%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWC229+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n005.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 20:16:57 EDT 2022 % Result : Theorem 36.35s 14.30s % Output : Proof 55.21s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.11 % Problem : SWC229+1 : TPTP v8.1.0. Released v2.4.0. % 0.03/0.11 % Command : ePrincess-casc -timeout=%d %s % 0.11/0.32 % Computer : n005.cluster.edu % 0.11/0.32 % Model : x86_64 x86_64 % 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.32 % Memory : 8042.1875MB % 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.32 % CPULimit : 300 % 0.11/0.32 % WCLimit : 600 % 0.11/0.32 % DateTime : Sun Jun 12 18:03:24 EDT 2022 % 0.11/0.32 % CPUTime : % 0.44/0.57 ____ _ % 0.44/0.57 ___ / __ \_____(_)___ ________ __________ % 0.44/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.44/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.44/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.44/0.57 % 0.44/0.57 A Theorem Prover for First-Order Logic % 0.44/0.57 (ePrincess v.1.0) % 0.44/0.57 % 0.44/0.57 (c) Philipp Rümmer, 2009-2015 % 0.44/0.57 (c) Peter Backeman, 2014-2015 % 0.44/0.57 (contributions by Angelo Brillout, Peter Baumgartner) % 0.44/0.57 Free software under GNU Lesser General Public License (LGPL). % 0.44/0.57 Bug reports to peter@backeman.se % 0.44/0.57 % 0.44/0.57 For more information, visit http://user.uu.se/~petba168/breu/ % 0.44/0.57 % 0.44/0.57 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ... % 0.57/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.18/1.37 Prover 0: Preprocessing ... % 4.85/2.52 Prover 0: Constructing countermodel ... % 15.10/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 15.65/6.08 Prover 1: Preprocessing ... % 17.08/6.53 Prover 1: Constructing countermodel ... % 22.66/8.54 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 22.83/8.61 Prover 2: Preprocessing ... % 24.45/9.09 Prover 2: Warning: ignoring some quantifiers % 24.58/9.13 Prover 2: Constructing countermodel ... % 30.85/11.55 Prover 0: stopped % 31.16/11.75 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 31.56/11.82 Prover 3: Preprocessing ... % 31.56/11.90 Prover 3: Constructing countermodel ... % 36.35/14.30 Prover 3: proved (2547ms) % 36.35/14.30 Prover 1: stopped % 36.35/14.30 Prover 2: stopped % 36.35/14.30 % 36.35/14.30 No countermodel exists, formula is valid % 36.35/14.30 % SZS status Theorem for theBenchmark % 36.35/14.30 % 36.35/14.30 Generating proof ... found it (size 116) % 54.30/22.47 % 54.30/22.47 % SZS output start Proof for theBenchmark % 54.30/22.47 Assumed formulas after preprocessing and simplification: % 54.30/22.48 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ( ~ (v3 = v2) & ~ (v0 = nil) & equalelemsP(nil) & duplicatefreeP(nil) & strictorderedP(nil) & totalorderedP(nil) & strictorderP(nil) & totalorderP(nil) & cyclefreeP(nil) & segmentP(v1, v0) & segmentP(nil, nil) & rearsegP(nil, nil) & frontsegP(nil, nil) & ssList(v1) & ssList(v0) & ssList(nil) & ssItem(v3) & ssItem(v2) & ~ 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(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(v7, v6) = v8) | ~ (app(v5, v4) = v6) | ~ ssList(v5) | ~ ssList(v4) | ~ ssItem(v7) | ? [v9] : (cons(v7, v5) = v9 & app(v9, v4) = v8)) & ! [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)) & ! [v4] : ( ~ ssItem(v4) | ? [v5] : (cons(v4, nil) = v5 & ! [v6] : ( ~ ssList(v6) | ? [v7] : (app(v6, v5) = v7 & ! [v8] : ( ~ ssList(v8) | ? [v9] : (( ~ (v9 = v0) & app(v7, v8) = v9) | (leq(v4, v9) & memberP(v8, v9) & memberP(v6, v9) & ssItem(v9) & ~ leq(v9, v4)))))))) & ( ~ neq(v1, nil) | singletonP(v0))) % 54.64/22.63 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3 yields: % 54.64/22.63 | (1) ~ (all_0_0_0 = all_0_1_1) & ~ (all_0_3_3 = nil) & equalelemsP(nil) & duplicatefreeP(nil) & strictorderedP(nil) & totalorderedP(nil) & strictorderP(nil) & totalorderP(nil) & cyclefreeP(nil) & segmentP(all_0_2_2, all_0_3_3) & segmentP(nil, nil) & rearsegP(nil, nil) & frontsegP(nil, nil) & ssList(all_0_2_2) & ssList(all_0_3_3) & ssList(nil) & ssItem(all_0_0_0) & ssItem(all_0_1_1) & ~ singletonP(nil) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v2, v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ strictorderedP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | lt(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v2, v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ totalorderedP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | leq(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v2, v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ strictorderP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | lt(v2, v1) | lt(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v2, v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ totalorderP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1) | leq(v2, v1) | leq(v1, v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v2, v7) = v8) | ~ (cons(v1, v4) = v5) | ~ (app(v6, v8) = v0) | ~ (app(v3, v5) = v6) | ~ leq(v2, v1) | ~ leq(v1, v2) | ~ cyclefreeP(v0) | ~ ssList(v7) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (cons(v1, v6) = v7) | ~ (cons(v1, v3) = v4) | ~ (app(v5, v7) = v0) | ~ (app(v2, v4) = v5) | ~ duplicatefreeP(v0) | ~ ssList(v6) | ~ ssList(v3) | ~ ssList(v2) | ~ ssList(v0) | ~ ssItem(v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (cons(v2, v4) = v5) | ~ (cons(v1, v5) = v6) | ~ (app(v3, v6) = v0) | ~ equalelemsP(v0) | ~ ssList(v4) | ~ ssList(v3) | ~ ssList(v0) | ~ ssItem(v2) | ~ ssItem(v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v1 = v0 | ~ (cons(v1, v4) = v5) | ~ (cons(v0, v2) = v3) | ~ frontsegP(v3, v5) | ~ ssList(v4) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (cons(v1, v4) = v5) | ~ (cons(v0, v2) = v3) | ~ frontsegP(v3, v5) | ~ ssList(v4) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | frontsegP(v2, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (app(v3, v4) = v5) | ~ (app(v2, v0) = v3) | ~ segmentP(v0, v1) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v5, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v3, v2) = v4) | ~ (app(v1, v0) = v2) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v3) | ? [v5] : (cons(v3, v1) = v5 & app(v5, v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v1, v3) = v4) | ~ (app(v2, v4) = v0) | ~ ssList(v3) | ~ ssList(v2) | ~ ssList(v0) | ~ ssItem(v1) | memberP(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v0, v3) = v4) | ~ (cons(v0, v1) = v2) | ~ frontsegP(v1, v3) | ~ ssList(v3) | ~ ssList(v1) | ~ ssItem(v0) | frontsegP(v2, v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0) | ? [v5] : (app(v1, v3) = v5 & app(v0, v5) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ~ ssList(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | ? [v4] : (tl(v4) = v3 & app(v0, v2) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | hd(v3) = v1) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ~ ssList(v0) | ~ ssItem(v1) | cons(v1, v0) = v3) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v2, v0) = v3) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0) | memberP(v1, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v1, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v0, v2) = v3) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v3, v1)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (hd(v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : ((v1 = nil | (cons(v0, v1) = v3 & ~ strictorderedP(v3)) | (strictorderedP(v1) & lt(v0, v2))) & (( ~ (v1 = nil) & ( ~ strictorderedP(v1) | ~ lt(v0, v2))) | (cons(v0, v1) = v3 & strictorderedP(v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (hd(v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | ? [v3] : ((v1 = nil | (cons(v0, v1) = v3 & ~ totalorderedP(v3)) | (totalorderedP(v1) & leq(v0, v2))) & (( ~ (v1 = nil) & ( ~ totalorderedP(v1) | ~ leq(v0, v2))) | (cons(v0, v1) = v3 & totalorderedP(v3))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | tl(v2) = v0) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | hd(v2) = v1) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v2, v1) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v1, v2) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v1)) & ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v0, v1) = v2) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ gt(v1, v2) | ~ gt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ geq(v1, v2) | ~ geq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ lt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ leq(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ segmentP(v1, v2) | ~ segmentP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ rearsegP(v1, v2) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v2)) & ! [v0] : ! [v1] : ! [v2] : ( ~ frontsegP(v1, v2) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ geq(v1, v0) | ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v1, v0) | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ segmentP(v1, v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ rearsegP(v1, v0) | ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ frontsegP(v1, v0) | ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v1 = v0 | ~ ssList(v1) | ~ ssList(v0) | neq(v0, v1)) & ! [v0] : ! [v1] : (v1 = v0 | ~ ssItem(v1) | ~ ssItem(v0) | neq(v0, v1)) & ! [v0] : ! [v1] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ~ ssList(v0) | ssList(v1)) & ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ~ ssList(v0) | ssItem(v1)) & ! [v0] : ! [v1] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0)) & ! [v0] : ! [v1] : ( ~ (tl(v0) = v1) | ~ ssList(v0) | ? [v2] : (hd(v0) = v2 & ! [v3] : (v3 = v0 | v3 = nil | v0 = nil | ~ (tl(v3) = v1) | ~ ssList(v3) | ? [v4] : ( ~ (v4 = v2) & hd(v3) = v4)))) & ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = v0) | ~ ssList(v0) | ~ ssItem(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = nil) | ~ ssList(v0) | ~ ssItem(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v1, nil) = v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | equalelemsP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | duplicatefreeP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderedP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderedP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderP(v1)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | cyclefreeP(v1)) & ! [v0] : ! [v1] : ( ~ gt(v1, v0) | ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0] : ! [v1] : ( ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v1, v0)) & ! [v0] : ! [v1] : ( ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v1, v0)) & ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) & ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v1)) & ! [v0] : ! [v1] : ( ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v1)) & ! [v0] : ! [v1] : ( ~ leq(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v1)) & ! [v0] : ! [v1] : ( ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : ? [v3] : ? [v4] : (app(v3, v4) = v0 & app(v2, v1) = v3 & ssList(v4) & ssList(v2))) & ! [v0] : ! [v1] : ( ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v2, v1) = v0 & ssList(v2))) & ! [v0] : ! [v1] : ( ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v1, v2) = v0 & ssList(v2))) & ! [v0] : ! [v1] : ( ~ memberP(v0, v1) | ~ ssList(v0) | ~ ssItem(v1) | ? [v2] : ? [v3] : ? [v4] : (cons(v1, v3) = v4 & app(v2, v4) = v0 & ssList(v3) & ssList(v2))) & ! [v0] : (v0 = 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)) & ! [v0] : ( ~ ssItem(v0) | ? [v1] : (cons(v0, nil) = v1 & ! [v2] : ( ~ ssList(v2) | ? [v3] : (app(v2, v1) = v3 & ! [v4] : ( ~ ssList(v4) | ? [v5] : (( ~ (v5 = all_0_3_3) & app(v3, v4) = v5) | (leq(v0, v5) & memberP(v4, v5) & memberP(v2, v5) & ssItem(v5) & ~ leq(v5, v0)))))))) & ( ~ neq(all_0_2_2, nil) | singletonP(all_0_3_3)) % 54.93/22.67 | % 54.93/22.67 | Applying alpha-rule on (1) yields: % 54.93/22.68 | (2) ! [v0] : (v0 = nil | ~ rearsegP(nil, v0) | ~ ssList(v0)) % 54.93/22.68 | (3) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) % 54.93/22.68 | (4) ! [v0] : ( ~ ssItem(v0) | ? [v1] : (cons(v0, nil) = v1 & ! [v2] : ( ~ ssList(v2) | ? [v3] : (app(v2, v1) = v3 & ! [v4] : ( ~ ssList(v4) | ? [v5] : (( ~ (v5 = all_0_3_3) & app(v3, v4) = v5) | (leq(v0, v5) & memberP(v4, v5) & memberP(v2, v5) & ssItem(v5) & ~ leq(v5, v0)))))))) % 54.93/22.68 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v2, v0)) % 54.93/22.68 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ geq(v1, v0) | ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 54.93/22.68 | (7) ! [v0] : ! [v1] : ( ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v2, v1) = v0 & ssList(v2))) % 54.93/22.68 | (8) ! [v0] : ! [v1] : ( ~ memberP(v0, v1) | ~ ssList(v0) | ~ ssItem(v1) | ? [v2] : ? [v3] : ? [v4] : (cons(v1, v3) = v4 & app(v2, v4) = v0 & ssList(v3) & ssList(v2))) % 54.93/22.68 | (9) totalorderedP(nil) % 54.93/22.68 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v1, v2) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v1)) % 54.93/22.68 | (11) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v3, v0)) % 54.93/22.68 | (12) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderP(v1)) % 54.93/22.68 | (13) ! [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)) % 54.93/22.68 | (14) ! [v0] : ( ~ ssList(v0) | segmentP(v0, nil)) % 54.93/22.68 | (15) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2)) % 54.93/22.68 | (16) ssList(all_0_2_2) % 54.93/22.68 | (17) ! [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))) % 54.93/22.68 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2)) % 54.93/22.68 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v1, v3) = v4) | ~ (app(v2, v4) = v0) | ~ ssList(v3) | ~ ssList(v2) | ~ ssList(v0) | ~ ssItem(v1) | memberP(v0, v1)) % 54.93/22.68 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v1, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) % 54.93/22.68 | (21) ! [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)) % 54.93/22.68 | (22) ! [v0] : ! [v1] : ( ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : ? [v3] : ? [v4] : (app(v3, v4) = v0 & app(v2, v1) = v3 & ssList(v4) & ssList(v2))) % 54.93/22.68 | (23) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | duplicatefreeP(v1)) % 54.93/22.68 | (24) ! [v0] : ( ~ ssList(v0) | cyclefreeP(v0) | ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : (cons(v2, v7) = v8 & cons(v1, v4) = v5 & app(v6, v8) = v0 & app(v3, v5) = v6 & leq(v2, v1) & leq(v1, v2) & ssList(v7) & ssList(v4) & ssList(v3) & ssItem(v2) & ssItem(v1))) % 55.01/22.68 | (25) ! [v0] : ! [v1] : (v1 = v0 | ~ segmentP(v1, v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) % 55.01/22.68 | (26) ! [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)) % 55.01/22.68 | (27) ! [v0] : ! [v1] : ( ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v1)) % 55.01/22.68 | (28) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderP(v1)) % 55.01/22.68 | (29) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ ssList(v0)) % 55.01/22.69 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 55.01/22.69 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ geq(v1, v2) | ~ geq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v2)) % 55.01/22.69 | (32) strictorderedP(nil) % 55.01/22.69 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) % 55.01/22.69 | (34) ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v1)) % 55.01/22.69 | (35) ! [v0] : ( ~ ssList(v0) | frontsegP(v0, v0)) % 55.01/22.69 | (36) ! [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)))) % 55.01/22.69 | (37) ! [v0] : ! [v1] : (v1 = v0 | ~ ssList(v1) | ~ ssList(v0) | neq(v0, v1)) % 55.01/22.69 | (38) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | hd(v3) = v1) % 55.01/22.69 | (39) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | cyclefreeP(v1)) % 55.01/22.69 | (40) ! [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)) % 55.01/22.69 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ~ ssList(v0)) % 55.01/22.70 | (42) ssItem(all_0_0_0) % 55.01/22.70 | (43) ! [v0] : ! [v1] : ( ~ leq(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v1)) % 55.01/22.70 | (44) ! [v0] : ( ~ ssList(v0) | rearsegP(v0, nil)) % 55.01/22.70 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) % 55.01/22.70 | (46) ! [v0] : ( ~ ssList(v0) | segmentP(v0, v0)) % 55.01/22.70 | (47) ! [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)) % 55.01/22.70 | (48) ! [v0] : ( ~ ssItem(v0) | leq(v0, v0)) % 55.01/22.70 | (49) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0)) % 55.01/22.70 | (50) ! [v0] : ( ~ neq(v0, v0) | ~ ssItem(v0)) % 55.01/22.70 | (51) ~ (all_0_0_0 = all_0_1_1) % 55.01/22.70 | (52) ! [v0] : (v0 = nil | ~ segmentP(nil, v0) | ~ ssList(v0)) % 55.01/22.70 | (53) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) % 55.01/22.70 | (54) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ~ ssList(v0) | ssItem(v1)) % 55.01/22.70 | (55) ! [v0] : ! [v1] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0)) % 55.01/22.70 | (56) ! [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))))) % 55.01/22.70 | (57) ! [v0] : ( ~ singletonP(v0) | ~ ssList(v0) | ? [v1] : (cons(v1, nil) = v0 & ssItem(v1))) % 55.01/22.70 | (58) ! [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)) % 55.01/22.70 | (59) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) % 55.01/22.70 | (60) ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = v0) | ~ ssList(v0) | ~ ssItem(v1)) % 55.01/22.70 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2)) % 55.01/22.70 | (62) ! [v0] : ! [v1] : ( ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v1, v0)) % 55.01/22.70 | (63) segmentP(nil, nil) % 55.01/22.70 | (64) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 55.01/22.70 | (65) ! [v0] : ( ~ ssList(v0) | rearsegP(v0, v0)) % 55.01/22.70 | (66) ! [v0] : ( ~ lt(v0, v0) | ~ ssItem(v0)) % 55.01/22.70 | (67) ! [v0] : ! [v1] : ( ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v1, v2) = v0 & ssList(v2))) % 55.01/22.70 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v0, v2) = v3) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v3, v1)) % 55.01/22.70 | (69) ! [v0] : ! [v1] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0)) % 55.01/22.70 | (70) cyclefreeP(nil) % 55.01/22.70 | (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))) % 55.01/22.70 | (72) ! [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))) % 55.01/22.70 | (73) ! [v0] : ! [v1] : (v1 = v0 | ~ rearsegP(v1, v0) | ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) % 55.01/22.70 | (74) frontsegP(nil, nil) % 55.01/22.71 | (75) ! [v0] : (v0 = nil | ~ ssList(v0) | ? [v1] : ? [v2] : (cons(v2, v1) = v0 & ssList(v1) & ssItem(v2))) % 55.01/22.71 | (76) ! [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))) % 55.01/22.71 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0) | memberP(v1, v0)) % 55.01/22.71 | (78) ! [v0] : ( ~ ssList(v0) | ~ neq(v0, v0)) % 55.01/22.71 | (79) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | equalelemsP(v1)) % 55.01/22.71 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v2, v0) = v3) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1)) % 55.01/22.71 | (81) ! [v0] : ( ~ ssList(v0) | frontsegP(v0, nil)) % 55.01/22.71 | (82) equalelemsP(nil) % 55.01/22.71 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0)) % 55.01/22.71 | (84) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | hd(v2) = v1) % 55.01/22.71 | (85) ~ neq(all_0_2_2, nil) | singletonP(all_0_3_3) % 55.01/22.71 | (86) ! [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))))) % 55.01/22.71 | (87) ! [v0] : ! [v1] : ! [v2] : ( ~ segmentP(v1, v2) | ~ segmentP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v2)) % 55.01/22.71 | (88) ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v1, v0) | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 55.01/22.71 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2)) % 55.01/22.71 | (90) ! [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)) % 55.01/22.71 | (91) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v0, v1) = v2) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2)) % 55.01/22.71 | (92) strictorderP(nil) % 55.01/22.71 | (93) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderedP(v1)) % 55.01/22.71 | (94) duplicatefreeP(nil) % 55.01/22.71 | (95) ~ singletonP(nil) % 55.01/22.71 | (96) ! [v0] : ! [v1] : ( ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v1, v0)) % 55.01/22.71 | (97) ! [v0] : ! [v1] : ! [v2] : ( ~ rearsegP(v1, v2) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v2)) % 55.01/22.71 | (98) ! [v0] : ! [v1] : ! [v2] : ( ~ gt(v1, v2) | ~ gt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v2)) % 55.01/22.71 | (99) rearsegP(nil, nil) % 55.01/22.71 | (100) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v2, v1) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v1)) % 55.01/22.71 | (101) ! [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)) % 55.01/22.71 | (102) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ~ ssList(v0) | ssList(v1)) % 55.01/22.71 | (103) ! [v0] : (v0 = nil | ~ frontsegP(nil, v0) | ~ ssList(v0)) % 55.01/22.71 | (104) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderedP(v1)) % 55.01/22.71 | (105) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | tl(v2) = v0) % 55.01/22.71 | (106) ! [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)) % 55.01/22.71 | (107) ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0)) % 55.01/22.71 | (108) ! [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)) % 55.01/22.71 | (109) segmentP(all_0_2_2, all_0_3_3) % 55.01/22.71 | (110) ssItem(all_0_1_1) % 55.01/22.71 | (111) ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ lt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2)) % 55.01/22.71 | (112) ! [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))) % 55.01/22.71 | (113) ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v1)) % 55.01/22.71 | (114) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ ssList(v0)) % 55.01/22.71 | (115) ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = nil) | ~ ssList(v0) | ~ ssItem(v1)) % 55.01/22.71 | (116) ! [v0] : ! [v1] : ( ~ gt(v1, v0) | ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 55.01/22.71 | (117) ! [v0] : ! [v1] : ( ~ (cons(v1, nil) = v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) % 55.01/22.71 | (118) ! [v0] : ( ~ ssItem(v0) | geq(v0, v0)) % 55.01/22.71 | (119) ! [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))) % 55.01/22.71 | (120) ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 55.01/22.71 | (121) ! [v0] : ( ~ memberP(nil, v0) | ~ ssItem(v0)) % 55.01/22.71 | (122) ! [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)) % 55.01/22.72 | (123) ! [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)) % 55.01/22.72 | (124) ssList(nil) % 55.01/22.72 | (125) ! [v0] : ! [v1] : (v1 = v0 | ~ frontsegP(v1, v0) | ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) % 55.01/22.72 | (126) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ~ ssList(v0) | ~ ssItem(v1) | cons(v1, v0) = v3) % 55.01/22.72 | (127) ! [v0] : ! [v1] : (v1 = v0 | ~ ssItem(v1) | ~ ssItem(v0) | neq(v0, v1)) % 55.01/22.72 | (128) ! [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)) % 55.01/22.72 | (129) totalorderP(nil) % 55.01/22.72 | (130) ! [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)) % 55.01/22.72 | (131) ~ (all_0_3_3 = nil) % 55.01/22.72 | (132) ssList(all_0_3_3) % 55.13/22.72 | (133) ! [v0] : ! [v1] : ! [v2] : ( ~ frontsegP(v1, v2) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v2)) % 55.13/22.73 | (134) ! [v0] : ! [v1] : ! [v2] : ( ~ leq(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v2)) % 55.13/22.73 | % 55.13/22.73 | Instantiating formula (52) with all_0_3_3 and discharging atoms ssList(all_0_3_3), yields: % 55.13/22.73 | (135) all_0_3_3 = nil | ~ segmentP(nil, all_0_3_3) % 55.13/22.73 | % 55.13/22.73 | Instantiating formula (75) with all_0_2_2 and discharging atoms ssList(all_0_2_2), yields: % 55.13/22.73 | (136) all_0_2_2 = nil | ? [v0] : ? [v1] : (cons(v1, v0) = all_0_2_2 & ssList(v0) & ssItem(v1)) % 55.13/22.73 | % 55.13/22.73 | Instantiating formula (75) with all_0_3_3 and discharging atoms ssList(all_0_3_3), yields: % 55.13/22.73 | (137) all_0_3_3 = nil | ? [v0] : ? [v1] : (cons(v1, v0) = all_0_3_3 & ssList(v0) & ssItem(v1)) % 55.13/22.73 | % 55.13/22.73 | Instantiating formula (81) with all_0_3_3 and discharging atoms ssList(all_0_3_3), yields: % 55.13/22.73 | (138) frontsegP(all_0_3_3, nil) % 55.13/22.73 | % 55.13/22.73 | Instantiating formula (22) with nil, nil and discharging atoms segmentP(nil, nil), ssList(nil), yields: % 55.13/22.73 | (139) ? [v0] : ? [v1] : ? [v2] : (app(v1, v2) = nil & app(v0, nil) = v1 & ssList(v2) & ssList(v0)) % 55.13/22.73 | % 55.13/22.73 | Instantiating formula (67) with nil, nil and discharging atoms frontsegP(nil, nil), ssList(nil), yields: % 55.13/22.73 | (140) ? [v0] : (app(nil, v0) = nil & ssList(v0)) % 55.13/22.73 | % 55.13/22.73 | Instantiating formula (37) with nil, all_0_2_2 and discharging atoms ssList(all_0_2_2), ssList(nil), yields: % 55.13/22.73 | (141) all_0_2_2 = nil | neq(all_0_2_2, nil) % 55.13/22.73 | % 55.13/22.73 | Instantiating (140) with all_14_0_8 yields: % 55.13/22.73 | (142) app(nil, all_14_0_8) = nil & ssList(all_14_0_8) % 55.13/22.73 | % 55.13/22.73 | Applying alpha-rule on (142) yields: % 55.13/22.73 | (143) app(nil, all_14_0_8) = nil % 55.13/22.73 | (144) ssList(all_14_0_8) % 55.13/22.73 | % 55.13/22.73 | Instantiating (139) with all_19_0_10, all_19_1_11, all_19_2_12 yields: % 55.13/22.73 | (145) app(all_19_1_11, all_19_0_10) = nil & app(all_19_2_12, nil) = all_19_1_11 & ssList(all_19_0_10) & ssList(all_19_2_12) % 55.13/22.73 | % 55.13/22.73 | Applying alpha-rule on (145) yields: % 55.13/22.73 | (146) app(all_19_1_11, all_19_0_10) = nil % 55.13/22.73 | (147) app(all_19_2_12, nil) = all_19_1_11 % 55.13/22.73 | (148) ssList(all_19_0_10) % 55.13/22.73 | (149) ssList(all_19_2_12) % 55.13/22.73 | % 55.13/22.73 +-Applying beta-rule and splitting (135), into two cases. % 55.13/22.73 |-Branch one: % 55.13/22.73 | (150) ~ segmentP(nil, all_0_3_3) % 55.13/22.73 | % 55.13/22.73 +-Applying beta-rule and splitting (137), into two cases. % 55.13/22.73 |-Branch one: % 55.13/22.73 | (151) all_0_3_3 = nil % 55.13/22.73 | % 55.13/22.74 | Equations (151) can reduce 131 to: % 55.13/22.74 | (152) $false % 55.13/22.74 | % 55.13/22.74 |-The branch is then unsatisfiable % 55.13/22.74 |-Branch two: % 55.13/22.74 | (131) ~ (all_0_3_3 = nil) % 55.13/22.74 | (154) ? [v0] : ? [v1] : (cons(v1, v0) = all_0_3_3 & ssList(v0) & ssItem(v1)) % 55.13/22.74 | % 55.13/22.74 | Instantiating (154) with all_87_0_41, all_87_1_42 yields: % 55.13/22.74 | (155) cons(all_87_0_41, all_87_1_42) = all_0_3_3 & ssList(all_87_1_42) & ssItem(all_87_0_41) % 55.13/22.74 | % 55.13/22.74 | Applying alpha-rule on (155) yields: % 55.13/22.74 | (156) cons(all_87_0_41, all_87_1_42) = all_0_3_3 % 55.13/22.74 | (157) ssList(all_87_1_42) % 55.13/22.74 | (158) ssItem(all_87_0_41) % 55.13/22.74 | % 55.13/22.74 | Instantiating formula (29) with all_19_1_11, all_19_2_12 and discharging atoms app(all_19_2_12, nil) = all_19_1_11, ssList(all_19_2_12), yields: % 55.13/22.74 | (159) all_19_1_11 = all_19_2_12 % 55.13/22.74 | % 55.13/22.74 | Instantiating formula (114) with nil, all_14_0_8 and discharging atoms app(nil, all_14_0_8) = nil, ssList(all_14_0_8), yields: % 55.13/22.74 | (160) all_14_0_8 = nil % 55.13/22.74 | % 55.13/22.74 | Instantiating formula (55) with all_19_0_10, all_19_2_12 and discharging atoms ssList(all_19_0_10), ssList(all_19_2_12), yields: % 55.13/22.74 | (161) all_19_2_12 = nil | ~ (app(all_19_2_12, all_19_0_10) = nil) % 55.13/22.74 | % 55.13/22.74 | Instantiating formula (69) with all_19_0_10, all_14_0_8 and discharging atoms ssList(all_19_0_10), ssList(all_14_0_8), yields: % 55.13/22.74 | (162) all_19_0_10 = nil | ~ (app(all_14_0_8, all_19_0_10) = nil) % 55.13/22.74 | % 55.13/22.74 | Using (109) and (150) yields: % 55.13/22.74 | (163) ~ (all_0_2_2 = nil) % 55.13/22.74 | % 55.13/22.74 | From (159) and (146) follows: % 55.13/22.74 | (164) app(all_19_2_12, all_19_0_10) = nil % 55.13/22.74 | % 55.13/22.74 +-Applying beta-rule and splitting (136), into two cases. % 55.13/22.74 |-Branch one: % 55.13/22.74 | (165) all_0_2_2 = nil % 55.13/22.74 | % 55.13/22.74 | Equations (165) can reduce 163 to: % 55.13/22.74 | (152) $false % 55.13/22.74 | % 55.13/22.74 |-The branch is then unsatisfiable % 55.13/22.74 |-Branch two: % 55.13/22.74 | (163) ~ (all_0_2_2 = nil) % 55.13/22.74 | (168) ? [v0] : ? [v1] : (cons(v1, v0) = all_0_2_2 & ssList(v0) & ssItem(v1)) % 55.13/22.74 | % 55.13/22.74 +-Applying beta-rule and splitting (161), into two cases. % 55.13/22.74 |-Branch one: % 55.13/22.74 | (169) ~ (app(all_19_2_12, all_19_0_10) = nil) % 55.13/22.74 | % 55.13/22.74 | Using (164) and (169) yields: % 55.13/22.74 | (170) $false % 55.13/22.74 | % 55.13/22.74 |-The branch is then unsatisfiable % 55.13/22.74 |-Branch two: % 55.13/22.74 | (164) app(all_19_2_12, all_19_0_10) = nil % 55.13/22.74 | (172) all_19_2_12 = nil % 55.13/22.74 | % 55.13/22.74 | From (172) and (164) follows: % 55.13/22.74 | (173) app(nil, all_19_0_10) = nil % 55.13/22.74 | % 55.13/22.74 +-Applying beta-rule and splitting (162), into two cases. % 55.13/22.74 |-Branch one: % 55.13/22.74 | (174) ~ (app(all_14_0_8, all_19_0_10) = nil) % 55.13/22.74 | % 55.13/22.74 | From (160) and (174) follows: % 55.13/22.74 | (175) ~ (app(nil, all_19_0_10) = nil) % 55.13/22.74 | % 55.13/22.74 | Using (173) and (175) yields: % 55.13/22.74 | (170) $false % 55.13/22.74 | % 55.13/22.74 |-The branch is then unsatisfiable % 55.13/22.74 |-Branch two: % 55.13/22.74 | (177) app(all_14_0_8, all_19_0_10) = nil % 55.13/22.74 | (178) all_19_0_10 = nil % 55.13/22.74 | % 55.13/22.74 | From (178) and (173) follows: % 55.13/22.74 | (179) app(nil, nil) = nil % 55.13/22.74 | % 55.13/22.74 | From (178) and (148) follows: % 55.13/22.74 | (124) ssList(nil) % 55.13/22.74 | % 55.13/22.74 +-Applying beta-rule and splitting (141), into two cases. % 55.13/22.74 |-Branch one: % 55.13/22.74 | (181) neq(all_0_2_2, nil) % 55.13/22.74 | % 55.13/22.74 +-Applying beta-rule and splitting (85), into two cases. % 55.13/22.74 |-Branch one: % 55.13/22.74 | (182) ~ neq(all_0_2_2, nil) % 55.13/22.74 | % 55.13/22.74 | Using (181) and (182) yields: % 55.13/22.74 | (170) $false % 55.13/22.74 | % 55.13/22.74 |-The branch is then unsatisfiable % 55.13/22.74 |-Branch two: % 55.13/22.74 | (181) neq(all_0_2_2, nil) % 55.13/22.74 | (185) singletonP(all_0_3_3) % 55.13/22.74 | % 55.13/22.74 | Instantiating formula (67) with nil, all_0_3_3 and discharging atoms frontsegP(all_0_3_3, nil), ssList(all_0_3_3), ssList(nil), yields: % 55.13/22.74 | (186) ? [v0] : (app(nil, v0) = all_0_3_3 & ssList(v0)) % 55.13/22.74 | % 55.13/22.74 | Instantiating formula (57) with all_0_3_3 and discharging atoms singletonP(all_0_3_3), ssList(all_0_3_3), yields: % 55.13/22.74 | (187) ? [v0] : (cons(v0, nil) = all_0_3_3 & ssItem(v0)) % 55.13/22.74 | % 55.21/22.75 | Instantiating formula (106) with all_0_3_3, all_87_0_41, nil, nil, nil and discharging atoms app(nil, nil) = nil, ssList(nil), ssItem(all_87_0_41), yields: % 55.21/22.75 | (188) ~ (cons(all_87_0_41, nil) = all_0_3_3) | ? [v0] : (cons(all_87_0_41, nil) = v0 & app(v0, nil) = all_0_3_3) % 55.21/22.75 | % 55.21/22.75 | Instantiating formula (79) with all_0_3_3, all_87_0_41 and discharging atoms ssItem(all_87_0_41), yields: % 55.21/22.75 | (189) ~ (cons(all_87_0_41, nil) = all_0_3_3) | equalelemsP(all_0_3_3) % 55.21/22.75 | % 55.21/22.75 | Instantiating formula (23) with all_0_3_3, all_87_0_41 and discharging atoms ssItem(all_87_0_41), yields: % 55.21/22.75 | (190) ~ (cons(all_87_0_41, nil) = all_0_3_3) | duplicatefreeP(all_0_3_3) % 55.21/22.75 | % 55.21/22.75 | Instantiating formula (104) with all_0_3_3, all_87_0_41 and discharging atoms ssItem(all_87_0_41), yields: % 55.21/22.75 | (191) ~ (cons(all_87_0_41, nil) = all_0_3_3) | strictorderedP(all_0_3_3) % 55.21/22.75 | % 55.21/22.76 | Instantiating formula (93) with all_0_3_3, all_87_0_41 and discharging atoms ssItem(all_87_0_41), yields: % 55.21/22.76 | (192) ~ (cons(all_87_0_41, nil) = all_0_3_3) | totalorderedP(all_0_3_3) % 55.21/22.76 | % 55.21/22.76 | Instantiating formula (12) with all_0_3_3, all_87_0_41 and discharging atoms ssItem(all_87_0_41), yields: % 55.21/22.76 | (193) ~ (cons(all_87_0_41, nil) = all_0_3_3) | strictorderP(all_0_3_3) % 55.21/22.76 | % 55.21/22.76 | Instantiating formula (28) with all_0_3_3, all_87_0_41 and discharging atoms ssItem(all_87_0_41), yields: % 55.21/22.76 | (194) ~ (cons(all_87_0_41, nil) = all_0_3_3) | totalorderP(all_0_3_3) % 55.21/22.76 | % 55.21/22.76 | Instantiating formula (39) with all_0_3_3, all_87_0_41 and discharging atoms ssItem(all_87_0_41), yields: % 55.21/22.76 | (195) ~ (cons(all_87_0_41, nil) = all_0_3_3) | cyclefreeP(all_0_3_3) % 55.21/22.76 | % 55.21/22.76 | Instantiating formula (4) with all_87_0_41 and discharging atoms ssItem(all_87_0_41), yields: % 55.21/22.76 | (196) ? [v0] : (cons(all_87_0_41, nil) = v0 & ! [v1] : ( ~ ssList(v1) | ? [v2] : (app(v1, v0) = v2 & ! [v3] : ( ~ ssList(v3) | ? [v4] : (( ~ (v4 = all_0_3_3) & app(v2, v3) = v4) | (leq(all_87_0_41, v4) & memberP(v3, v4) & memberP(v1, v4) & ssItem(v4) & ~ leq(v4, all_87_0_41))))))) % 55.21/22.76 | % 55.21/22.76 | Instantiating (187) with all_156_0_45 yields: % 55.21/22.76 | (197) cons(all_156_0_45, nil) = all_0_3_3 & ssItem(all_156_0_45) % 55.21/22.76 | % 55.21/22.76 | Applying alpha-rule on (197) yields: % 55.21/22.76 | (198) cons(all_156_0_45, nil) = all_0_3_3 % 55.21/22.76 | (199) ssItem(all_156_0_45) % 55.21/22.76 | % 55.21/22.76 | Instantiating (186) with all_158_0_46 yields: % 55.21/22.76 | (200) app(nil, all_158_0_46) = all_0_3_3 & ssList(all_158_0_46) % 55.21/22.76 | % 55.21/22.76 | Applying alpha-rule on (200) yields: % 55.21/22.76 | (201) app(nil, all_158_0_46) = all_0_3_3 % 55.21/22.76 | (202) ssList(all_158_0_46) % 55.21/22.76 | % 55.21/22.76 | Instantiating (196) with all_165_0_50 yields: % 55.21/22.76 | (203) cons(all_87_0_41, nil) = all_165_0_50 & ! [v0] : ( ~ ssList(v0) | ? [v1] : (app(v0, all_165_0_50) = v1 & ! [v2] : ( ~ ssList(v2) | ? [v3] : (( ~ (v3 = all_0_3_3) & app(v1, v2) = v3) | (leq(all_87_0_41, v3) & memberP(v2, v3) & memberP(v0, v3) & ssItem(v3) & ~ leq(v3, all_87_0_41)))))) % 55.21/22.76 | % 55.21/22.76 | Applying alpha-rule on (203) yields: % 55.21/22.76 | (204) cons(all_87_0_41, nil) = all_165_0_50 % 55.21/22.76 | (205) ! [v0] : ( ~ ssList(v0) | ? [v1] : (app(v0, all_165_0_50) = v1 & ! [v2] : ( ~ ssList(v2) | ? [v3] : (( ~ (v3 = all_0_3_3) & app(v1, v2) = v3) | (leq(all_87_0_41, v3) & memberP(v2, v3) & memberP(v0, v3) & ssItem(v3) & ~ leq(v3, all_87_0_41)))))) % 55.21/22.76 | % 55.21/22.76 | Instantiating formula (205) with nil and discharging atoms ssList(nil), yields: % 55.21/22.76 | (206) ? [v0] : (app(nil, all_165_0_50) = v0 & ! [v1] : ( ~ ssList(v1) | ? [v2] : (( ~ (v2 = all_0_3_3) & app(v0, v1) = v2) | (leq(all_87_0_41, v2) & memberP(v1, v2) & memberP(nil, v2) & ssItem(v2) & ~ leq(v2, all_87_0_41))))) % 55.21/22.77 | % 55.21/22.77 | Instantiating (206) with all_266_0_117 yields: % 55.21/22.77 | (207) app(nil, all_165_0_50) = all_266_0_117 & ! [v0] : ( ~ ssList(v0) | ? [v1] : (( ~ (v1 = all_0_3_3) & app(all_266_0_117, v0) = v1) | (leq(all_87_0_41, v1) & memberP(v0, v1) & memberP(nil, v1) & ssItem(v1) & ~ leq(v1, all_87_0_41)))) % 55.21/22.77 | % 55.21/22.77 | Applying alpha-rule on (207) yields: % 55.21/22.77 | (208) app(nil, all_165_0_50) = all_266_0_117 % 55.21/22.77 | (209) ! [v0] : ( ~ ssList(v0) | ? [v1] : (( ~ (v1 = all_0_3_3) & app(all_266_0_117, v0) = v1) | (leq(all_87_0_41, v1) & memberP(v0, v1) & memberP(nil, v1) & ssItem(v1) & ~ leq(v1, all_87_0_41)))) % 55.21/22.77 | % 55.21/22.77 | Instantiating formula (209) with all_87_1_42 and discharging atoms ssList(all_87_1_42), yields: % 55.21/22.77 | (210) ? [v0] : (( ~ (v0 = all_0_3_3) & app(all_266_0_117, all_87_1_42) = v0) | (leq(all_87_0_41, v0) & memberP(all_87_1_42, v0) & memberP(nil, v0) & ssItem(v0) & ~ leq(v0, all_87_0_41))) % 55.21/22.77 | % 55.21/22.77 | Instantiating (210) with all_434_0_249 yields: % 55.21/22.77 | (211) ( ~ (all_434_0_249 = all_0_3_3) & app(all_266_0_117, all_87_1_42) = all_434_0_249) | (leq(all_87_0_41, all_434_0_249) & memberP(all_87_1_42, all_434_0_249) & memberP(nil, all_434_0_249) & ssItem(all_434_0_249) & ~ leq(all_434_0_249, all_87_0_41)) % 55.21/22.77 | % 55.21/22.77 | Instantiating formula (3) with all_87_0_41, nil, all_165_0_50, all_0_3_3 and discharging atoms cons(all_87_0_41, nil) = all_165_0_50, yields: % 55.21/22.77 | (212) all_165_0_50 = all_0_3_3 | ~ (cons(all_87_0_41, nil) = all_0_3_3) % 55.21/22.77 | % 55.21/22.77 | Instantiating formula (30) with nil, all_158_0_46, all_0_3_3, all_266_0_117 and discharging atoms app(nil, all_158_0_46) = all_0_3_3, yields: % 55.21/22.77 | (213) all_266_0_117 = all_0_3_3 | ~ (app(nil, all_158_0_46) = all_266_0_117) % 55.21/22.77 | % 55.21/22.77 | Instantiating formula (114) with all_0_3_3, all_158_0_46 and discharging atoms app(nil, all_158_0_46) = all_0_3_3, ssList(all_158_0_46), yields: % 55.21/22.77 | (214) all_158_0_46 = all_0_3_3 % 55.21/22.77 | % 55.21/22.77 | Instantiating formula (61) with all_87_0_41, all_0_3_3, all_156_0_45, all_87_1_42, nil and discharging atoms cons(all_156_0_45, nil) = all_0_3_3, cons(all_87_0_41, all_87_1_42) = all_0_3_3, ssList(all_87_1_42), ssList(nil), ssItem(all_156_0_45), ssItem(all_87_0_41), yields: % 55.21/22.77 | (215) all_87_1_42 = nil % 55.21/22.77 | % 55.21/22.77 | From (215) and (156) follows: % 55.21/22.77 | (216) cons(all_87_0_41, nil) = all_0_3_3 % 55.21/22.77 | % 55.21/22.77 | From (214) and (202) follows: % 55.21/22.77 | (132) ssList(all_0_3_3) % 55.21/22.77 | % 55.21/22.77 +-Applying beta-rule and splitting (192), into two cases. % 55.21/22.77 |-Branch one: % 55.21/22.77 | (218) ~ (cons(all_87_0_41, nil) = all_0_3_3) % 55.21/22.78 | % 55.21/22.78 | Using (216) and (218) yields: % 55.21/22.78 | (170) $false % 55.21/22.78 | % 55.21/22.78 |-The branch is then unsatisfiable % 55.21/22.78 |-Branch two: % 55.21/22.78 | (216) cons(all_87_0_41, nil) = all_0_3_3 % 55.21/22.78 | (221) totalorderedP(all_0_3_3) % 55.21/22.78 | % 55.21/22.78 +-Applying beta-rule and splitting (193), into two cases. % 55.21/22.78 |-Branch one: % 55.21/22.78 | (218) ~ (cons(all_87_0_41, nil) = all_0_3_3) % 55.21/22.78 | % 55.21/22.78 | Using (216) and (218) yields: % 55.21/22.78 | (170) $false % 55.21/22.78 | % 55.21/22.78 |-The branch is then unsatisfiable % 55.21/22.78 |-Branch two: % 55.21/22.78 | (216) cons(all_87_0_41, nil) = all_0_3_3 % 55.21/22.78 | (225) strictorderP(all_0_3_3) % 55.21/22.78 | % 55.21/22.78 +-Applying beta-rule and splitting (195), into two cases. % 55.21/22.78 |-Branch one: % 55.21/22.78 | (218) ~ (cons(all_87_0_41, nil) = all_0_3_3) % 55.21/22.78 | % 55.21/22.78 | Using (216) and (218) yields: % 55.21/22.78 | (170) $false % 55.21/22.78 | % 55.21/22.78 |-The branch is then unsatisfiable % 55.21/22.78 |-Branch two: % 55.21/22.78 | (216) cons(all_87_0_41, nil) = all_0_3_3 % 55.21/22.78 | (229) cyclefreeP(all_0_3_3) % 55.21/22.78 | % 55.21/22.78 +-Applying beta-rule and splitting (194), into two cases. % 55.21/22.78 |-Branch one: % 55.21/22.78 | (218) ~ (cons(all_87_0_41, nil) = all_0_3_3) % 55.21/22.78 | % 55.21/22.78 | Using (216) and (218) yields: % 55.21/22.78 | (170) $false % 55.21/22.78 | % 55.21/22.78 |-The branch is then unsatisfiable % 55.21/22.78 |-Branch two: % 55.21/22.78 | (216) cons(all_87_0_41, nil) = all_0_3_3 % 55.21/22.78 | (233) totalorderP(all_0_3_3) % 55.21/22.78 | % 55.21/22.78 +-Applying beta-rule and splitting (190), into two cases. % 55.21/22.78 |-Branch one: % 55.21/22.78 | (218) ~ (cons(all_87_0_41, nil) = all_0_3_3) % 55.21/22.78 | % 55.21/22.78 | Using (216) and (218) yields: % 55.21/22.78 | (170) $false % 55.21/22.78 | % 55.21/22.78 |-The branch is then unsatisfiable % 55.21/22.78 |-Branch two: % 55.21/22.78 | (216) cons(all_87_0_41, nil) = all_0_3_3 % 55.21/22.78 | (237) duplicatefreeP(all_0_3_3) % 55.21/22.78 | % 55.21/22.78 +-Applying beta-rule and splitting (188), into two cases. % 55.21/22.78 |-Branch one: % 55.21/22.78 | (218) ~ (cons(all_87_0_41, nil) = all_0_3_3) % 55.21/22.78 | % 55.21/22.78 | Using (216) and (218) yields: % 55.21/22.78 | (170) $false % 55.21/22.78 | % 55.21/22.78 |-The branch is then unsatisfiable % 55.21/22.78 |-Branch two: % 55.21/22.78 | (216) cons(all_87_0_41, nil) = all_0_3_3 % 55.21/22.78 | (241) ? [v0] : (cons(all_87_0_41, nil) = v0 & app(v0, nil) = all_0_3_3) % 55.21/22.78 | % 55.21/22.78 +-Applying beta-rule and splitting (189), into two cases. % 55.21/22.78 |-Branch one: % 55.21/22.78 | (218) ~ (cons(all_87_0_41, nil) = all_0_3_3) % 55.21/22.78 | % 55.21/22.78 | Using (216) and (218) yields: % 55.21/22.78 | (170) $false % 55.21/22.78 | % 55.21/22.78 |-The branch is then unsatisfiable % 55.21/22.78 |-Branch two: % 55.21/22.78 | (216) cons(all_87_0_41, nil) = all_0_3_3 % 55.21/22.78 | (245) equalelemsP(all_0_3_3) % 55.21/22.78 | % 55.21/22.78 +-Applying beta-rule and splitting (191), into two cases. % 55.21/22.78 |-Branch one: % 55.21/22.78 | (218) ~ (cons(all_87_0_41, nil) = all_0_3_3) % 55.21/22.78 | % 55.21/22.78 | Using (216) and (218) yields: % 55.21/22.78 | (170) $false % 55.21/22.78 | % 55.21/22.78 |-The branch is then unsatisfiable % 55.21/22.78 |-Branch two: % 55.21/22.78 | (216) cons(all_87_0_41, nil) = all_0_3_3 % 55.21/22.78 | (249) strictorderedP(all_0_3_3) % 55.21/22.78 | % 55.21/22.78 +-Applying beta-rule and splitting (212), into two cases. % 55.21/22.78 |-Branch one: % 55.21/22.78 | (218) ~ (cons(all_87_0_41, nil) = all_0_3_3) % 55.21/22.78 | % 55.21/22.79 | Using (216) and (218) yields: % 55.21/22.79 | (170) $false % 55.21/22.79 | % 55.21/22.79 |-The branch is then unsatisfiable % 55.21/22.79 |-Branch two: % 55.21/22.79 | (216) cons(all_87_0_41, nil) = all_0_3_3 % 55.21/22.79 | (253) all_165_0_50 = all_0_3_3 % 55.21/22.79 | % 55.21/22.79 | From (253) and (208) follows: % 55.21/22.79 | (254) app(nil, all_0_3_3) = all_266_0_117 % 55.21/22.79 | % 55.21/22.79 +-Applying beta-rule and splitting (213), into two cases. % 55.21/22.79 |-Branch one: % 55.21/22.79 | (255) ~ (app(nil, all_158_0_46) = all_266_0_117) % 55.21/22.79 | % 55.21/22.79 | From (214) and (255) follows: % 55.21/22.79 | (256) ~ (app(nil, all_0_3_3) = all_266_0_117) % 55.21/22.79 | % 55.21/22.79 | Using (254) and (256) yields: % 55.21/22.79 | (170) $false % 55.21/22.79 | % 55.21/22.79 |-The branch is then unsatisfiable % 55.21/22.79 |-Branch two: % 55.21/22.79 | (258) app(nil, all_158_0_46) = all_266_0_117 % 55.21/22.79 | (259) all_266_0_117 = all_0_3_3 % 55.21/22.79 | % 55.21/22.79 +-Applying beta-rule and splitting (211), into two cases. % 55.21/22.79 |-Branch one: % 55.21/22.79 | (260) ~ (all_434_0_249 = all_0_3_3) & app(all_266_0_117, all_87_1_42) = all_434_0_249 % 55.21/22.79 | % 55.21/22.79 | Applying alpha-rule on (260) yields: % 55.21/22.79 | (261) ~ (all_434_0_249 = all_0_3_3) % 55.21/22.79 | (262) app(all_266_0_117, all_87_1_42) = all_434_0_249 % 55.21/22.79 | % 55.21/22.79 | From (259)(215) and (262) follows: % 55.21/22.79 | (263) app(all_0_3_3, nil) = all_434_0_249 % 55.21/22.79 | % 55.21/22.79 | Instantiating formula (29) with all_434_0_249, all_0_3_3 and discharging atoms app(all_0_3_3, nil) = all_434_0_249, ssList(all_0_3_3), yields: % 55.21/22.79 | (264) all_434_0_249 = all_0_3_3 % 55.21/22.79 | % 55.21/22.79 | Equations (264) can reduce 261 to: % 55.21/22.79 | (152) $false % 55.21/22.79 | % 55.21/22.79 |-The branch is then unsatisfiable % 55.21/22.79 |-Branch two: % 55.21/22.79 | (266) leq(all_87_0_41, all_434_0_249) & memberP(all_87_1_42, all_434_0_249) & memberP(nil, all_434_0_249) & ssItem(all_434_0_249) & ~ leq(all_434_0_249, all_87_0_41) % 55.21/22.79 | % 55.21/22.79 | Applying alpha-rule on (266) yields: % 55.21/22.79 | (267) ssItem(all_434_0_249) % 55.21/22.79 | (268) memberP(nil, all_434_0_249) % 55.21/22.79 | (269) memberP(all_87_1_42, all_434_0_249) % 55.21/22.79 | (270) leq(all_87_0_41, all_434_0_249) % 55.21/22.79 | (271) ~ leq(all_434_0_249, all_87_0_41) % 55.21/22.79 | % 55.21/22.79 | From (215) and (269) follows: % 55.21/22.79 | (268) memberP(nil, all_434_0_249) % 55.21/22.79 | % 55.21/22.79 | Instantiating formula (121) with all_434_0_249 and discharging atoms memberP(nil, all_434_0_249), ssItem(all_434_0_249), yields: % 55.21/22.79 | (170) $false % 55.21/22.79 | % 55.21/22.79 |-The branch is then unsatisfiable % 55.21/22.79 |-Branch two: % 55.21/22.79 | (182) ~ neq(all_0_2_2, nil) % 55.21/22.79 | (165) all_0_2_2 = nil % 55.21/22.79 | % 55.21/22.79 | Equations (165) can reduce 163 to: % 55.21/22.79 | (152) $false % 55.21/22.79 | % 55.21/22.79 |-The branch is then unsatisfiable % 55.21/22.80 |-Branch two: % 55.21/22.80 | (277) segmentP(nil, all_0_3_3) % 55.21/22.80 | (151) all_0_3_3 = nil % 55.21/22.80 | % 55.21/22.80 | Equations (151) can reduce 131 to: % 55.21/22.80 | (152) $false % 55.21/22.80 | % 55.21/22.80 |-The branch is then unsatisfiable % 55.21/22.80 % SZS output end Proof for theBenchmark % 55.21/22.80 % 55.21/22.80 22217ms %------------------------------------------------------------------------------