%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWC357+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n016.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 20:17:41 EDT 2022 % Result : Theorem 42.92s 13.00s % Output : Proof 51.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SWC357+1 : TPTP v8.1.0. Released v2.4.0. % 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n016.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sun Jun 12 14:43:28 EDT 2022 % 0.12/0.33 % CPUTime : % 0.59/0.59 ____ _ % 0.59/0.59 ___ / __ \_____(_)___ ________ __________ % 0.59/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.59/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.59/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.59/0.59 % 0.59/0.59 A Theorem Prover for First-Order Logic % 0.59/0.60 (ePrincess v.1.0) % 0.59/0.60 % 0.59/0.60 (c) Philipp Rümmer, 2009-2015 % 0.59/0.60 (c) Peter Backeman, 2014-2015 % 0.59/0.60 (contributions by Angelo Brillout, Peter Baumgartner) % 0.59/0.60 Free software under GNU Lesser General Public License (LGPL). % 0.59/0.60 Bug reports to peter@backeman.se % 0.59/0.60 % 0.59/0.60 For more information, visit http://user.uu.se/~petba168/breu/ % 0.59/0.60 % 0.59/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.68/0.68 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.33/1.12 Prover 0: Preprocessing ... % 4.50/1.70 Prover 0: Constructing countermodel ... % 18.20/5.96 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 19.04/6.12 Prover 1: Preprocessing ... % 20.02/6.39 Prover 1: Constructing countermodel ... % 28.85/8.56 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 29.24/8.70 Prover 2: Preprocessing ... % 31.50/9.19 Prover 2: Warning: ignoring some quantifiers % 31.65/9.21 Prover 2: Constructing countermodel ... % 37.89/11.58 Prover 0: stopped % 38.15/11.78 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 38.33/11.86 Prover 3: Preprocessing ... % 38.56/11.92 Prover 3: Constructing countermodel ... % 42.92/13.00 Prover 3: proved (1217ms) % 42.92/13.00 Prover 2: stopped % 42.92/13.00 Prover 1: stopped % 42.92/13.00 % 42.92/13.00 No countermodel exists, formula is valid % 42.92/13.00 % SZS status Theorem for theBenchmark % 42.92/13.00 % 42.92/13.00 Generating proof ... found it (size 65) % 50.59/14.92 % 50.59/14.92 % SZS output start Proof for theBenchmark % 50.59/14.92 Assumed formulas after preprocessing and simplification: % 50.59/14.92 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & equalelemsP(nil) & duplicatefreeP(nil) & strictorderedP(nil) & totalorderedP(nil) & strictorderP(nil) & totalorderP(nil) & cyclefreeP(nil) & segmentP(nil, nil) & rearsegP(nil, nil) & frontsegP(nil, nil) & ssList(v1) & ssList(v0) & ssList(nil) & neq(v1, nil) & ssItem(v3) & ssItem(v2) & ~ segmentP(v1, v0) & ~ singletonP(nil) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cons(v6, v11) = v12) | ~ (cons(v5, v8) = v9) | ~ (app(v10, v12) = v4) | ~ (app(v7, v9) = v10) | ~ strictorderedP(v4) | ~ ssList(v11) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v4) | ~ ssItem(v6) | ~ ssItem(v5) | lt(v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cons(v6, v11) = v12) | ~ (cons(v5, v8) = v9) | ~ (app(v10, v12) = v4) | ~ (app(v7, v9) = v10) | ~ totalorderedP(v4) | ~ ssList(v11) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v4) | ~ ssItem(v6) | ~ ssItem(v5) | leq(v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cons(v6, v11) = v12) | ~ (cons(v5, v8) = v9) | ~ (app(v10, v12) = v4) | ~ (app(v7, v9) = v10) | ~ strictorderP(v4) | ~ ssList(v11) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v4) | ~ ssItem(v6) | ~ ssItem(v5) | lt(v6, v5) | lt(v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cons(v6, v11) = v12) | ~ (cons(v5, v8) = v9) | ~ (app(v10, v12) = v4) | ~ (app(v7, v9) = v10) | ~ totalorderP(v4) | ~ ssList(v11) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v4) | ~ ssItem(v6) | ~ ssItem(v5) | leq(v6, v5) | leq(v5, v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cons(v6, v11) = v12) | ~ (cons(v5, v8) = v9) | ~ (app(v10, v12) = v4) | ~ (app(v7, v9) = v10) | ~ leq(v6, v5) | ~ leq(v5, v6) | ~ cyclefreeP(v4) | ~ ssList(v11) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v4) | ~ ssItem(v6) | ~ ssItem(v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (cons(v5, v10) = v11) | ~ (cons(v5, v7) = v8) | ~ (app(v9, v11) = v4) | ~ (app(v6, v8) = v9) | ~ duplicatefreeP(v4) | ~ ssList(v10) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v4) | ~ ssItem(v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v6 = v5 | ~ (cons(v6, v8) = v9) | ~ (cons(v5, v9) = v10) | ~ (app(v7, v10) = v4) | ~ equalelemsP(v4) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v4) | ~ ssItem(v6) | ~ ssItem(v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v5 = v4 | ~ (cons(v5, v8) = v9) | ~ (cons(v4, v6) = v7) | ~ frontsegP(v7, v9) | ~ ssList(v8) | ~ ssList(v6) | ~ ssItem(v5) | ~ ssItem(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (cons(v7, v5) = v8) | ~ (app(v8, v4) = v9) | ~ (app(v5, v4) = v6) | ~ ssList(v5) | ~ ssList(v4) | ~ ssItem(v7) | cons(v7, v6) = v9) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (cons(v5, v8) = v9) | ~ (cons(v4, v6) = v7) | ~ frontsegP(v7, v9) | ~ ssList(v8) | ~ ssList(v6) | ~ ssItem(v5) | ~ ssItem(v4) | frontsegP(v6, v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (app(v7, v8) = v9) | ~ (app(v6, v4) = v7) | ~ segmentP(v4, v5) | ~ ssList(v8) | ~ ssList(v6) | ~ ssList(v5) | ~ ssList(v4) | segmentP(v9, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v6 | ~ (cons(v8, v5) = v7) | ~ (cons(v6, v4) = v7) | ~ ssList(v5) | ~ ssList(v4) | ~ ssItem(v8) | ~ ssItem(v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = v4 | ~ (cons(v8, v5) = v7) | ~ (cons(v6, v4) = v7) | ~ ssList(v5) | ~ ssList(v4) | ~ ssItem(v8) | ~ ssItem(v6)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v5, v7) = v8) | ~ (app(v6, v8) = v4) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v4) | ~ ssItem(v5) | memberP(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v4, v7) = v8) | ~ (cons(v4, v5) = v6) | ~ frontsegP(v5, v7) | ~ ssList(v7) | ~ ssList(v5) | ~ ssItem(v4) | frontsegP(v6, v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (app(v7, v8) = v4) | ~ (app(v6, v5) = v7) | ~ ssList(v8) | ~ ssList(v6) | ~ ssList(v5) | ~ ssList(v4) | segmentP(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (app(v6, v7) = v8) | ~ (app(v4, v5) = v6) | ~ ssList(v7) | ~ ssList(v5) | ~ ssList(v4) | ? [v9] : (app(v5, v7) = v9 & app(v4, v9) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v4 | v4 = nil | ~ (tl(v4) = v6) | ~ (hd(v4) = v5) | ~ (cons(v5, v6) = v7) | ~ ssList(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v4 | ~ (app(v7, v5) = v6) | ~ (app(v4, v5) = v6) | ~ ssList(v7) | ~ ssList(v5) | ~ ssList(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v7 = v4 | ~ (app(v5, v7) = v6) | ~ (app(v5, v4) = v6) | ~ ssList(v7) | ~ ssList(v5) | ~ ssList(v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (cons(v7, v6) = v5) | ~ (cons(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (cons(v5, v6) = v7) | ~ memberP(v7, v4) | ~ ssList(v6) | ~ ssItem(v5) | ~ ssItem(v4) | memberP(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v5 = v4 | ~ (app(v7, v6) = v5) | ~ (app(v7, v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v4 = nil | ~ (tl(v4) = v5) | ~ (app(v5, v6) = v7) | ~ ssList(v6) | ~ ssList(v4) | ? [v8] : (tl(v8) = v7 & app(v4, v6) = v8)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : (v4 = nil | ~ (hd(v4) = v5) | ~ (app(v4, v6) = v7) | ~ ssList(v6) | ~ ssList(v4) | hd(v7) = v5) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (cons(v5, v6) = v7) | ~ memberP(v6, v4) | ~ ssList(v6) | ~ ssItem(v5) | ~ ssItem(v4) | memberP(v7, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (cons(v5, nil) = v6) | ~ (app(v6, v4) = v7) | ~ ssList(v4) | ~ ssItem(v5) | cons(v5, v4) = v7) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (app(v6, v4) = v7) | ~ rearsegP(v4, v5) | ~ ssList(v6) | ~ ssList(v5) | ~ ssList(v4) | rearsegP(v7, v5)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (app(v5, v6) = v7) | ~ memberP(v7, v4) | ~ ssList(v6) | ~ ssList(v5) | ~ ssItem(v4) | memberP(v6, v4) | memberP(v5, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (app(v5, v6) = v7) | ~ memberP(v6, v4) | ~ ssList(v6) | ~ ssList(v5) | ~ ssItem(v4) | memberP(v7, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (app(v5, v6) = v7) | ~ memberP(v5, v4) | ~ ssList(v6) | ~ ssList(v5) | ~ ssItem(v4) | memberP(v7, v4)) & ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (app(v4, v6) = v7) | ~ frontsegP(v4, v5) | ~ ssList(v6) | ~ ssList(v5) | ~ ssList(v4) | frontsegP(v7, v5)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (tl(v6) = v5) | ~ (tl(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : (v5 = v4 | ~ (hd(v6) = v5) | ~ (hd(v6) = v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (hd(v5) = v6) | ~ ssList(v5) | ~ ssItem(v4) | ? [v7] : ((v5 = nil | (cons(v4, v5) = v7 & ~ strictorderedP(v7)) | (strictorderedP(v5) & lt(v4, v6))) & (( ~ (v5 = nil) & ( ~ strictorderedP(v5) | ~ lt(v4, v6))) | (cons(v4, v5) = v7 & strictorderedP(v7))))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (hd(v5) = v6) | ~ ssList(v5) | ~ ssItem(v4) | ? [v7] : ((v5 = nil | (cons(v4, v5) = v7 & ~ totalorderedP(v7)) | (totalorderedP(v5) & leq(v4, v6))) & (( ~ (v5 = nil) & ( ~ totalorderedP(v5) | ~ leq(v4, v6))) | (cons(v4, v5) = v7 & totalorderedP(v7))))) & ! [v4] : ! [v5] : ! [v6] : ( ~ (cons(v5, v4) = v6) | ~ ssList(v4) | ~ ssItem(v5) | tl(v6) = v4) & ! [v4] : ! [v5] : ! [v6] : ( ~ (cons(v5, v4) = v6) | ~ ssList(v4) | ~ ssItem(v5) | hd(v6) = v5) & ! [v4] : ! [v5] : ! [v6] : ( ~ (cons(v5, v4) = v6) | ~ ssList(v4) | ~ ssItem(v5) | ssList(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (cons(v4, v5) = v6) | ~ ssList(v5) | ~ ssItem(v4) | memberP(v6, v4)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (app(v6, v5) = v4) | ~ ssList(v6) | ~ ssList(v5) | ~ ssList(v4) | rearsegP(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (app(v5, v6) = v4) | ~ ssList(v6) | ~ ssList(v5) | ~ ssList(v4) | frontsegP(v4, v5)) & ! [v4] : ! [v5] : ! [v6] : ( ~ (app(v4, v5) = v6) | ~ ssList(v5) | ~ ssList(v4) | ssList(v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ gt(v5, v6) | ~ gt(v4, v5) | ~ ssItem(v6) | ~ ssItem(v5) | ~ ssItem(v4) | gt(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ geq(v5, v6) | ~ geq(v4, v5) | ~ ssItem(v6) | ~ ssItem(v5) | ~ ssItem(v4) | geq(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ lt(v5, v6) | ~ lt(v4, v5) | ~ ssItem(v6) | ~ ssItem(v5) | ~ ssItem(v4) | lt(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ lt(v5, v6) | ~ leq(v4, v5) | ~ ssItem(v6) | ~ ssItem(v5) | ~ ssItem(v4) | lt(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ leq(v5, v6) | ~ leq(v4, v5) | ~ ssItem(v6) | ~ ssItem(v5) | ~ ssItem(v4) | leq(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ segmentP(v5, v6) | ~ segmentP(v4, v5) | ~ ssList(v6) | ~ ssList(v5) | ~ ssList(v4) | segmentP(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ rearsegP(v5, v6) | ~ rearsegP(v4, v5) | ~ ssList(v6) | ~ ssList(v5) | ~ ssList(v4) | rearsegP(v4, v6)) & ! [v4] : ! [v5] : ! [v6] : ( ~ frontsegP(v5, v6) | ~ frontsegP(v4, v5) | ~ ssList(v6) | ~ ssList(v5) | ~ ssList(v4) | frontsegP(v4, v6)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (app(v4, nil) = v5) | ~ ssList(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ (app(nil, v4) = v5) | ~ ssList(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ geq(v5, v4) | ~ geq(v4, v5) | ~ ssItem(v5) | ~ ssItem(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ leq(v5, v4) | ~ leq(v4, v5) | ~ ssItem(v5) | ~ ssItem(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ leq(v4, v5) | ~ ssItem(v5) | ~ ssItem(v4) | lt(v4, v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ segmentP(v5, v4) | ~ segmentP(v4, v5) | ~ ssList(v5) | ~ ssList(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ rearsegP(v5, v4) | ~ rearsegP(v4, v5) | ~ ssList(v5) | ~ ssList(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ frontsegP(v5, v4) | ~ frontsegP(v4, v5) | ~ ssList(v5) | ~ ssList(v4)) & ! [v4] : ! [v5] : (v5 = v4 | ~ ssList(v5) | ~ ssList(v4) | neq(v4, v5)) & ! [v4] : ! [v5] : (v5 = v4 | ~ ssItem(v5) | ~ ssItem(v4) | neq(v4, v5)) & ! [v4] : ! [v5] : (v5 = nil | ~ (app(v4, v5) = nil) | ~ ssList(v5) | ~ ssList(v4)) & ! [v4] : ! [v5] : (v4 = nil | ~ (tl(v4) = v5) | ~ ssList(v4) | ssList(v5)) & ! [v4] : ! [v5] : (v4 = nil | ~ (hd(v4) = v5) | ~ ssList(v4) | ssItem(v5)) & ! [v4] : ! [v5] : (v4 = nil | ~ (app(v4, v5) = nil) | ~ ssList(v5) | ~ ssList(v4)) & ! [v4] : ! [v5] : ( ~ (tl(v4) = v5) | ~ ssList(v4) | ? [v6] : (hd(v4) = v6 & ! [v7] : (v7 = v4 | v7 = nil | v4 = nil | ~ (tl(v7) = v5) | ~ ssList(v7) | ? [v8] : ( ~ (v8 = v6) & hd(v7) = v8)))) & ! [v4] : ! [v5] : ( ~ (cons(v5, v4) = v4) | ~ ssList(v4) | ~ ssItem(v5)) & ! [v4] : ! [v5] : ( ~ (cons(v5, v4) = nil) | ~ ssList(v4) | ~ ssItem(v5)) & ! [v4] : ! [v5] : ( ~ (cons(v5, nil) = v4) | ~ ssList(v4) | ~ ssItem(v5) | singletonP(v4)) & ! [v4] : ! [v5] : ( ~ (cons(v4, nil) = v5) | ~ ssItem(v4) | equalelemsP(v5)) & ! [v4] : ! [v5] : ( ~ (cons(v4, nil) = v5) | ~ ssItem(v4) | duplicatefreeP(v5)) & ! [v4] : ! [v5] : ( ~ (cons(v4, nil) = v5) | ~ ssItem(v4) | strictorderedP(v5)) & ! [v4] : ! [v5] : ( ~ (cons(v4, nil) = v5) | ~ ssItem(v4) | totalorderedP(v5)) & ! [v4] : ! [v5] : ( ~ (cons(v4, nil) = v5) | ~ ssItem(v4) | strictorderP(v5)) & ! [v4] : ! [v5] : ( ~ (cons(v4, nil) = v5) | ~ ssItem(v4) | totalorderP(v5)) & ! [v4] : ! [v5] : ( ~ (cons(v4, nil) = v5) | ~ ssItem(v4) | cyclefreeP(v5)) & ! [v4] : ! [v5] : ( ~ gt(v5, v4) | ~ gt(v4, v5) | ~ ssItem(v5) | ~ ssItem(v4)) & ! [v4] : ! [v5] : ( ~ gt(v4, v5) | ~ ssItem(v5) | ~ ssItem(v4) | lt(v5, v4)) & ! [v4] : ! [v5] : ( ~ geq(v4, v5) | ~ ssItem(v5) | ~ ssItem(v4) | leq(v5, v4)) & ! [v4] : ! [v5] : ( ~ lt(v5, v4) | ~ lt(v4, v5) | ~ ssItem(v5) | ~ ssItem(v4)) & ! [v4] : ! [v5] : ( ~ lt(v5, v4) | ~ ssItem(v5) | ~ ssItem(v4) | gt(v4, v5)) & ! [v4] : ! [v5] : ( ~ lt(v4, v5) | ~ ssItem(v5) | ~ ssItem(v4) | leq(v4, v5)) & ! [v4] : ! [v5] : ( ~ leq(v5, v4) | ~ ssItem(v5) | ~ ssItem(v4) | geq(v4, v5)) & ! [v4] : ! [v5] : ( ~ segmentP(v4, v5) | ~ ssList(v5) | ~ ssList(v4) | ? [v6] : ? [v7] : ? [v8] : (app(v7, v8) = v4 & app(v6, v5) = v7 & ssList(v8) & ssList(v6))) & ! [v4] : ! [v5] : ( ~ rearsegP(v4, v5) | ~ ssList(v5) | ~ ssList(v4) | ? [v6] : (app(v6, v5) = v4 & ssList(v6))) & ! [v4] : ! [v5] : ( ~ frontsegP(v4, v5) | ~ ssList(v5) | ~ ssList(v4) | ? [v6] : (app(v5, v6) = v4 & ssList(v6))) & ! [v4] : ! [v5] : ( ~ memberP(v4, v5) | ~ ssList(v4) | ~ ssItem(v5) | ? [v6] : ? [v7] : ? [v8] : (cons(v5, v7) = v8 & app(v6, v8) = v4 & ssList(v7) & ssList(v6))) & ! [v4] : (v4 = nil | ~ (app(nil, nil) = v4)) & ! [v4] : (v4 = nil | ~ segmentP(nil, v4) | ~ ssList(v4)) & ! [v4] : (v4 = nil | ~ rearsegP(nil, v4) | ~ ssList(v4)) & ! [v4] : (v4 = nil | ~ frontsegP(nil, v4) | ~ ssList(v4)) & ! [v4] : (v4 = nil | ~ ssList(v4) | ? [v5] : ? [v6] : (cons(v6, v5) = v4 & ssList(v5) & ssItem(v6))) & ! [v4] : ( ~ lt(v4, v4) | ~ ssItem(v4)) & ! [v4] : ( ~ singletonP(v4) | ~ ssList(v4) | ? [v5] : (cons(v5, nil) = v4 & ssItem(v5))) & ! [v4] : ( ~ memberP(nil, v4) | ~ ssItem(v4)) & ! [v4] : ( ~ ssList(v4) | ~ neq(v4, v4)) & ! [v4] : ( ~ ssList(v4) | equalelemsP(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v6 = v5) & cons(v6, v8) = v9 & cons(v5, v9) = v10 & app(v7, v10) = v4 & ssList(v8) & ssList(v7) & ssItem(v6) & ssItem(v5))) & ! [v4] : ( ~ ssList(v4) | duplicatefreeP(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : (cons(v5, v10) = v11 & cons(v5, v7) = v8 & app(v9, v11) = v4 & app(v6, v8) = v9 & ssList(v10) & ssList(v7) & ssList(v6) & ssItem(v5))) & ! [v4] : ( ~ ssList(v4) | strictorderedP(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (cons(v6, v11) = v12 & cons(v5, v8) = v9 & app(v10, v12) = v4 & app(v7, v9) = v10 & ssList(v11) & ssList(v8) & ssList(v7) & ssItem(v6) & ssItem(v5) & ~ lt(v5, v6))) & ! [v4] : ( ~ ssList(v4) | totalorderedP(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (cons(v6, v11) = v12 & cons(v5, v8) = v9 & app(v10, v12) = v4 & app(v7, v9) = v10 & ssList(v11) & ssList(v8) & ssList(v7) & ssItem(v6) & ssItem(v5) & ~ leq(v5, v6))) & ! [v4] : ( ~ ssList(v4) | strictorderP(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (cons(v6, v11) = v12 & cons(v5, v8) = v9 & app(v10, v12) = v4 & app(v7, v9) = v10 & ssList(v11) & ssList(v8) & ssList(v7) & ssItem(v6) & ssItem(v5) & ~ lt(v6, v5) & ~ lt(v5, v6))) & ! [v4] : ( ~ ssList(v4) | totalorderP(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (cons(v6, v11) = v12 & cons(v5, v8) = v9 & app(v10, v12) = v4 & app(v7, v9) = v10 & ssList(v11) & ssList(v8) & ssList(v7) & ssItem(v6) & ssItem(v5) & ~ leq(v6, v5) & ~ leq(v5, v6))) & ! [v4] : ( ~ ssList(v4) | cyclefreeP(v4) | ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (cons(v6, v11) = v12 & cons(v5, v8) = v9 & app(v10, v12) = v4 & app(v7, v9) = v10 & leq(v6, v5) & leq(v5, v6) & ssList(v11) & ssList(v8) & ssList(v7) & ssItem(v6) & ssItem(v5))) & ! [v4] : ( ~ ssList(v4) | segmentP(v4, v4)) & ! [v4] : ( ~ ssList(v4) | segmentP(v4, nil)) & ! [v4] : ( ~ ssList(v4) | rearsegP(v4, v4)) & ! [v4] : ( ~ ssList(v4) | rearsegP(v4, nil)) & ! [v4] : ( ~ ssList(v4) | frontsegP(v4, v4)) & ! [v4] : ( ~ ssList(v4) | frontsegP(v4, nil)) & ! [v4] : ( ~ neq(v4, v4) | ~ ssItem(v4)) & ! [v4] : ( ~ ssItem(v4) | geq(v4, v4)) & ! [v4] : ( ~ ssItem(v4) | leq(v4, v4)) & ((v1 = nil & v0 = nil) | (frontsegP(v1, v0) & neq(v0, nil)))) % 51.19/15.01 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 51.19/15.01 | (1) ~ (all_0_0_0 = all_0_1_1) & 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_3_3) & ssList(nil) & neq(all_0_2_2, nil) & ssItem(all_0_0_0) & ssItem(all_0_1_1) & ~ segmentP(all_0_2_2, 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] : (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(v1, v3) = v4) | ~ (app(v2, v4) = v0) | ~ ssList(v3) | ~ ssList(v2) | ~ ssList(v0) | ~ ssItem(v1) | memberP(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v0, v3) = v4) | ~ (cons(v0, v1) = v2) | ~ frontsegP(v1, v3) | ~ ssList(v3) | ~ ssList(v1) | ~ ssItem(v0) | frontsegP(v2, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5] : (app(v1, v3) = v5 & app(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ~ ssList(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | ? [v4] : (tl(v4) = v3 & app(v0, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | hd(v3) = v1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ~ ssList(v0) | ~ ssItem(v1) | cons(v1, v0) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v2, v0) = v3) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0) | memberP(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v1, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v0, v2) = v3) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (hd(v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : ((v1 = nil | (cons(v0, v1) = v3 & ~ strictorderedP(v3)) | (strictorderedP(v1) & lt(v0, v2))) & (( ~ (v1 = nil) & ( ~ strictorderedP(v1) | ~ lt(v0, v2))) | (cons(v0, v1) = v3 & strictorderedP(v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (hd(v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : ((v1 = nil | (cons(v0, v1) = v3 & ~ totalorderedP(v3)) | (totalorderedP(v1) & leq(v0, v2))) & (( ~ (v1 = nil) & ( ~ totalorderedP(v1) | ~ leq(v0, v2))) | (cons(v0, v1) = v3 & totalorderedP(v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | tl(v2) = v0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | hd(v2) = v1) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v2, v1) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v1, v2) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v0, v1) = v2) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ gt(v1, v2) | ~ gt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ geq(v1, v2) | ~ geq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ lt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ leq(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ segmentP(v1, v2) | ~ segmentP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ rearsegP(v1, v2) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ frontsegP(v1, v2) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ geq(v1, v0) | ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v1, v0) | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ segmentP(v1, v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ rearsegP(v1, v0) | ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ frontsegP(v1, v0) | ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ ssList(v1) | ~ ssList(v0) | neq(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ ssItem(v1) | ~ ssItem(v0) | neq(v0, v1)) & ! [v0] : ! [v1] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ~ ssList(v0) | ssList(v1)) & ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ~ ssList(v0) | ssItem(v1)) & ! [v0] : ! [v1] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : ( ~ (tl(v0) = v1) | ~ ssList(v0) | ? [v2] : (hd(v0) = v2 & ! [v3] : (v3 = v0 | v3 = nil | v0 = nil | ~ (tl(v3) = v1) | ~ ssList(v3) | ? [v4] : ( ~ (v4 = v2) & hd(v3) = v4)))) & ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = v0) | ~ ssList(v0) | ~ ssItem(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = nil) | ~ ssList(v0) | ~ ssItem(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v1, nil) = v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | equalelemsP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | duplicatefreeP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderedP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderedP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | cyclefreeP(v1)) & ! [v0] : ! [v1] : ( ~ gt(v1, v0) | ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0] : ! [v1] : ( ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v1, v0)) & ! [v0] : ! [v1] : ( ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v1, v0)) & ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v1)) & ! [v0] : ! [v1] : ( ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v1)) & ! [v0] : ! [v1] : ( ~ leq(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v1)) & ! [v0] : ! [v1] : ( ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : ? [v3] : ? [v4] : (app(v3, v4) = v0 & app(v2, v1) = v3 & ssList(v4) & ssList(v2))) & ! [v0] : ! [v1] : ( ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v2, v1) = v0 & ssList(v2))) & ! [v0] : ! [v1] : ( ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v1, v2) = v0 & ssList(v2))) & ! [v0] : ! [v1] : ( ~ memberP(v0, v1) | ~ ssList(v0) | ~ ssItem(v1) | ? [v2] : ? [v3] : ? [v4] : (cons(v1, v3) = v4 & app(v2, v4) = v0 & ssList(v3) & ssList(v2))) & ! [v0] : (v0 = 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)) & ((all_0_2_2 = nil & all_0_3_3 = nil) | (frontsegP(all_0_2_2, all_0_3_3) & neq(all_0_3_3, nil))) % 51.19/15.04 | % 51.19/15.04 | Applying alpha-rule on (1) yields: % 51.19/15.04 | (2) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | hd(v2) = v1) % 51.19/15.04 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 51.19/15.04 | (4) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v2, v1) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v1)) % 51.19/15.04 | (5) ! [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))) % 51.19/15.04 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ segmentP(v1, v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) % 51.19/15.04 | (7) ssList(all_0_2_2) % 51.19/15.04 | (8) ! [v0] : ! [v1] : (v1 = v0 | ~ frontsegP(v1, v0) | ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) % 51.19/15.04 | (9) ! [v0] : ( ~ ssList(v0) | ~ neq(v0, v0)) % 51.19/15.04 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ ssList(v0)) % 51.19/15.04 | (11) ! [v0] : ! [v1] : ! [v2] : ( ~ rearsegP(v1, v2) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v2)) % 51.19/15.04 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | tl(v2) = v0) % 51.19/15.04 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2)) % 51.19/15.04 | (14) ! [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)) % 51.19/15.04 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v3, v0)) % 51.19/15.04 | (16) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v0, v1) = v2) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2)) % 51.19/15.04 | (17) ! [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))) % 51.19/15.04 | (18) ! [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)) % 51.19/15.04 | (19) ! [v0] : ( ~ singletonP(v0) | ~ ssList(v0) | ? [v1] : (cons(v1, nil) = v0 & ssItem(v1))) % 51.19/15.04 | (20) ! [v0] : ( ~ ssList(v0) | segmentP(v0, nil)) % 51.19/15.04 | (21) ! [v0] : ! [v1] : ( ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v2, v1) = v0 & ssList(v2))) % 51.19/15.04 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) % 51.36/15.04 | (23) ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ lt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2)) % 51.36/15.04 | (24) ! [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) % 51.36/15.04 | (25) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v1, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) % 51.36/15.04 | (26) totalorderedP(nil) % 51.36/15.05 | (27) ! [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)) % 51.36/15.05 | (28) neq(all_0_2_2, nil) % 51.36/15.05 | (29) ~ singletonP(nil) % 51.36/15.05 | (30) ! [v0] : ! [v1] : (v1 = v0 | ~ ssItem(v1) | ~ ssItem(v0) | neq(v0, v1)) % 51.36/15.05 | (31) ~ segmentP(all_0_2_2, all_0_3_3) % 51.36/15.05 | (32) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderP(v1)) % 51.36/15.05 | (33) ~ (all_0_0_0 = all_0_1_1) % 51.36/15.05 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2)) % 51.36/15.05 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) % 51.36/15.05 | (36) ! [v0] : (v0 = nil | ~ frontsegP(nil, v0) | ~ ssList(v0)) % 51.36/15.05 | (37) ssItem(all_0_1_1) % 51.36/15.05 | (38) ! [v0] : ! [v1] : ! [v2] : ( ~ (hd(v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : ((v1 = nil | (cons(v0, v1) = v3 & ~ totalorderedP(v3)) | (totalorderedP(v1) & leq(v0, v2))) & (( ~ (v1 = nil) & ( ~ totalorderedP(v1) | ~ leq(v0, v2))) | (cons(v0, v1) = v3 & totalorderedP(v3))))) % 51.36/15.05 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | hd(v3) = v1) % 51.36/15.05 | (40) ! [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)) % 51.36/15.05 | (41) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderedP(v1)) % 51.36/15.05 | (42) ! [v0] : ( ~ memberP(nil, v0) | ~ ssItem(v0)) % 51.36/15.05 | (43) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ ssList(v0)) % 51.36/15.05 | (44) ! [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))) % 51.36/15.05 | (45) ! [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))) % 51.36/15.05 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ~ ssList(v0) | ~ ssItem(v1) | cons(v1, v0) = v3) % 51.36/15.05 | (47) equalelemsP(nil) % 51.36/15.05 | (48) ssList(all_0_3_3) % 51.36/15.05 | (49) ! [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)) % 51.36/15.05 | (50) ! [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)) % 51.36/15.05 | (51) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | equalelemsP(v1)) % 51.36/15.05 | (52) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderP(v1)) % 51.36/15.05 | (53) ! [v0] : (v0 = nil | ~ segmentP(nil, v0) | ~ ssList(v0)) % 51.36/15.05 | (54) ! [v0] : ! [v1] : ( ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v1, v0)) % 51.36/15.05 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) % 51.36/15.05 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) % 51.36/15.05 | (57) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0)) % 51.36/15.05 | (58) ! [v0] : ! [v1] : ! [v2] : ( ~ (hd(v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : ((v1 = nil | (cons(v0, v1) = v3 & ~ strictorderedP(v3)) | (strictorderedP(v1) & lt(v0, v2))) & (( ~ (v1 = nil) & ( ~ strictorderedP(v1) | ~ lt(v0, v2))) | (cons(v0, v1) = v3 & strictorderedP(v3))))) % 51.36/15.06 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2)) % 51.36/15.06 | (60) ! [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))) % 51.36/15.06 | (61) strictorderP(nil) % 51.36/15.06 | (62) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2)) % 51.36/15.06 | (63) ! [v0] : ( ~ ssList(v0) | frontsegP(v0, v0)) % 51.36/15.06 | (64) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0)) % 51.36/15.06 | (65) ! [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))) % 51.36/15.06 | (66) totalorderP(nil) % 51.36/15.06 | (67) ! [v0] : ! [v1] : ! [v2] : ( ~ gt(v1, v2) | ~ gt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v2)) % 51.36/15.06 | (68) ! [v0] : (v0 = nil | ~ rearsegP(nil, v0) | ~ ssList(v0)) % 51.36/15.06 | (69) ! [v0] : ( ~ ssItem(v0) | leq(v0, v0)) % 51.36/15.06 | (70) ! [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)) % 51.36/15.06 | (71) ! [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)) % 51.36/15.06 | (72) ! [v0] : ( ~ ssList(v0) | rearsegP(v0, v0)) % 51.36/15.06 | (73) frontsegP(nil, nil) % 51.36/15.06 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 51.36/15.06 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v2, v0)) % 51.36/15.06 | (76) ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v1)) % 51.36/15.06 | (77) ! [v0] : ! [v1] : ! [v2] : ( ~ frontsegP(v1, v2) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v2)) % 51.36/15.06 | (78) ! [v0] : ( ~ ssItem(v0) | geq(v0, v0)) % 51.36/15.06 | (79) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderedP(v1)) % 51.36/15.06 | (80) ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 51.36/15.06 | (81) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | cyclefreeP(v1)) % 51.36/15.06 | (82) ! [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)) % 51.36/15.06 | (83) ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = v0) | ~ ssList(v0) | ~ ssItem(v1)) % 51.36/15.06 | (84) ! [v0] : ! [v1] : ( ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v1)) % 51.36/15.06 | (85) ! [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)) % 51.36/15.06 | (86) strictorderedP(nil) % 51.36/15.06 | (87) ! [v0] : ! [v1] : ( ~ leq(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v1)) % 51.36/15.06 | (88) ssList(nil) % 51.36/15.06 | (89) ! [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)) % 51.36/15.06 | (90) ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v1)) % 51.36/15.06 | (91) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v1, v2) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v1)) % 51.36/15.06 | (92) ! [v0] : ! [v1] : ( ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v1, v0)) % 51.36/15.06 | (93) ! [v0] : ! [v1] : (v1 = v0 | ~ rearsegP(v1, v0) | ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) % 51.36/15.07 | (94) ssItem(all_0_0_0) % 51.36/15.07 | (95) ! [v0] : ( ~ ssList(v0) | frontsegP(v0, nil)) % 51.36/15.07 | (96) ! [v0] : ! [v1] : ( ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v1, v2) = v0 & ssList(v2))) % 51.36/15.07 | (97) ! [v0] : ! [v1] : (v1 = v0 | ~ ssList(v1) | ~ ssList(v0) | neq(v0, v1)) % 51.36/15.07 | (98) duplicatefreeP(nil) % 51.36/15.07 | (99) (all_0_2_2 = nil & all_0_3_3 = nil) | (frontsegP(all_0_2_2, all_0_3_3) & neq(all_0_3_3, nil)) % 51.36/15.07 | (100) rearsegP(nil, nil) % 51.36/15.07 | (101) ! [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)) % 51.36/15.07 | (102) ! [v0] : ( ~ ssList(v0) | rearsegP(v0, nil)) % 51.36/15.07 | (103) ! [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)) % 51.36/15.07 | (104) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v0, v2) = v3) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v3, v1)) % 51.36/15.07 | (105) ! [v0] : ! [v1] : ( ~ (cons(v1, nil) = v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) % 51.36/15.07 | (106) ! [v0] : ! [v1] : ( ~ gt(v1, v0) | ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 51.36/15.07 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v1, v3) = v4) | ~ (app(v2, v4) = v0) | ~ ssList(v3) | ~ ssList(v2) | ~ ssList(v0) | ~ ssItem(v1) | memberP(v0, v1)) % 51.36/15.07 | (108) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | duplicatefreeP(v1)) % 51.36/15.07 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v2, v0) = v3) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1)) % 51.36/15.07 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) % 51.36/15.07 | (111) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ~ ssList(v0) | ssItem(v1)) % 51.36/15.07 | (112) ! [v0] : (v0 = nil | ~ ssList(v0) | ? [v1] : ? [v2] : (cons(v2, v1) = v0 & ssList(v1) & ssItem(v2))) % 51.36/15.07 | (113) ! [v0] : ! [v1] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0)) % 51.36/15.07 | (114) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ~ ssList(v0) | ssList(v1)) % 51.36/15.07 | (115) ! [v0] : ! [v1] : ! [v2] : ( ~ geq(v1, v2) | ~ geq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v2)) % 51.36/15.07 | (116) ! [v0] : ( ~ ssList(v0) | segmentP(v0, v0)) % 51.36/15.07 | (117) ! [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)))) % 51.36/15.07 | (118) ! [v0] : ! [v1] : ( ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : ? [v3] : ? [v4] : (app(v3, v4) = v0 & app(v2, v1) = v3 & ssList(v4) & ssList(v2))) % 51.36/15.07 | (119) segmentP(nil, nil) % 51.36/15.07 | (120) ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v1, v0) | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 51.36/15.07 | (121) ! [v0] : ( ~ neq(v0, v0) | ~ ssItem(v0)) % 51.36/15.07 | (122) ! [v0] : ( ~ lt(v0, v0) | ~ ssItem(v0)) % 51.36/15.07 | (123) ! [v0] : ! [v1] : ! [v2] : ( ~ segmentP(v1, v2) | ~ segmentP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v2)) % 51.36/15.07 | (124) ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = nil) | ~ ssList(v0) | ~ ssItem(v1)) % 51.36/15.07 | (125) cyclefreeP(nil) % 51.36/15.07 | (126) ! [v0] : ! [v1] : (v1 = v0 | ~ geq(v1, v0) | ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 51.36/15.07 | (127) ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0)) % 51.36/15.07 | (128) ! [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))) % 51.36/15.07 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0) | memberP(v1, v0)) % 51.36/15.07 | (130) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ~ ssList(v0)) % 51.36/15.08 | (131) ! [v0] : ! [v1] : ! [v2] : ( ~ leq(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v2)) % 51.36/15.08 | (132) ! [v0] : ! [v1] : ( ~ memberP(v0, v1) | ~ ssList(v0) | ~ ssItem(v1) | ? [v2] : ? [v3] : ? [v4] : (cons(v1, v3) = v4 & app(v2, v4) = v0 & ssList(v3) & ssList(v2))) % 51.36/15.08 | (133) ! [v0] : ! [v1] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0)) % 51.36/15.08 | % 51.36/15.08 | Instantiating formula (20) with all_0_2_2 and discharging atoms ssList(all_0_2_2), yields: % 51.36/15.08 | (134) segmentP(all_0_2_2, nil) % 51.36/15.08 | % 51.36/15.08 | Instantiating formula (102) with all_0_2_2 and discharging atoms ssList(all_0_2_2), yields: % 51.36/15.08 | (135) rearsegP(all_0_2_2, nil) % 51.36/15.08 | % 51.36/15.08 | Instantiating formula (72) with all_0_3_3 and discharging atoms ssList(all_0_3_3), yields: % 51.36/15.08 | (136) rearsegP(all_0_3_3, all_0_3_3) % 51.36/15.08 | % 51.36/15.08 | Instantiating formula (102) with all_0_3_3 and discharging atoms ssList(all_0_3_3), yields: % 51.36/15.08 | (137) rearsegP(all_0_3_3, nil) % 51.36/15.08 | % 51.36/15.08 | Instantiating formula (63) with all_0_3_3 and discharging atoms ssList(all_0_3_3), yields: % 51.36/15.08 | (138) frontsegP(all_0_3_3, all_0_3_3) % 51.36/15.08 | % 51.36/15.08 | Instantiating formula (95) with all_0_3_3 and discharging atoms ssList(all_0_3_3), yields: % 51.36/15.08 | (139) frontsegP(all_0_3_3, nil) % 51.36/15.08 | % 51.36/15.08 | Instantiating formula (118) with nil, nil and discharging atoms segmentP(nil, nil), ssList(nil), yields: % 51.36/15.08 | (140) ? [v0] : ? [v1] : ? [v2] : (app(v1, v2) = nil & app(v0, nil) = v1 & ssList(v2) & ssList(v0)) % 51.36/15.08 | % 51.36/15.08 | Instantiating formula (21) with nil, nil and discharging atoms rearsegP(nil, nil), ssList(nil), yields: % 51.36/15.08 | (141) ? [v0] : (app(v0, nil) = nil & ssList(v0)) % 51.36/15.08 | % 51.36/15.08 | Instantiating (141) with all_11_0_5 yields: % 51.36/15.08 | (142) app(all_11_0_5, nil) = nil & ssList(all_11_0_5) % 51.36/15.08 | % 51.36/15.08 | Applying alpha-rule on (142) yields: % 51.36/15.08 | (143) app(all_11_0_5, nil) = nil % 51.36/15.08 | (144) ssList(all_11_0_5) % 51.36/15.08 | % 51.36/15.08 | Instantiating (140) with all_13_0_6, all_13_1_7, all_13_2_8 yields: % 51.36/15.08 | (145) app(all_13_1_7, all_13_0_6) = nil & app(all_13_2_8, nil) = all_13_1_7 & ssList(all_13_0_6) & ssList(all_13_2_8) % 51.36/15.08 | % 51.36/15.08 | Applying alpha-rule on (145) yields: % 51.36/15.08 | (146) app(all_13_1_7, all_13_0_6) = nil % 51.36/15.08 | (147) app(all_13_2_8, nil) = all_13_1_7 % 51.36/15.08 | (148) ssList(all_13_0_6) % 51.36/15.08 | (149) ssList(all_13_2_8) % 51.36/15.08 | % 51.36/15.08 | Using (134) and (31) yields: % 51.36/15.08 | (150) ~ (all_0_3_3 = nil) % 51.36/15.08 | % 51.36/15.08 | Instantiating formula (43) with all_13_1_7, all_13_2_8 and discharging atoms app(all_13_2_8, nil) = all_13_1_7, ssList(all_13_2_8), yields: % 51.36/15.08 | (151) all_13_1_7 = all_13_2_8 % 51.36/15.08 | % 51.36/15.08 | Instantiating formula (43) with nil, all_11_0_5 and discharging atoms app(all_11_0_5, nil) = nil, ssList(all_11_0_5), yields: % 51.36/15.08 | (152) all_11_0_5 = nil % 51.36/15.08 | % 51.36/15.08 | Instantiating formula (133) with all_13_0_6, all_13_2_8 and discharging atoms ssList(all_13_0_6), ssList(all_13_2_8), yields: % 51.36/15.08 | (153) all_13_2_8 = nil | ~ (app(all_13_2_8, all_13_0_6) = nil) % 51.36/15.08 | % 51.36/15.08 | Instantiating formula (113) with all_13_0_6, all_11_0_5 and discharging atoms ssList(all_13_0_6), ssList(all_11_0_5), yields: % 51.36/15.08 | (154) all_13_0_6 = nil | ~ (app(all_11_0_5, all_13_0_6) = nil) % 51.36/15.08 | % 51.36/15.08 | From (151) and (146) follows: % 51.36/15.08 | (155) app(all_13_2_8, all_13_0_6) = nil % 51.36/15.08 | % 51.36/15.08 +-Applying beta-rule and splitting (99), into two cases. % 51.36/15.08 |-Branch one: % 51.36/15.08 | (156) all_0_2_2 = nil & all_0_3_3 = nil % 51.36/15.08 | % 51.36/15.08 | Applying alpha-rule on (156) yields: % 51.36/15.08 | (157) all_0_2_2 = nil % 51.36/15.08 | (158) all_0_3_3 = nil % 51.36/15.08 | % 51.36/15.08 | Equations (158) can reduce 150 to: % 51.36/15.08 | (159) $false % 51.36/15.08 | % 51.36/15.08 |-The branch is then unsatisfiable % 51.36/15.08 |-Branch two: % 51.36/15.08 | (160) frontsegP(all_0_2_2, all_0_3_3) & neq(all_0_3_3, nil) % 51.36/15.08 | % 51.36/15.08 | Applying alpha-rule on (160) yields: % 51.36/15.08 | (161) frontsegP(all_0_2_2, all_0_3_3) % 51.36/15.08 | (162) neq(all_0_3_3, nil) % 51.36/15.08 | % 51.36/15.08 +-Applying beta-rule and splitting (153), into two cases. % 51.36/15.08 |-Branch one: % 51.36/15.08 | (163) ~ (app(all_13_2_8, all_13_0_6) = nil) % 51.36/15.08 | % 51.36/15.08 | Using (155) and (163) yields: % 51.36/15.08 | (164) $false % 51.36/15.08 | % 51.36/15.08 |-The branch is then unsatisfiable % 51.36/15.08 |-Branch two: % 51.36/15.08 | (155) app(all_13_2_8, all_13_0_6) = nil % 51.36/15.08 | (166) all_13_2_8 = nil % 51.36/15.08 | % 51.36/15.08 | From (166) and (155) follows: % 51.36/15.08 | (167) app(nil, all_13_0_6) = nil % 51.36/15.08 | % 51.36/15.08 +-Applying beta-rule and splitting (154), into two cases. % 51.36/15.08 |-Branch one: % 51.36/15.08 | (168) ~ (app(all_11_0_5, all_13_0_6) = nil) % 51.36/15.08 | % 51.36/15.08 | From (152) and (168) follows: % 51.36/15.08 | (169) ~ (app(nil, all_13_0_6) = nil) % 51.36/15.09 | % 51.36/15.09 | Using (167) and (169) yields: % 51.36/15.09 | (164) $false % 51.36/15.09 | % 51.36/15.09 |-The branch is then unsatisfiable % 51.36/15.09 |-Branch two: % 51.36/15.09 | (171) app(all_11_0_5, all_13_0_6) = nil % 51.36/15.09 | (172) all_13_0_6 = nil % 51.36/15.09 | % 51.36/15.09 | From (172) and (148) follows: % 51.36/15.09 | (88) ssList(nil) % 51.36/15.09 | % 51.36/15.09 | Instantiating formula (21) with nil, all_0_2_2 and discharging atoms rearsegP(all_0_2_2, nil), ssList(all_0_2_2), ssList(nil), yields: % 51.36/15.09 | (174) ? [v0] : (app(v0, nil) = all_0_2_2 & ssList(v0)) % 51.36/15.09 | % 51.36/15.09 | Instantiating formula (21) with all_0_3_3, all_0_3_3 and discharging atoms rearsegP(all_0_3_3, all_0_3_3), ssList(all_0_3_3), yields: % 51.36/15.09 | (175) ? [v0] : (app(v0, all_0_3_3) = all_0_3_3 & ssList(v0)) % 51.36/15.09 | % 51.36/15.09 | Instantiating formula (21) with nil, all_0_3_3 and discharging atoms rearsegP(all_0_3_3, nil), ssList(all_0_3_3), ssList(nil), yields: % 51.36/15.09 | (176) ? [v0] : (app(v0, nil) = all_0_3_3 & ssList(v0)) % 51.36/15.09 | % 51.36/15.09 | Instantiating formula (96) with all_0_3_3, all_0_2_2 and discharging atoms frontsegP(all_0_2_2, all_0_3_3), ssList(all_0_2_2), ssList(all_0_3_3), yields: % 51.36/15.09 | (177) ? [v0] : (app(all_0_3_3, v0) = all_0_2_2 & ssList(v0)) % 51.36/15.09 | % 51.36/15.09 | Instantiating formula (96) with all_0_3_3, all_0_3_3 and discharging atoms frontsegP(all_0_3_3, all_0_3_3), ssList(all_0_3_3), yields: % 51.36/15.09 | (178) ? [v0] : (app(all_0_3_3, v0) = all_0_3_3 & ssList(v0)) % 51.36/15.09 | % 51.36/15.09 | Instantiating formula (96) with nil, all_0_3_3 and discharging atoms frontsegP(all_0_3_3, nil), ssList(all_0_3_3), ssList(nil), yields: % 51.36/15.09 | (179) ? [v0] : (app(nil, v0) = all_0_3_3 & ssList(v0)) % 51.36/15.09 | % 51.36/15.09 | Instantiating (179) with all_70_0_11 yields: % 51.36/15.09 | (180) app(nil, all_70_0_11) = all_0_3_3 & ssList(all_70_0_11) % 51.36/15.09 | % 51.36/15.09 | Applying alpha-rule on (180) yields: % 51.36/15.09 | (181) app(nil, all_70_0_11) = all_0_3_3 % 51.36/15.09 | (182) ssList(all_70_0_11) % 51.36/15.09 | % 51.36/15.09 | Instantiating (178) with all_72_0_12 yields: % 51.36/15.09 | (183) app(all_0_3_3, all_72_0_12) = all_0_3_3 & ssList(all_72_0_12) % 51.36/15.09 | % 51.36/15.09 | Applying alpha-rule on (183) yields: % 51.36/15.09 | (184) app(all_0_3_3, all_72_0_12) = all_0_3_3 % 51.36/15.09 | (185) ssList(all_72_0_12) % 51.36/15.09 | % 51.36/15.09 | Instantiating (176) with all_74_0_13 yields: % 51.36/15.09 | (186) app(all_74_0_13, nil) = all_0_3_3 & ssList(all_74_0_13) % 51.36/15.09 | % 51.36/15.09 | Applying alpha-rule on (186) yields: % 51.36/15.09 | (187) app(all_74_0_13, nil) = all_0_3_3 % 51.36/15.09 | (188) ssList(all_74_0_13) % 51.36/15.09 | % 51.36/15.09 | Instantiating (175) with all_76_0_14 yields: % 51.36/15.09 | (189) app(all_76_0_14, all_0_3_3) = all_0_3_3 & ssList(all_76_0_14) % 51.36/15.09 | % 51.36/15.09 | Applying alpha-rule on (189) yields: % 51.36/15.09 | (190) app(all_76_0_14, all_0_3_3) = all_0_3_3 % 51.36/15.09 | (191) ssList(all_76_0_14) % 51.36/15.09 | % 51.36/15.09 | Instantiating (174) with all_78_0_15 yields: % 51.36/15.09 | (192) app(all_78_0_15, nil) = all_0_2_2 & ssList(all_78_0_15) % 51.36/15.09 | % 51.36/15.09 | Applying alpha-rule on (192) yields: % 51.36/15.09 | (193) app(all_78_0_15, nil) = all_0_2_2 % 51.36/15.09 | (194) ssList(all_78_0_15) % 51.36/15.09 | % 51.36/15.09 | Instantiating (177) with all_92_0_30 yields: % 51.36/15.09 | (195) app(all_0_3_3, all_92_0_30) = all_0_2_2 & ssList(all_92_0_30) % 51.36/15.09 | % 51.36/15.09 | Applying alpha-rule on (195) yields: % 51.36/15.09 | (196) app(all_0_3_3, all_92_0_30) = all_0_2_2 % 51.36/15.09 | (197) ssList(all_92_0_30) % 51.36/15.09 | % 51.36/15.09 | Instantiating formula (43) with all_0_2_2, all_78_0_15 and discharging atoms app(all_78_0_15, nil) = all_0_2_2, ssList(all_78_0_15), yields: % 51.36/15.09 | (198) all_78_0_15 = all_0_2_2 % 51.36/15.09 | % 51.36/15.09 | Instantiating formula (43) with all_0_3_3, all_74_0_13 and discharging atoms app(all_74_0_13, nil) = all_0_3_3, ssList(all_74_0_13), yields: % 51.36/15.09 | (199) all_74_0_13 = all_0_3_3 % 51.36/15.09 | % 51.36/15.09 | Instantiating formula (10) with all_0_3_3, all_70_0_11 and discharging atoms app(nil, all_70_0_11) = all_0_3_3, ssList(all_70_0_11), yields: % 51.36/15.09 | (200) all_70_0_11 = all_0_3_3 % 51.36/15.09 | % 51.36/15.09 | From (199) and (187) follows: % 51.36/15.09 | (201) app(all_0_3_3, nil) = all_0_3_3 % 51.36/15.09 | % 51.36/15.09 | From (200) and (181) follows: % 51.36/15.09 | (202) app(nil, all_0_3_3) = all_0_3_3 % 51.36/15.09 | % 51.36/15.09 | From (198) and (194) follows: % 51.36/15.09 | (7) ssList(all_0_2_2) % 51.36/15.09 | % 51.36/15.09 | From (200) and (182) follows: % 51.36/15.09 | (48) ssList(all_0_3_3) % 51.36/15.09 | % 51.36/15.09 | Instantiating formula (35) with nil, all_0_3_3, all_0_3_3, all_72_0_12 and discharging atoms app(all_0_3_3, all_72_0_12) = all_0_3_3, app(all_0_3_3, nil) = all_0_3_3, ssList(all_72_0_12), ssList(all_0_3_3), ssList(nil), yields: % 51.36/15.09 | (205) all_72_0_12 = nil % 51.36/15.09 | % 51.36/15.09 | Instantiating formula (55) with nil, all_0_3_3, all_0_3_3, all_76_0_14 and discharging atoms app(all_76_0_14, all_0_3_3) = all_0_3_3, app(nil, all_0_3_3) = all_0_3_3, ssList(all_76_0_14), ssList(all_0_3_3), ssList(nil), yields: % 51.36/15.09 | (206) all_76_0_14 = nil % 51.36/15.09 | % 51.36/15.09 | From (206) and (190) follows: % 51.36/15.09 | (202) app(nil, all_0_3_3) = all_0_3_3 % 51.36/15.09 | % 51.36/15.09 | From (205) and (185) follows: % 51.36/15.09 | (88) ssList(nil) % 51.36/15.09 | % 51.36/15.09 | Instantiating formula (22) with all_92_0_30, all_0_3_3, nil, all_0_3_3, all_0_2_2 and discharging atoms app(all_0_3_3, all_92_0_30) = all_0_2_2, app(nil, all_0_3_3) = all_0_3_3, ssList(all_92_0_30), ssList(all_0_2_2), ssList(all_0_3_3), ssList(nil), ~ segmentP(all_0_2_2, all_0_3_3), yields: % 51.36/15.09 | (164) $false % 51.36/15.09 | % 51.36/15.09 |-The branch is then unsatisfiable % 51.36/15.09 % SZS output end Proof for theBenchmark % 51.36/15.09 % 51.36/15.09 14477ms %------------------------------------------------------------------------------