all_0_3_3))) & (strictorderedP(all_98_0_55) | ( ~ (all_0_5_5 = nil) & ( ~ strictorderedP(all_0_5_5) | ~ lt(all_0_3_3, all_0_3_3)))) % 15.06/4.05 | % 15.06/4.05 | Applying alpha-rule on (217) yields: % 15.06/4.05 | (218) cons(all_0_3_3, all_0_5_5) = all_98_0_55 % 15.06/4.05 | (219) all_0_5_5 = nil | ~ strictorderedP(all_98_0_55) | (strictorderedP(all_0_5_5) & lt(all_0_3_3, all_0_3_3)) % 15.06/4.05 | (220) strictorderedP(all_98_0_55) | ( ~ (all_0_5_5 = nil) & ( ~ strictorderedP(all_0_5_5) | ~ lt(all_0_3_3, all_0_3_3))) % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (109) with all_0_3_3, all_0_5_5, all_86_0_47, all_98_0_55 and discharging atoms cons(all_0_3_3, all_0_5_5) = all_98_0_55, cons(all_0_3_3, all_0_5_5) = all_86_0_47, yields: % 15.06/4.05 | (221) all_98_0_55 = all_86_0_47 % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (32) with all_0_4_4, all_90_0_49 and discharging atoms app(all_90_0_49, nil) = all_0_4_4, ssList(all_90_0_49), yields: % 15.06/4.05 | (222) all_90_0_49 = all_0_4_4 % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (91) with all_0_4_4, all_80_0_44 and discharging atoms app(nil, all_80_0_44) = all_0_4_4, ssList(all_80_0_44), yields: % 15.06/4.05 | (223) all_80_0_44 = all_0_4_4 % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (140) with nil, all_0_5_5, all_0_5_5, all_78_0_43 and discharging atoms app(all_0_5_5, all_78_0_43) = all_0_5_5, app(all_0_5_5, nil) = all_0_5_5, ssList(all_78_0_43), ssList(all_0_5_5), ssList(nil), yields: % 15.06/4.05 | (224) all_78_0_43 = nil % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (91) with all_0_5_5, all_76_0_42 and discharging atoms app(nil, all_76_0_42) = all_0_5_5, ssList(all_76_0_42), yields: % 15.06/4.05 | (225) all_76_0_42 = all_0_5_5 % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (32) with all_0_5_5, all_55_0_24 and discharging atoms app(all_55_0_24, nil) = all_0_5_5, ssList(all_55_0_24), yields: % 15.06/4.05 | (226) all_55_0_24 = all_0_5_5 % 15.06/4.05 | % 15.06/4.05 | Instantiating formula (130) with all_0_5_5, nil, all_0_4_4, all_0_2_2, all_82_0_45, all_0_3_3 and discharging atoms cons(all_82_0_45, nil) = all_0_5_5, cons(all_0_3_3, all_0_2_2) = all_0_4_4, frontsegP(all_0_4_4, all_0_5_5), ssList(all_0_2_2), ssList(nil), ssItem(all_82_0_45), ssItem(all_0_3_3), yields: % 15.06/4.05 | (227) all_82_0_45 = all_0_3_3 % 15.06/4.05 | % 15.06/4.05 | From (227) and (208) follows: % 15.06/4.06 | (83) cons(all_0_3_3, nil) = all_0_5_5 % 15.06/4.06 | % 15.06/4.06 | From (221) and (218) follows: % 15.06/4.06 | (211) cons(all_0_3_3, all_0_5_5) = all_86_0_47 % 15.06/4.06 | % 15.06/4.06 | From (222) and (215) follows: % 15.06/4.06 | (230) app(all_0_4_4, nil) = all_0_4_4 % 15.06/4.06 | % 15.06/4.06 | From (225) and (199) follows: % 15.06/4.06 | (231) app(nil, all_0_5_5) = all_0_5_5 % 15.06/4.06 | % 15.06/4.06 | From (223) and (206) follows: % 15.06/4.06 | (47) ssList(all_0_4_4) % 15.06/4.06 | % 15.06/4.06 | From (224) and (203) follows: % 15.06/4.06 | (22) ssList(nil) % 15.06/4.06 | % 15.06/4.06 | From (226) and (189) follows: % 15.06/4.06 | (3) ssList(all_0_5_5) % 15.06/4.06 | % 15.06/4.06 | From (227) and (209) follows: % 15.06/4.06 | (114) ssItem(all_0_3_3) % 15.06/4.06 | % 15.06/4.06 | Instantiating formula (140) with all_43_0_14, all_0_4_4, all_0_4_4, nil and discharging atoms app(all_0_4_4, all_43_0_14) = all_0_4_4, app(all_0_4_4, nil) = all_0_4_4, ssList(all_43_0_14), ssList(all_0_4_4), ssList(nil), yields: % 15.06/4.06 | (236) all_43_0_14 = nil % 15.06/4.06 | % 15.06/4.06 | Instantiating formula (69) with all_67_0_36, all_0_5_5, all_0_5_5, nil and discharging atoms app(all_67_0_36, all_0_5_5) = all_0_5_5, app(nil, all_0_5_5) = all_0_5_5, ssList(all_67_0_36), ssList(all_0_5_5), ssList(nil), yields: % 15.06/4.06 | (237) all_67_0_36 = nil % 15.06/4.06 | % 15.06/4.06 | From (237) and (191) follows: % 15.06/4.06 | (231) app(nil, all_0_5_5) = all_0_5_5 % 15.06/4.06 | % 15.06/4.06 | From (236) and (186) follows: % 15.06/4.06 | (22) ssList(nil) % 15.06/4.06 | % 15.06/4.06 | Instantiating formula (60) with all_86_0_47, all_0_3_3, all_0_5_5, nil, all_0_5_5 and discharging atoms cons(all_0_3_3, all_0_5_5) = all_86_0_47, app(nil, all_0_5_5) = all_0_5_5, ssList(all_0_5_5), ssList(nil), ssItem(all_0_3_3), yields: % 15.06/4.06 | (240) ? [v0] : (cons(all_0_3_3, nil) = v0 & app(v0, all_0_5_5) = all_86_0_47) % 15.06/4.06 | % 15.06/4.06 | Instantiating formula (7) with all_0_3_3 and discharging atoms memberP(all_0_4_4, all_0_3_3), ssItem(all_0_3_3), yields: % 15.06/4.06 | (241) ? [v0] : ( ~ (v0 = all_0_5_5) & cons(all_0_3_3, nil) = v0) % 15.06/4.06 | % 15.06/4.06 | Instantiating formula (90) with all_74_0_39, all_0_3_3, all_74_1_40 and discharging atoms cons(all_0_3_3, all_74_1_40) = all_74_0_39, ssList(all_74_1_40), ssItem(all_0_3_3), yields: % 15.06/4.06 | (242) ? [v0] : (cons(all_0_3_3, nil) = v0 & app(v0, all_74_1_40) = all_74_0_39) % 15.06/4.06 | % 15.06/4.06 | Instantiating (241) with all_161_0_79 yields: % 15.06/4.06 | (243) ~ (all_161_0_79 = all_0_5_5) & cons(all_0_3_3, nil) = all_161_0_79 % 15.06/4.06 | % 15.06/4.06 | Applying alpha-rule on (243) yields: % 15.06/4.06 | (244) ~ (all_161_0_79 = all_0_5_5) % 15.06/4.06 | (245) cons(all_0_3_3, nil) = all_161_0_79 % 15.06/4.06 | % 15.06/4.06 | Instantiating (242) with all_171_0_84 yields: % 15.06/4.06 | (246) cons(all_0_3_3, nil) = all_171_0_84 & app(all_171_0_84, all_74_1_40) = all_74_0_39 % 15.06/4.06 | % 15.06/4.06 | Applying alpha-rule on (246) yields: % 15.06/4.06 | (247) cons(all_0_3_3, nil) = all_171_0_84 % 15.06/4.06 | (248) app(all_171_0_84, all_74_1_40) = all_74_0_39 % 15.06/4.06 | % 15.06/4.06 | Instantiating (240) with all_203_0_99 yields: % 15.06/4.06 | (249) cons(all_0_3_3, nil) = all_203_0_99 & app(all_203_0_99, all_0_5_5) = all_86_0_47 % 15.06/4.06 | % 15.06/4.06 | Applying alpha-rule on (249) yields: % 15.06/4.06 | (250) cons(all_0_3_3, nil) = all_203_0_99 % 15.06/4.06 | (251) app(all_203_0_99, all_0_5_5) = all_86_0_47 % 15.06/4.06 | % 15.06/4.06 | Instantiating formula (109) with all_0_3_3, nil, all_203_0_99, all_0_5_5 and discharging atoms cons(all_0_3_3, nil) = all_203_0_99, cons(all_0_3_3, nil) = all_0_5_5, yields: % 15.06/4.06 | (252) all_203_0_99 = all_0_5_5 % 15.06/4.06 | % 15.06/4.06 | Instantiating formula (109) with all_0_3_3, nil, all_171_0_84, all_203_0_99 and discharging atoms cons(all_0_3_3, nil) = all_203_0_99, cons(all_0_3_3, nil) = all_171_0_84, yields: % 15.06/4.06 | (253) all_203_0_99 = all_171_0_84 % 15.06/4.06 | % 15.06/4.06 | Instantiating formula (109) with all_0_3_3, nil, all_161_0_79, all_203_0_99 and discharging atoms cons(all_0_3_3, nil) = all_203_0_99, cons(all_0_3_3, nil) = all_161_0_79, yields: % 15.06/4.06 | (254) all_203_0_99 = all_161_0_79 % 15.06/4.06 | % 15.06/4.06 | Combining equations (254,253) yields a new equation: % 15.06/4.06 | (255) all_171_0_84 = all_161_0_79 % 15.06/4.06 | % 15.06/4.06 | Combining equations (252,253) yields a new equation: % 15.06/4.06 | (256) all_171_0_84 = all_0_5_5 % 15.06/4.06 | % 15.06/4.06 | Combining equations (256,255) yields a new equation: % 15.06/4.06 | (257) all_161_0_79 = all_0_5_5 % 15.06/4.06 | % 15.06/4.06 | Equations (257) can reduce 244 to: % 15.06/4.06 | (258) $false % 15.06/4.06 | % 15.06/4.06 |-The branch is then unsatisfiable % 15.06/4.06 % SZS output end Proof for theBenchmark % 15.21/4.06 % 15.21/4.06 3474ms %------------------------------------------------------------------------------