%------------------------------------------------------------------------------ % File : ePrincess---1.0 % Problem : SWC393+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : ePrincess-casc -timeout=%d %s % Computer : n029.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 20:17:54 EDT 2022 % Result : Theorem 56.60s 27.58s % Output : Proof 273.34s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWC393+1 : TPTP v8.1.0. Released v2.4.0. % 0.06/0.12 % Command : ePrincess-casc -timeout=%d %s % 0.12/0.33 % Computer : n029.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 17:49:24 EDT 2022 % 0.12/0.33 % CPUTime : % 0.48/0.58 ____ _ % 0.48/0.58 ___ / __ \_____(_)___ ________ __________ % 0.48/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/ % 0.48/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ ) % 0.48/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/ % 0.48/0.58 % 0.48/0.58 A Theorem Prover for First-Order Logic % 0.48/0.58 (ePrincess v.1.0) % 0.48/0.58 % 0.48/0.58 (c) Philipp Rümmer, 2009-2015 % 0.48/0.58 (c) Peter Backeman, 2014-2015 % 0.48/0.58 (contributions by Angelo Brillout, Peter Baumgartner) % 0.48/0.58 Free software under GNU Lesser General Public License (LGPL). % 0.48/0.58 Bug reports to peter@backeman.se % 0.48/0.58 % 0.48/0.58 For more information, visit http://user.uu.se/~petba168/breu/ % 0.48/0.58 % 0.48/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ... % 0.48/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 2.20/1.03 Prover 0: Preprocessing ... % 4.71/1.61 Prover 0: Constructing countermodel ... % 15.35/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all % 15.86/6.07 Prover 1: Preprocessing ... % 17.58/6.49 Prover 1: Constructing countermodel ... % 26.12/8.52 Prover 2: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 26.88/8.65 Prover 2: Preprocessing ... % 29.17/9.21 Prover 2: Warning: ignoring some quantifiers % 29.29/9.23 Prover 2: Constructing countermodel ... % 36.86/11.55 Prover 0: stopped % 37.24/11.75 Prover 3: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all % 37.56/11.83 Prover 3: Preprocessing ... % 37.85/11.89 Prover 3: Constructing countermodel ... % 56.60/27.58 Prover 3: proved (15820ms) % 56.60/27.58 Prover 1: stopped % 56.60/27.58 Prover 2: stopped % 56.60/27.58 % 56.60/27.58 No countermodel exists, formula is valid % 56.60/27.58 % SZS status Theorem for theBenchmark % 56.60/27.58 % 56.60/27.58 Generating proof ... found it (size 109) % 272.45/191.82 % 272.45/191.82 % SZS output start Proof for theBenchmark % 272.45/191.82 Assumed formulas after preprocessing and simplification: % 272.45/191.82 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ( ~ (v4 = v3) & equalelemsP(nil) & duplicatefreeP(nil) & strictorderedP(nil) & totalorderedP(nil) & strictorderP(nil) & totalorderP(nil) & cyclefreeP(nil) & segmentP(nil, nil) & rearsegP(nil, nil) & frontsegP(nil, nil) & memberP(v0, v2) & ssList(v1) & ssList(v0) & ssList(nil) & ssItem(v4) & ssItem(v3) & ssItem(v2) & ~ singletonP(nil) & ~ memberP(v1, v2) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cons(v7, v12) = v13) | ~ (cons(v6, v9) = v10) | ~ (app(v11, v13) = v5) | ~ (app(v8, v10) = v11) | ~ strictorderedP(v5) | ~ ssList(v12) | ~ ssList(v9) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v7) | ~ ssItem(v6) | lt(v6, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cons(v7, v12) = v13) | ~ (cons(v6, v9) = v10) | ~ (app(v11, v13) = v5) | ~ (app(v8, v10) = v11) | ~ totalorderedP(v5) | ~ ssList(v12) | ~ ssList(v9) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v7) | ~ ssItem(v6) | leq(v6, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cons(v7, v12) = v13) | ~ (cons(v6, v9) = v10) | ~ (app(v11, v13) = v5) | ~ (app(v8, v10) = v11) | ~ strictorderP(v5) | ~ ssList(v12) | ~ ssList(v9) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v7) | ~ ssItem(v6) | lt(v7, v6) | lt(v6, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cons(v7, v12) = v13) | ~ (cons(v6, v9) = v10) | ~ (app(v11, v13) = v5) | ~ (app(v8, v10) = v11) | ~ totalorderP(v5) | ~ ssList(v12) | ~ ssList(v9) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v7) | ~ ssItem(v6) | leq(v7, v6) | leq(v6, v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cons(v7, v12) = v13) | ~ (cons(v6, v9) = v10) | ~ (app(v11, v13) = v5) | ~ (app(v8, v10) = v11) | ~ leq(v7, v6) | ~ leq(v6, v7) | ~ cyclefreeP(v5) | ~ ssList(v12) | ~ ssList(v9) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v7) | ~ ssItem(v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cons(v6, v11) = v12) | ~ (cons(v6, v8) = v9) | ~ (app(v10, v12) = v5) | ~ (app(v7, v9) = v10) | ~ duplicatefreeP(v5) | ~ ssList(v11) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v5) | ~ ssItem(v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v7 = v6 | ~ (cons(v7, v9) = v10) | ~ (cons(v6, v10) = v11) | ~ (app(v8, v11) = v5) | ~ equalelemsP(v5) | ~ ssList(v9) | ~ ssList(v8) | ~ ssList(v5) | ~ ssItem(v7) | ~ ssItem(v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v6 = v5 | ~ (cons(v6, v9) = v10) | ~ (cons(v5, v7) = v8) | ~ frontsegP(v8, v10) | ~ ssList(v9) | ~ ssList(v7) | ~ ssItem(v6) | ~ ssItem(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (cons(v8, v6) = v9) | ~ (app(v9, v5) = v10) | ~ (app(v6, v5) = v7) | ~ ssList(v6) | ~ ssList(v5) | ~ ssItem(v8) | cons(v8, v7) = v10) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (cons(v6, v9) = v10) | ~ (cons(v5, v7) = v8) | ~ frontsegP(v8, v10) | ~ ssList(v9) | ~ ssList(v7) | ~ ssItem(v6) | ~ ssItem(v5) | frontsegP(v7, v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (app(v8, v9) = v10) | ~ (app(v7, v5) = v8) | ~ segmentP(v5, v6) | ~ ssList(v9) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | segmentP(v10, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v9 = v7 | ~ (cons(v9, v6) = v8) | ~ (cons(v7, v5) = v8) | ~ ssList(v6) | ~ ssList(v5) | ~ ssItem(v9) | ~ ssItem(v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v6 = v5 | ~ (cons(v9, v6) = v8) | ~ (cons(v7, v5) = v8) | ~ ssList(v6) | ~ ssList(v5) | ~ ssItem(v9) | ~ ssItem(v7)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (cons(v6, v8) = v9) | ~ (app(v7, v9) = v5) | ~ ssList(v8) | ~ ssList(v7) | ~ ssList(v5) | ~ ssItem(v6) | memberP(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (cons(v5, v8) = v9) | ~ (cons(v5, v6) = v7) | ~ frontsegP(v6, v8) | ~ ssList(v8) | ~ ssList(v6) | ~ ssItem(v5) | frontsegP(v7, v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (app(v8, v9) = v5) | ~ (app(v7, v6) = v8) | ~ ssList(v9) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | segmentP(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : ( ~ (app(v7, v8) = v9) | ~ (app(v5, v6) = v7) | ~ ssList(v8) | ~ ssList(v6) | ~ ssList(v5) | ? [v10] : (app(v6, v8) = v10 & app(v5, v10) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v5 | v5 = nil | ~ (tl(v5) = v7) | ~ (hd(v5) = v6) | ~ (cons(v6, v7) = v8) | ~ ssList(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v5 | ~ (app(v8, v6) = v7) | ~ (app(v5, v6) = v7) | ~ ssList(v8) | ~ ssList(v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v8 = v5 | ~ (app(v6, v8) = v7) | ~ (app(v6, v5) = v7) | ~ ssList(v8) | ~ ssList(v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (cons(v8, v7) = v6) | ~ (cons(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (cons(v6, v7) = v8) | ~ memberP(v8, v5) | ~ ssList(v7) | ~ ssItem(v6) | ~ ssItem(v5) | memberP(v7, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v6 = v5 | ~ (app(v8, v7) = v6) | ~ (app(v8, v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = nil | ~ (tl(v5) = v6) | ~ (app(v6, v7) = v8) | ~ ssList(v7) | ~ ssList(v5) | ? [v9] : (tl(v9) = v8 & app(v5, v7) = v9)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : (v5 = nil | ~ (hd(v5) = v6) | ~ (app(v5, v7) = v8) | ~ ssList(v7) | ~ ssList(v5) | hd(v8) = v6) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v6, v7) = v8) | ~ memberP(v7, v5) | ~ ssList(v7) | ~ ssItem(v6) | ~ ssItem(v5) | memberP(v8, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (cons(v6, nil) = v7) | ~ (app(v7, v5) = v8) | ~ ssList(v5) | ~ ssItem(v6) | cons(v6, v5) = v8) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (app(v7, v5) = v8) | ~ rearsegP(v5, v6) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | rearsegP(v8, v6)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (app(v6, v7) = v8) | ~ memberP(v8, v5) | ~ ssList(v7) | ~ ssList(v6) | ~ ssItem(v5) | memberP(v7, v5) | memberP(v6, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (app(v6, v7) = v8) | ~ memberP(v7, v5) | ~ ssList(v7) | ~ ssList(v6) | ~ ssItem(v5) | memberP(v8, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (app(v6, v7) = v8) | ~ memberP(v6, v5) | ~ ssList(v7) | ~ ssList(v6) | ~ ssItem(v5) | memberP(v8, v5)) & ! [v5] : ! [v6] : ! [v7] : ! [v8] : ( ~ (app(v5, v7) = v8) | ~ frontsegP(v5, v6) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | frontsegP(v8, v6)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (tl(v7) = v6) | ~ (tl(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : (v6 = v5 | ~ (hd(v7) = v6) | ~ (hd(v7) = v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (hd(v6) = v7) | ~ ssList(v6) | ~ ssItem(v5) | ? [v8] : ((v6 = nil | (cons(v5, v6) = v8 & ~ strictorderedP(v8)) | (strictorderedP(v6) & lt(v5, v7))) & (( ~ (v6 = nil) & ( ~ strictorderedP(v6) | ~ lt(v5, v7))) | (cons(v5, v6) = v8 & strictorderedP(v8))))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (hd(v6) = v7) | ~ ssList(v6) | ~ ssItem(v5) | ? [v8] : ((v6 = nil | (cons(v5, v6) = v8 & ~ totalorderedP(v8)) | (totalorderedP(v6) & leq(v5, v7))) & (( ~ (v6 = nil) & ( ~ totalorderedP(v6) | ~ leq(v5, v7))) | (cons(v5, v6) = v8 & totalorderedP(v8))))) & ! [v5] : ! [v6] : ! [v7] : ( ~ (cons(v6, v5) = v7) | ~ ssList(v5) | ~ ssItem(v6) | tl(v7) = v5) & ! [v5] : ! [v6] : ! [v7] : ( ~ (cons(v6, v5) = v7) | ~ ssList(v5) | ~ ssItem(v6) | hd(v7) = v6) & ! [v5] : ! [v6] : ! [v7] : ( ~ (cons(v6, v5) = v7) | ~ ssList(v5) | ~ ssItem(v6) | ssList(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (cons(v5, v6) = v7) | ~ ssList(v6) | ~ ssItem(v5) | memberP(v7, v5)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (app(v7, v6) = v5) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | rearsegP(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (app(v6, v7) = v5) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | frontsegP(v5, v6)) & ! [v5] : ! [v6] : ! [v7] : ( ~ (app(v5, v6) = v7) | ~ ssList(v6) | ~ ssList(v5) | ssList(v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ gt(v6, v7) | ~ gt(v5, v6) | ~ ssItem(v7) | ~ ssItem(v6) | ~ ssItem(v5) | gt(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ geq(v6, v7) | ~ geq(v5, v6) | ~ ssItem(v7) | ~ ssItem(v6) | ~ ssItem(v5) | geq(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ lt(v6, v7) | ~ lt(v5, v6) | ~ ssItem(v7) | ~ ssItem(v6) | ~ ssItem(v5) | lt(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ lt(v6, v7) | ~ leq(v5, v6) | ~ ssItem(v7) | ~ ssItem(v6) | ~ ssItem(v5) | lt(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ leq(v6, v7) | ~ leq(v5, v6) | ~ ssItem(v7) | ~ ssItem(v6) | ~ ssItem(v5) | leq(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ segmentP(v6, v7) | ~ segmentP(v5, v6) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | segmentP(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ rearsegP(v6, v7) | ~ rearsegP(v5, v6) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | rearsegP(v5, v7)) & ! [v5] : ! [v6] : ! [v7] : ( ~ frontsegP(v6, v7) | ~ frontsegP(v5, v6) | ~ ssList(v7) | ~ ssList(v6) | ~ ssList(v5) | frontsegP(v5, v7)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (app(v5, nil) = v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ (app(nil, v5) = v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ geq(v6, v5) | ~ geq(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ leq(v6, v5) | ~ leq(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ leq(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5) | lt(v5, v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ segmentP(v6, v5) | ~ segmentP(v5, v6) | ~ ssList(v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ rearsegP(v6, v5) | ~ rearsegP(v5, v6) | ~ ssList(v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ frontsegP(v6, v5) | ~ frontsegP(v5, v6) | ~ ssList(v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : (v6 = v5 | ~ ssList(v6) | ~ ssList(v5) | neq(v5, v6)) & ! [v5] : ! [v6] : (v6 = v5 | ~ ssItem(v6) | ~ ssItem(v5) | neq(v5, v6)) & ! [v5] : ! [v6] : (v6 = nil | ~ (app(v5, v6) = nil) | ~ ssList(v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : (v5 = nil | ~ (tl(v5) = v6) | ~ ssList(v5) | ssList(v6)) & ! [v5] : ! [v6] : (v5 = nil | ~ (hd(v5) = v6) | ~ ssList(v5) | ssItem(v6)) & ! [v5] : ! [v6] : (v5 = nil | ~ (app(v5, v6) = nil) | ~ ssList(v6) | ~ ssList(v5)) & ! [v5] : ! [v6] : ( ~ (tl(v5) = v6) | ~ ssList(v5) | ? [v7] : (hd(v5) = v7 & ! [v8] : (v8 = v5 | v8 = nil | v5 = nil | ~ (tl(v8) = v6) | ~ ssList(v8) | ? [v9] : ( ~ (v9 = v7) & hd(v8) = v9)))) & ! [v5] : ! [v6] : ( ~ (cons(v6, v5) = v5) | ~ ssList(v5) | ~ ssItem(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v6, v5) = nil) | ~ ssList(v5) | ~ ssItem(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v6, nil) = v5) | ~ ssList(v5) | ~ ssItem(v6) | singletonP(v5)) & ! [v5] : ! [v6] : ( ~ (cons(v5, nil) = v6) | ~ ssItem(v5) | equalelemsP(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v5, nil) = v6) | ~ ssItem(v5) | duplicatefreeP(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v5, nil) = v6) | ~ ssItem(v5) | strictorderedP(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v5, nil) = v6) | ~ ssItem(v5) | totalorderedP(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v5, nil) = v6) | ~ ssItem(v5) | strictorderP(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v5, nil) = v6) | ~ ssItem(v5) | totalorderP(v6)) & ! [v5] : ! [v6] : ( ~ (cons(v5, nil) = v6) | ~ ssItem(v5) | cyclefreeP(v6)) & ! [v5] : ! [v6] : ( ~ gt(v6, v5) | ~ gt(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5)) & ! [v5] : ! [v6] : ( ~ gt(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5) | lt(v6, v5)) & ! [v5] : ! [v6] : ( ~ geq(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5) | leq(v6, v5)) & ! [v5] : ! [v6] : ( ~ lt(v6, v5) | ~ lt(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5)) & ! [v5] : ! [v6] : ( ~ lt(v6, v5) | ~ ssItem(v6) | ~ ssItem(v5) | gt(v5, v6)) & ! [v5] : ! [v6] : ( ~ lt(v5, v6) | ~ ssItem(v6) | ~ ssItem(v5) | leq(v5, v6)) & ! [v5] : ! [v6] : ( ~ leq(v6, v5) | ~ ssItem(v6) | ~ ssItem(v5) | geq(v5, v6)) & ! [v5] : ! [v6] : ( ~ segmentP(v5, v6) | ~ ssList(v6) | ~ ssList(v5) | ? [v7] : ? [v8] : ? [v9] : (app(v8, v9) = v5 & app(v7, v6) = v8 & ssList(v9) & ssList(v7))) & ! [v5] : ! [v6] : ( ~ rearsegP(v5, v6) | ~ ssList(v6) | ~ ssList(v5) | ? [v7] : (app(v7, v6) = v5 & ssList(v7))) & ! [v5] : ! [v6] : ( ~ frontsegP(v5, v6) | ~ ssList(v6) | ~ ssList(v5) | ? [v7] : (app(v6, v7) = v5 & ssList(v7))) & ! [v5] : ! [v6] : ( ~ memberP(v5, v6) | ~ ssList(v5) | ~ ssItem(v6) | ? [v7] : ? [v8] : ? [v9] : (cons(v6, v8) = v9 & app(v7, v9) = v5 & ssList(v8) & ssList(v7))) & ! [v5] : (v5 = nil | ~ (app(nil, nil) = v5)) & ! [v5] : (v5 = nil | ~ segmentP(nil, v5) | ~ ssList(v5)) & ! [v5] : (v5 = nil | ~ rearsegP(nil, v5) | ~ ssList(v5)) & ! [v5] : (v5 = nil | ~ frontsegP(nil, v5) | ~ ssList(v5)) & ! [v5] : (v5 = nil | ~ ssList(v5) | ? [v6] : ? [v7] : (cons(v7, v6) = v5 & ssList(v6) & ssItem(v7))) & ! [v5] : ( ~ lt(v5, v5) | ~ ssItem(v5)) & ! [v5] : ( ~ singletonP(v5) | ~ ssList(v5) | ? [v6] : (cons(v6, nil) = v5 & ssItem(v6))) & ! [v5] : ( ~ memberP(nil, v5) | ~ ssItem(v5)) & ! [v5] : ( ~ ssList(v5) | ~ neq(v5, v5)) & ! [v5] : ( ~ ssList(v5) | equalelemsP(v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ( ~ (v7 = v6) & cons(v7, v9) = v10 & cons(v6, v10) = v11 & app(v8, v11) = v5 & ssList(v9) & ssList(v8) & ssItem(v7) & ssItem(v6))) & ! [v5] : ( ~ ssList(v5) | duplicatefreeP(v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : (cons(v6, v11) = v12 & cons(v6, v8) = v9 & app(v10, v12) = v5 & app(v7, v9) = v10 & ssList(v11) & ssList(v8) & ssList(v7) & ssItem(v6))) & ! [v5] : ( ~ ssList(v5) | strictorderedP(v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (cons(v7, v12) = v13 & cons(v6, v9) = v10 & app(v11, v13) = v5 & app(v8, v10) = v11 & ssList(v12) & ssList(v9) & ssList(v8) & ssItem(v7) & ssItem(v6) & ~ lt(v6, v7))) & ! [v5] : ( ~ ssList(v5) | totalorderedP(v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (cons(v7, v12) = v13 & cons(v6, v9) = v10 & app(v11, v13) = v5 & app(v8, v10) = v11 & ssList(v12) & ssList(v9) & ssList(v8) & ssItem(v7) & ssItem(v6) & ~ leq(v6, v7))) & ! [v5] : ( ~ ssList(v5) | strictorderP(v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (cons(v7, v12) = v13 & cons(v6, v9) = v10 & app(v11, v13) = v5 & app(v8, v10) = v11 & ssList(v12) & ssList(v9) & ssList(v8) & ssItem(v7) & ssItem(v6) & ~ lt(v7, v6) & ~ lt(v6, v7))) & ! [v5] : ( ~ ssList(v5) | totalorderP(v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (cons(v7, v12) = v13 & cons(v6, v9) = v10 & app(v11, v13) = v5 & app(v8, v10) = v11 & ssList(v12) & ssList(v9) & ssList(v8) & ssItem(v7) & ssItem(v6) & ~ leq(v7, v6) & ~ leq(v6, v7))) & ! [v5] : ( ~ ssList(v5) | cyclefreeP(v5) | ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : (cons(v7, v12) = v13 & cons(v6, v9) = v10 & app(v11, v13) = v5 & app(v8, v10) = v11 & leq(v7, v6) & leq(v6, v7) & ssList(v12) & ssList(v9) & ssList(v8) & ssItem(v7) & ssItem(v6))) & ! [v5] : ( ~ ssList(v5) | segmentP(v5, v5)) & ! [v5] : ( ~ ssList(v5) | segmentP(v5, nil)) & ! [v5] : ( ~ ssList(v5) | rearsegP(v5, v5)) & ! [v5] : ( ~ ssList(v5) | rearsegP(v5, nil)) & ! [v5] : ( ~ ssList(v5) | frontsegP(v5, v5)) & ! [v5] : ( ~ ssList(v5) | frontsegP(v5, nil)) & ! [v5] : ( ~ neq(v5, v5) | ~ ssItem(v5)) & ! [v5] : ( ~ ssItem(v5) | geq(v5, v5)) & ! [v5] : ( ~ ssItem(v5) | leq(v5, v5)) & ( ~ (v1 = nil) | v0 = nil) & ( ~ neq(v1, nil) | (segmentP(v1, v0) & neq(v0, nil)))) % 272.45/191.89 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4 yields: % 272.45/191.89 | (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) & memberP(all_0_4_4, all_0_2_2) & ssList(all_0_3_3) & ssList(all_0_4_4) & ssList(nil) & ssItem(all_0_0_0) & ssItem(all_0_1_1) & ssItem(all_0_2_2) & ~ singletonP(nil) & ~ memberP(all_0_3_3, all_0_2_2) & ! [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_3_3 = nil) | all_0_4_4 = nil) & ( ~ neq(all_0_3_3, nil) | (segmentP(all_0_3_3, all_0_4_4) & neq(all_0_4_4, nil))) % 272.87/191.92 | % 272.87/191.92 | Applying alpha-rule on (1) yields: % 272.87/191.92 | (2) ! [v0] : ( ~ ssList(v0) | frontsegP(v0, nil)) % 272.87/191.92 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) % 272.87/191.92 | (4) ! [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)) % 272.87/191.92 | (5) segmentP(nil, nil) % 272.87/191.92 | (6) ! [v0] : ! [v1] : (v1 = v0 | ~ segmentP(v1, v0) | ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) % 272.87/191.92 | (7) ! [v0] : (v0 = nil | ~ ssList(v0) | ? [v1] : ? [v2] : (cons(v2, v1) = v0 & ssList(v1) & ssItem(v2))) % 272.87/191.92 | (8) ! [v0] : (v0 = nil | ~ segmentP(nil, v0) | ~ ssList(v0)) % 272.87/191.92 | (9) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ~ ssList(v0)) % 272.87/191.92 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ frontsegP(v1, v0) | ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) % 272.87/191.92 | (11) ! [v0] : ( ~ ssList(v0) | ~ neq(v0, v0)) % 272.87/191.92 | (12) ! [v0] : ! [v1] : ! [v2] : ( ~ rearsegP(v1, v2) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v2)) % 272.87/191.92 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (cons(v1, v3) = v4) | ~ (app(v2, v4) = v0) | ~ ssList(v3) | ~ ssList(v2) | ~ ssList(v0) | ~ ssItem(v1) | memberP(v0, v1)) % 272.87/191.92 | (14) ! [v0] : ! [v1] : ( ~ segmentP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : ? [v3] : ? [v4] : (app(v3, v4) = v0 & app(v2, v1) = v3 & ssList(v4) & ssList(v2))) % 272.87/191.92 | (15) ! [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)))) % 272.87/191.92 | (16) strictorderedP(nil) % 272.87/191.92 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v3, v0)) % 272.87/191.92 | (18) ! [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))) % 272.87/191.92 | (19) ! [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)) % 272.87/191.92 | (20) ~ neq(all_0_3_3, nil) | (segmentP(all_0_3_3, all_0_4_4) & neq(all_0_4_4, nil)) % 272.87/191.92 | (21) ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = v0) | ~ ssList(v0) | ~ ssItem(v1)) % 272.87/191.92 | (22) ~ memberP(all_0_3_3, all_0_2_2) % 272.87/191.92 | (23) duplicatefreeP(nil) % 272.87/191.92 | (24) ! [v0] : ! [v1] : (v0 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0)) % 272.87/191.93 | (25) ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ lt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2)) % 272.87/191.93 | (26) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | duplicatefreeP(v1)) % 272.87/191.93 | (27) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | equalelemsP(v1)) % 272.87/191.93 | (28) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v2, v1) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v0, v1)) % 272.87/191.93 | (29) totalorderedP(nil) % 272.87/191.93 | (30) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ~ ssList(v0) | ssItem(v1)) % 272.87/191.93 | (31) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | ssList(v2)) % 272.87/191.93 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ ssItem(v1) | ~ ssItem(v0) | neq(v0, v1)) % 272.87/191.93 | (33) ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0)) % 272.87/191.93 | (34) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) % 272.87/191.93 | (35) ! [v0] : ! [v1] : ! [v2] : ( ~ lt(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v2)) % 272.87/191.93 | (36) ! [v0] : ( ~ ssList(v0) | rearsegP(v0, nil)) % 272.87/191.93 | (37) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v0, v1) = v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0)) % 272.87/191.93 | (38) ! [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)) % 272.87/191.93 | (39) totalorderP(nil) % 272.87/191.93 | (40) ! [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))) % 272.87/191.93 | (41) ssList(all_0_3_3) % 272.87/191.93 | (42) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ~ ssList(v0)) % 272.87/191.93 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssItem(v1) | ~ ssItem(v0) | memberP(v2, v0)) % 272.87/191.93 | (44) ~ singletonP(nil) % 272.87/191.93 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) % 272.87/191.93 | (46) ! [v0] : ! [v1] : ( ~ frontsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v1, v2) = v0 & ssList(v2))) % 272.87/191.93 | (47) ! [v0] : (v0 = nil | ~ rearsegP(nil, v0) | ~ ssList(v0)) % 272.87/191.93 | (48) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ~ ssList(v0) | ~ ssItem(v1) | cons(v1, v0) = v3) % 272.87/191.93 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v2, v0) = v3) | ~ rearsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | rearsegP(v3, v1)) % 272.87/191.93 | (50) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v0, v1) = v2) | ~ ssList(v1) | ~ ssList(v0) | ssList(v2)) % 272.87/191.93 | (51) ! [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))) % 272.87/191.93 | (52) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2)) % 272.87/191.93 | (53) ! [v0] : ! [v1] : ( ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v1, v0)) % 272.87/191.93 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v3, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v2, v0) | memberP(v1, v0)) % 272.87/191.93 | (55) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) % 272.87/191.93 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v0, v2) = v3) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v3, v1)) % 272.87/191.93 | (57) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ~ ssList(v3) | ~ ssList(v1) | ~ ssList(v0)) % 272.87/191.93 | (58) ! [v0] : ! [v1] : (v1 = nil | ~ (app(v0, v1) = nil) | ~ ssList(v1) | ~ ssList(v0)) % 272.87/191.93 | (59) ~ (all_0_3_3 = nil) | all_0_4_4 = nil % 272.87/191.93 | (60) ! [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))) % 272.87/191.94 | (61) ! [v0] : ( ~ ssList(v0) | frontsegP(v0, v0)) % 272.87/191.94 | (62) ! [v0] : ! [v1] : ( ~ (cons(v1, nil) = v0) | ~ ssList(v0) | ~ ssItem(v1) | singletonP(v0)) % 272.87/191.94 | (63) equalelemsP(nil) % 272.87/191.94 | (64) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v1, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) % 272.87/191.94 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ~ ssList(v2) | ~ ssList(v0) | hd(v3) = v1) % 272.87/191.94 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ gt(v1, v2) | ~ gt(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v2)) % 272.87/191.94 | (67) ! [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)) % 272.87/191.94 | (68) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | tl(v2) = v0) % 272.87/191.94 | (69) ! [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)) % 272.87/191.94 | (70) cyclefreeP(nil) % 272.87/191.94 | (71) ! [v0] : ( ~ ssItem(v0) | leq(v0, v0)) % 272.87/191.94 | (72) ! [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)) % 272.87/191.94 | (73) ! [v0] : ( ~ ssList(v0) | rearsegP(v0, v0)) % 272.87/191.94 | (74) ssList(nil) % 272.87/191.94 | (75) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderP(v1)) % 272.87/191.94 | (76) ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | gt(v0, v1)) % 272.87/191.94 | (77) ! [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) % 272.87/191.94 | (78) ! [v0] : ! [v1] : ! [v2] : ( ~ frontsegP(v1, v2) | ~ frontsegP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v2)) % 272.87/191.94 | (79) ! [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)) % 272.87/191.94 | (80) ! [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))) % 272.87/191.94 | (81) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | cyclefreeP(v1)) % 272.87/191.94 | (82) ! [v0] : ( ~ ssItem(v0) | geq(v0, v0)) % 272.87/191.94 | (83) ! [v0] : ! [v1] : ( ~ lt(v1, v0) | ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 272.87/191.94 | (84) frontsegP(nil, nil) % 272.87/191.94 | (85) ! [v0] : ! [v1] : ( ~ (cons(v1, v0) = nil) | ~ ssList(v0) | ~ ssItem(v1)) % 272.87/191.94 | (86) ! [v0] : ! [v1] : ( ~ lt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v1)) % 272.87/191.94 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ~ ssList(v1) | ~ ssList(v0) | ~ ssItem(v4) | ~ ssItem(v2)) % 272.87/191.94 | (88) ! [v0] : ! [v1] : ( ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0) | ? [v2] : (app(v2, v1) = v0 & ssList(v2))) % 272.87/191.94 | (89) ! [v0] : ! [v1] : ( ~ leq(v1, v0) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v1)) % 272.87/191.94 | (90) ssList(all_0_4_4) % 272.87/191.94 | (91) ssItem(all_0_0_0) % 272.87/191.94 | (92) ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | lt(v0, v1)) % 272.87/191.94 | (93) ! [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))))) % 272.87/191.95 | (94) ! [v0] : ! [v1] : ( ~ memberP(v0, v1) | ~ ssList(v0) | ~ ssItem(v1) | ? [v2] : ? [v3] : ? [v4] : (cons(v1, v3) = v4 & app(v2, v4) = v0 & ssList(v3) & ssList(v2))) % 272.87/191.95 | (95) ! [v0] : ! [v1] : ( ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v1, v0)) % 272.87/191.95 | (96) ! [v0] : ! [v1] : (v1 = v0 | ~ rearsegP(v1, v0) | ~ rearsegP(v0, v1) | ~ ssList(v1) | ~ ssList(v0)) % 272.87/191.95 | (97) ! [v0] : ( ~ singletonP(v0) | ~ ssList(v0) | ? [v1] : (cons(v1, nil) = v0 & ssItem(v1))) % 272.87/191.95 | (98) ! [v0] : ! [v1] : ! [v2] : ( ~ (cons(v1, v0) = v2) | ~ ssList(v0) | ~ ssItem(v1) | hd(v2) = v1) % 272.87/191.95 | (99) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0)) % 272.87/191.95 | (100) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ~ ssList(v0)) % 272.87/191.95 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (app(v1, v2) = v3) | ~ memberP(v2, v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssItem(v0) | memberP(v3, v0)) % 272.87/191.95 | (102) ! [v0] : ! [v1] : (v1 = v0 | ~ ssList(v1) | ~ ssList(v0) | neq(v0, v1)) % 272.87/191.95 | (103) ~ (all_0_0_0 = all_0_1_1) % 272.87/191.95 | (104) rearsegP(nil, nil) % 272.87/191.95 | (105) ! [v0] : ! [v1] : ( ~ gt(v1, v0) | ~ gt(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 272.87/191.95 | (106) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderedP(v1)) % 272.87/191.95 | (107) ssItem(all_0_1_1) % 272.87/191.95 | (108) ! [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)) % 272.87/191.95 | (109) ! [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)) % 272.87/191.95 | (110) ! [v0] : (v0 = nil | ~ frontsegP(nil, v0) | ~ ssList(v0)) % 272.87/191.95 | (111) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | strictorderedP(v1)) % 272.87/191.95 | (112) ! [v0] : ! [v1] : ! [v2] : ( ~ geq(v1, v2) | ~ geq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | geq(v0, v2)) % 272.87/191.95 | (113) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ~ ssList(v0) | ssList(v1)) % 272.87/191.95 | (114) ! [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))) % 272.87/191.95 | (115) strictorderP(nil) % 272.87/191.95 | (116) ! [v0] : ( ~ ssList(v0) | segmentP(v0, v0)) % 272.87/191.95 | (117) ! [v0] : ! [v1] : ! [v2] : ( ~ (app(v1, v2) = v0) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | frontsegP(v0, v1)) % 272.87/191.95 | (118) ! [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)) % 272.87/191.95 | (119) ! [v0] : ! [v1] : (v1 = v0 | ~ leq(v1, v0) | ~ leq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 272.87/191.95 | (120) ! [v0] : ( ~ neq(v0, v0) | ~ ssItem(v0)) % 272.87/191.95 | (121) ! [v0] : ( ~ lt(v0, v0) | ~ ssItem(v0)) % 272.87/191.95 | (122) ! [v0] : ( ~ ssList(v0) | segmentP(v0, nil)) % 272.87/191.95 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (app(v3, v4) = v0) | ~ (app(v2, v1) = v3) | ~ ssList(v4) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v1)) % 272.87/191.95 | (124) ! [v0] : ( ~ memberP(nil, v0) | ~ ssItem(v0)) % 272.87/191.95 | (125) ! [v0] : ! [v1] : ! [v2] : ( ~ segmentP(v1, v2) | ~ segmentP(v0, v1) | ~ ssList(v2) | ~ ssList(v1) | ~ ssList(v0) | segmentP(v0, v2)) % 272.87/191.95 | (126) memberP(all_0_4_4, all_0_2_2) % 272.87/191.95 | (127) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ~ ssItem(v0) | totalorderP(v1)) % 272.87/191.95 | (128) ! [v0] : ! [v1] : (v1 = v0 | ~ geq(v1, v0) | ~ geq(v0, v1) | ~ ssItem(v1) | ~ ssItem(v0)) % 272.87/191.95 | (129) ! [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)) % 272.87/191.96 | (130) ssItem(all_0_2_2) % 272.87/191.96 | (131) ! [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))) % 272.87/191.96 | (132) ! [v0] : ! [v1] : ! [v2] : ( ~ leq(v1, v2) | ~ leq(v0, v1) | ~ ssItem(v2) | ~ ssItem(v1) | ~ ssItem(v0) | leq(v0, v2)) % 272.87/191.96 | (133) ! [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)) % 272.87/191.96 | (134) ! [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)) % 272.87/191.96 | (135) ! [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))))) % 272.87/191.96 | % 272.87/191.96 | Instantiating formula (124) with all_0_2_2 and discharging atoms ssItem(all_0_2_2), yields: % 272.87/191.96 | (136) ~ memberP(nil, all_0_2_2) % 272.87/191.96 | % 272.87/191.96 | Using (126) and (136) yields: % 272.87/191.96 | (137) ~ (all_0_4_4 = nil) % 272.87/191.96 | % 272.87/191.96 +-Applying beta-rule and splitting (59), into two cases. % 272.87/191.96 |-Branch one: % 272.87/191.96 | (138) ~ (all_0_3_3 = nil) % 272.87/191.96 | % 272.87/191.96 | Instantiating formula (36) with all_0_3_3 and discharging atoms ssList(all_0_3_3), yields: % 272.87/191.96 | (139) rearsegP(all_0_3_3, nil) % 272.87/191.96 | % 272.87/191.96 | Instantiating formula (61) with all_0_3_3 and discharging atoms ssList(all_0_3_3), yields: % 272.87/191.96 | (140) frontsegP(all_0_3_3, all_0_3_3) % 272.87/191.96 | % 272.87/191.96 | Instantiating formula (2) with all_0_3_3 and discharging atoms ssList(all_0_3_3), yields: % 272.87/191.96 | (141) frontsegP(all_0_3_3, nil) % 272.87/191.96 | % 272.87/191.96 | Instantiating formula (2) with all_0_4_4 and discharging atoms ssList(all_0_4_4), yields: % 272.87/191.96 | (142) frontsegP(all_0_4_4, nil) % 272.87/191.96 | % 272.87/191.96 | Instantiating formula (14) with nil, nil and discharging atoms segmentP(nil, nil), ssList(nil), yields: % 272.87/191.96 | (143) ? [v0] : ? [v1] : ? [v2] : (app(v1, v2) = nil & app(v0, nil) = v1 & ssList(v2) & ssList(v0)) % 272.87/191.96 | % 272.87/191.96 | Instantiating formula (102) with nil, all_0_3_3 and discharging atoms ssList(all_0_3_3), ssList(nil), yields: % 272.87/191.96 | (144) all_0_3_3 = nil | neq(all_0_3_3, nil) % 272.87/191.96 | % 272.87/191.96 | Instantiating formula (94) with all_0_2_2, all_0_4_4 and discharging atoms memberP(all_0_4_4, all_0_2_2), ssList(all_0_4_4), ssItem(all_0_2_2), yields: % 272.87/191.96 | (145) ? [v0] : ? [v1] : ? [v2] : (cons(all_0_2_2, v1) = v2 & app(v0, v2) = all_0_4_4 & ssList(v1) & ssList(v0)) % 272.87/191.96 | % 272.87/191.96 | Instantiating (145) with all_21_0_5, all_21_1_6, all_21_2_7 yields: % 272.87/191.96 | (146) cons(all_0_2_2, all_21_1_6) = all_21_0_5 & app(all_21_2_7, all_21_0_5) = all_0_4_4 & ssList(all_21_1_6) & ssList(all_21_2_7) % 272.87/191.96 | % 272.87/191.96 | Applying alpha-rule on (146) yields: % 272.87/191.96 | (147) cons(all_0_2_2, all_21_1_6) = all_21_0_5 % 272.87/191.96 | (148) app(all_21_2_7, all_21_0_5) = all_0_4_4 % 272.87/191.96 | (149) ssList(all_21_1_6) % 272.87/191.96 | (150) ssList(all_21_2_7) % 272.87/191.96 | % 272.87/191.96 | Instantiating (143) with all_25_0_9, all_25_1_10, all_25_2_11 yields: % 272.87/191.96 | (151) app(all_25_1_10, all_25_0_9) = nil & app(all_25_2_11, nil) = all_25_1_10 & ssList(all_25_0_9) & ssList(all_25_2_11) % 272.87/191.96 | % 272.87/191.96 | Applying alpha-rule on (151) yields: % 272.87/191.96 | (152) app(all_25_1_10, all_25_0_9) = nil % 272.87/191.96 | (153) app(all_25_2_11, nil) = all_25_1_10 % 272.87/191.96 | (154) ssList(all_25_0_9) % 272.87/191.96 | (155) ssList(all_25_2_11) % 272.87/191.96 | % 272.87/191.96 +-Applying beta-rule and splitting (144), into two cases. % 272.87/191.96 |-Branch one: % 272.87/191.96 | (156) neq(all_0_3_3, nil) % 272.87/191.96 | % 272.87/191.96 +-Applying beta-rule and splitting (20), into two cases. % 272.87/191.96 |-Branch one: % 272.87/191.96 | (157) ~ neq(all_0_3_3, nil) % 272.87/191.96 | % 272.87/191.96 | Using (156) and (157) yields: % 272.87/191.96 | (158) $false % 272.87/191.96 | % 272.87/191.97 |-The branch is then unsatisfiable % 272.87/191.97 |-Branch two: % 272.87/191.97 | (156) neq(all_0_3_3, nil) % 272.87/191.97 | (160) segmentP(all_0_3_3, all_0_4_4) & neq(all_0_4_4, nil) % 272.87/191.97 | % 272.87/191.97 | Applying alpha-rule on (160) yields: % 272.87/191.97 | (161) segmentP(all_0_3_3, all_0_4_4) % 272.87/191.97 | (162) neq(all_0_4_4, nil) % 272.87/191.97 | % 272.87/191.97 | Instantiating formula (9) with all_25_1_10, all_25_2_11 and discharging atoms app(all_25_2_11, nil) = all_25_1_10, ssList(all_25_2_11), yields: % 272.87/191.97 | (163) all_25_1_10 = all_25_2_11 % 272.87/191.97 | % 272.87/191.97 | Instantiating formula (58) with all_25_0_9, all_25_2_11 and discharging atoms ssList(all_25_0_9), ssList(all_25_2_11), yields: % 272.87/191.97 | (164) all_25_0_9 = nil | ~ (app(all_25_2_11, all_25_0_9) = nil) % 272.87/191.97 | % 272.87/191.97 | Instantiating formula (24) with all_25_0_9, all_25_2_11 and discharging atoms ssList(all_25_0_9), ssList(all_25_2_11), yields: % 272.87/191.97 | (165) all_25_2_11 = nil | ~ (app(all_25_2_11, all_25_0_9) = nil) % 272.87/191.97 | % 272.87/191.97 | Instantiating formula (85) with all_0_2_2, all_21_1_6 and discharging atoms ssList(all_21_1_6), ssItem(all_0_2_2), yields: % 272.87/191.97 | (166) ~ (cons(all_0_2_2, all_21_1_6) = nil) % 272.87/191.97 | % 272.87/191.97 | From (163) and (152) follows: % 272.87/191.97 | (167) app(all_25_2_11, all_25_0_9) = nil % 272.87/191.97 | % 272.87/191.97 +-Applying beta-rule and splitting (165), into two cases. % 272.87/191.97 |-Branch one: % 272.87/191.97 | (168) ~ (app(all_25_2_11, all_25_0_9) = nil) % 272.87/191.97 | % 272.87/191.97 | Using (167) and (168) yields: % 272.87/191.97 | (158) $false % 272.87/191.97 | % 272.87/191.97 |-The branch is then unsatisfiable % 272.87/191.97 |-Branch two: % 272.87/191.97 | (167) app(all_25_2_11, all_25_0_9) = nil % 272.87/191.97 | (171) all_25_2_11 = nil % 272.87/191.97 | % 272.87/191.97 | From (171) and (167) follows: % 272.87/191.97 | (172) app(nil, all_25_0_9) = nil % 272.87/191.97 | % 272.87/191.97 +-Applying beta-rule and splitting (164), into two cases. % 272.87/191.97 |-Branch one: % 272.87/191.97 | (168) ~ (app(all_25_2_11, all_25_0_9) = nil) % 272.87/191.97 | % 272.87/191.97 | From (171) and (168) follows: % 272.87/191.97 | (174) ~ (app(nil, all_25_0_9) = nil) % 272.87/191.97 | % 272.87/191.97 | Using (172) and (174) yields: % 272.87/191.97 | (158) $false % 272.87/191.97 | % 272.87/191.97 |-The branch is then unsatisfiable % 272.87/191.97 |-Branch two: % 272.87/191.97 | (167) app(all_25_2_11, all_25_0_9) = nil % 272.87/191.97 | (177) all_25_0_9 = nil % 272.87/191.97 | % 272.87/191.97 | From (177) and (154) follows: % 272.87/191.97 | (74) ssList(nil) % 272.87/191.97 | % 272.87/191.97 | Using (147) and (166) yields: % 272.87/191.97 | (179) ~ (all_21_0_5 = nil) % 272.87/191.97 | % 272.87/191.97 | Instantiating formula (14) with all_0_4_4, all_0_3_3 and discharging atoms segmentP(all_0_3_3, all_0_4_4), ssList(all_0_3_3), ssList(all_0_4_4), yields: % 272.87/191.97 | (180) ? [v0] : ? [v1] : ? [v2] : (app(v1, v2) = all_0_3_3 & app(v0, all_0_4_4) = v1 & ssList(v2) & ssList(v0)) % 272.87/191.97 | % 272.87/191.97 | Instantiating formula (88) with nil, all_0_3_3 and discharging atoms rearsegP(all_0_3_3, nil), ssList(all_0_3_3), ssList(nil), yields: % 272.87/191.97 | (181) ? [v0] : (app(v0, nil) = all_0_3_3 & ssList(v0)) % 272.87/191.97 | % 272.87/191.97 | Instantiating formula (46) 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: % 272.87/191.97 | (182) ? [v0] : (app(all_0_3_3, v0) = all_0_3_3 & ssList(v0)) % 272.87/191.97 | % 272.87/191.97 | Instantiating formula (46) with nil, all_0_3_3 and discharging atoms frontsegP(all_0_3_3, nil), ssList(all_0_3_3), ssList(nil), yields: % 272.87/191.97 | (183) ? [v0] : (app(nil, v0) = all_0_3_3 & ssList(v0)) % 272.87/191.97 | % 272.87/191.97 | Instantiating formula (46) with nil, all_0_4_4 and discharging atoms frontsegP(all_0_4_4, nil), ssList(all_0_4_4), ssList(nil), yields: % 272.87/191.97 | (184) ? [v0] : (app(nil, v0) = all_0_4_4 & ssList(v0)) % 272.87/191.97 | % 272.87/191.97 | Instantiating formula (31) with all_21_0_5, all_0_2_2, all_21_1_6 and discharging atoms cons(all_0_2_2, all_21_1_6) = all_21_0_5, ssList(all_21_1_6), ssItem(all_0_2_2), yields: % 272.87/191.97 | (185) ssList(all_21_0_5) % 272.87/191.97 | % 272.87/191.97 | Instantiating formula (28) with all_21_2_7, all_21_0_5, all_0_4_4 and discharging atoms app(all_21_2_7, all_21_0_5) = all_0_4_4, ssList(all_21_2_7), ssList(all_0_4_4), yields: % 272.87/191.97 | (186) ~ ssList(all_21_0_5) | rearsegP(all_0_4_4, all_21_0_5) % 272.87/191.97 | % 272.87/191.97 | Instantiating formula (117) with all_21_0_5, all_21_2_7, all_0_4_4 and discharging atoms app(all_21_2_7, all_21_0_5) = all_0_4_4, ssList(all_21_2_7), ssList(all_0_4_4), yields: % 272.87/191.97 | (187) ~ ssList(all_21_0_5) | frontsegP(all_0_4_4, all_21_2_7) % 272.87/191.97 | % 272.87/191.97 | Instantiating (184) with all_109_0_17 yields: % 272.87/191.97 | (188) app(nil, all_109_0_17) = all_0_4_4 & ssList(all_109_0_17) % 272.87/191.97 | % 272.87/191.97 | Applying alpha-rule on (188) yields: % 272.87/191.97 | (189) app(nil, all_109_0_17) = all_0_4_4 % 272.87/191.97 | (190) ssList(all_109_0_17) % 272.87/191.97 | % 272.87/191.97 | Instantiating (183) with all_111_0_18 yields: % 272.87/191.97 | (191) app(nil, all_111_0_18) = all_0_3_3 & ssList(all_111_0_18) % 272.87/191.97 | % 272.87/191.97 | Applying alpha-rule on (191) yields: % 272.87/191.97 | (192) app(nil, all_111_0_18) = all_0_3_3 % 272.87/191.97 | (193) ssList(all_111_0_18) % 272.87/191.97 | % 272.87/191.97 | Instantiating (182) with all_113_0_19 yields: % 272.87/191.97 | (194) app(all_0_3_3, all_113_0_19) = all_0_3_3 & ssList(all_113_0_19) % 272.87/191.97 | % 272.87/191.97 | Applying alpha-rule on (194) yields: % 272.87/191.98 | (195) app(all_0_3_3, all_113_0_19) = all_0_3_3 % 272.87/191.98 | (196) ssList(all_113_0_19) % 272.87/191.98 | % 272.87/191.98 | Instantiating (180) with all_119_0_26, all_119_1_27, all_119_2_28 yields: % 272.87/191.98 | (197) app(all_119_1_27, all_119_0_26) = all_0_3_3 & app(all_119_2_28, all_0_4_4) = all_119_1_27 & ssList(all_119_0_26) & ssList(all_119_2_28) % 272.87/191.98 | % 272.87/191.98 | Applying alpha-rule on (197) yields: % 272.87/191.98 | (198) app(all_119_1_27, all_119_0_26) = all_0_3_3 % 272.87/191.98 | (199) app(all_119_2_28, all_0_4_4) = all_119_1_27 % 272.87/191.98 | (200) ssList(all_119_0_26) % 272.87/191.98 | (201) ssList(all_119_2_28) % 272.87/191.98 | % 272.87/191.98 | Instantiating (181) with all_127_0_32 yields: % 272.87/191.98 | (202) app(all_127_0_32, nil) = all_0_3_3 & ssList(all_127_0_32) % 272.87/191.98 | % 272.87/191.98 | Applying alpha-rule on (202) yields: % 272.87/191.98 | (203) app(all_127_0_32, nil) = all_0_3_3 % 272.87/191.98 | (204) ssList(all_127_0_32) % 272.87/191.98 | % 272.87/191.98 +-Applying beta-rule and splitting (187), into two cases. % 272.87/191.98 |-Branch one: % 272.87/191.98 | (205) ~ ssList(all_21_0_5) % 272.87/191.98 | % 272.87/191.98 | Using (185) and (205) yields: % 272.87/191.98 | (158) $false % 272.87/191.98 | % 272.87/191.98 |-The branch is then unsatisfiable % 272.87/191.98 |-Branch two: % 272.87/191.98 | (185) ssList(all_21_0_5) % 272.87/191.98 | (208) frontsegP(all_0_4_4, all_21_2_7) % 272.87/191.98 | % 272.87/191.98 +-Applying beta-rule and splitting (186), into two cases. % 272.87/191.98 |-Branch one: % 272.87/191.98 | (205) ~ ssList(all_21_0_5) % 272.87/191.98 | % 272.87/191.98 | Using (185) and (205) yields: % 272.87/191.98 | (158) $false % 272.87/191.98 | % 272.87/191.98 |-The branch is then unsatisfiable % 272.87/191.98 |-Branch two: % 272.87/191.98 | (185) ssList(all_21_0_5) % 272.87/191.98 | (212) rearsegP(all_0_4_4, all_21_0_5) % 272.87/191.98 | % 272.87/191.98 | Instantiating formula (9) with all_0_3_3, all_127_0_32 and discharging atoms app(all_127_0_32, nil) = all_0_3_3, ssList(all_127_0_32), yields: % 272.87/191.98 | (213) all_127_0_32 = all_0_3_3 % 272.87/191.98 | % 272.87/191.98 | Instantiating formula (42) with all_0_3_3, all_111_0_18 and discharging atoms app(nil, all_111_0_18) = all_0_3_3, ssList(all_111_0_18), yields: % 272.87/191.98 | (214) all_111_0_18 = all_0_3_3 % 272.87/191.98 | % 272.87/191.98 | Instantiating formula (42) with all_0_4_4, all_109_0_17 and discharging atoms app(nil, all_109_0_17) = all_0_4_4, ssList(all_109_0_17), yields: % 272.87/191.98 | (215) all_109_0_17 = all_0_4_4 % 272.87/191.98 | % 272.87/191.98 | From (213) and (203) follows: % 272.87/191.98 | (216) app(all_0_3_3, nil) = all_0_3_3 % 272.87/191.98 | % 272.87/191.98 | From (214) and (193) follows: % 272.87/191.98 | (41) ssList(all_0_3_3) % 272.87/191.98 | % 272.87/191.98 | From (215) and (190) follows: % 272.87/191.98 | (90) ssList(all_0_4_4) % 272.87/191.98 | % 272.87/191.98 | Instantiating formula (57) with nil, all_0_3_3, all_0_3_3, all_113_0_19 and discharging atoms app(all_0_3_3, all_113_0_19) = all_0_3_3, app(all_0_3_3, nil) = all_0_3_3, ssList(all_113_0_19), ssList(all_0_3_3), ssList(nil), yields: % 272.87/191.98 | (219) all_113_0_19 = nil % 272.87/191.98 | % 272.87/191.98 | From (219) and (195) follows: % 272.87/191.98 | (216) app(all_0_3_3, nil) = all_0_3_3 % 272.87/191.98 | % 272.87/191.98 | From (219) and (196) follows: % 272.87/191.98 | (74) ssList(nil) % 272.87/191.98 | % 272.87/191.98 | Instantiating formula (101) with all_119_1_27, all_0_4_4, all_119_2_28, all_0_2_2 and discharging atoms app(all_119_2_28, all_0_4_4) = all_119_1_27, memberP(all_0_4_4, all_0_2_2), ssList(all_119_2_28), ssList(all_0_4_4), ssItem(all_0_2_2), yields: % 272.87/191.98 | (222) memberP(all_119_1_27, all_0_2_2) % 272.87/191.98 | % 272.87/191.98 | Instantiating formula (50) with all_119_1_27, all_0_4_4, all_119_2_28 and discharging atoms app(all_119_2_28, all_0_4_4) = all_119_1_27, ssList(all_119_2_28), ssList(all_0_4_4), yields: % 272.87/191.98 | (223) ssList(all_119_1_27) % 272.87/191.98 | % 272.87/191.98 | Instantiating formula (28) with all_119_1_27, all_119_0_26, all_0_3_3 and discharging atoms app(all_119_1_27, all_119_0_26) = all_0_3_3, ssList(all_119_0_26), ssList(all_0_3_3), yields: % 272.87/191.98 | (224) ~ ssList(all_119_1_27) | rearsegP(all_0_3_3, all_119_0_26) % 272.87/191.98 | % 272.87/191.98 | Instantiating formula (117) with all_119_0_26, all_119_1_27, all_0_3_3 and discharging atoms app(all_119_1_27, all_119_0_26) = all_0_3_3, ssList(all_119_0_26), ssList(all_0_3_3), yields: % 272.87/191.98 | (225) ~ ssList(all_119_1_27) | frontsegP(all_0_3_3, all_119_1_27) % 272.87/191.98 | % 272.87/191.98 | Instantiating formula (123) with nil, all_0_3_3, all_119_1_27, all_119_0_26, all_0_3_3 and discharging atoms app(all_119_1_27, all_119_0_26) = all_0_3_3, app(all_0_3_3, nil) = all_0_3_3, ssList(all_119_0_26), ssList(all_0_3_3), ssList(nil), yields: % 272.87/191.98 | (226) ~ ssList(all_119_1_27) | segmentP(all_0_3_3, all_119_0_26) % 272.87/191.98 | % 272.87/191.98 | Instantiating formula (72) with all_0_3_3, nil, all_0_3_3, all_119_0_26, all_119_1_27 and discharging atoms app(all_119_1_27, all_119_0_26) = all_0_3_3, app(all_0_3_3, nil) = all_0_3_3, ssList(all_119_0_26), ssList(nil), yields: % 272.87/191.98 | (227) ~ ssList(all_119_1_27) | ? [v0] : (app(all_119_0_26, nil) = v0 & app(all_119_1_27, v0) = all_0_3_3) % 273.32/191.98 | % 273.32/191.98 | Instantiating formula (117) with all_0_4_4, all_119_2_28, all_119_1_27 and discharging atoms app(all_119_2_28, all_0_4_4) = all_119_1_27, ssList(all_119_2_28), ssList(all_0_4_4), yields: % 273.32/191.98 | (228) ~ ssList(all_119_1_27) | frontsegP(all_119_1_27, all_119_2_28) % 273.32/191.98 | % 273.32/191.98 | Instantiating formula (7) with all_21_0_5 and discharging atoms ssList(all_21_0_5), yields: % 273.32/191.98 | (229) all_21_0_5 = nil | ? [v0] : ? [v1] : (cons(v1, v0) = all_21_0_5 & ssList(v0) & ssItem(v1)) % 273.32/191.98 | % 273.32/191.98 +-Applying beta-rule and splitting (226), into two cases. % 273.32/191.98 |-Branch one: % 273.32/191.98 | (230) ~ ssList(all_119_1_27) % 273.32/191.98 | % 273.32/191.98 | Using (223) and (230) yields: % 273.32/191.98 | (158) $false % 273.32/191.98 | % 273.32/191.98 |-The branch is then unsatisfiable % 273.32/191.98 |-Branch two: % 273.32/191.98 | (223) ssList(all_119_1_27) % 273.32/191.98 | (233) segmentP(all_0_3_3, all_119_0_26) % 273.32/191.98 | % 273.32/191.98 +-Applying beta-rule and splitting (228), into two cases. % 273.32/191.98 |-Branch one: % 273.32/191.98 | (230) ~ ssList(all_119_1_27) % 273.32/191.98 | % 273.32/191.98 | Using (223) and (230) yields: % 273.32/191.98 | (158) $false % 273.32/191.98 | % 273.32/191.98 |-The branch is then unsatisfiable % 273.32/191.98 |-Branch two: % 273.32/191.98 | (223) ssList(all_119_1_27) % 273.32/191.98 | (237) frontsegP(all_119_1_27, all_119_2_28) % 273.32/191.98 | % 273.32/191.98 +-Applying beta-rule and splitting (229), into two cases. % 273.32/191.98 |-Branch one: % 273.32/191.98 | (238) all_21_0_5 = nil % 273.32/191.98 | % 273.32/191.99 | Equations (238) can reduce 179 to: % 273.32/191.99 | (239) $false % 273.32/191.99 | % 273.32/191.99 |-The branch is then unsatisfiable % 273.32/191.99 |-Branch two: % 273.32/191.99 | (179) ~ (all_21_0_5 = nil) % 273.32/191.99 | (241) ? [v0] : ? [v1] : (cons(v1, v0) = all_21_0_5 & ssList(v0) & ssItem(v1)) % 273.32/191.99 | % 273.32/191.99 | Instantiating (241) with all_381_0_132, all_381_1_133 yields: % 273.32/191.99 | (242) cons(all_381_0_132, all_381_1_133) = all_21_0_5 & ssList(all_381_1_133) & ssItem(all_381_0_132) % 273.32/191.99 | % 273.32/191.99 | Applying alpha-rule on (242) yields: % 273.32/191.99 | (243) cons(all_381_0_132, all_381_1_133) = all_21_0_5 % 273.32/191.99 | (244) ssList(all_381_1_133) % 273.32/191.99 | (245) ssItem(all_381_0_132) % 273.32/191.99 | % 273.32/191.99 +-Applying beta-rule and splitting (225), into two cases. % 273.34/191.99 |-Branch one: % 273.34/191.99 | (230) ~ ssList(all_119_1_27) % 273.34/191.99 | % 273.34/191.99 | Using (223) and (230) yields: % 273.34/191.99 | (158) $false % 273.34/191.99 | % 273.34/191.99 |-The branch is then unsatisfiable % 273.34/191.99 |-Branch two: % 273.34/191.99 | (223) ssList(all_119_1_27) % 273.34/191.99 | (249) frontsegP(all_0_3_3, all_119_1_27) % 273.34/191.99 | % 273.34/191.99 +-Applying beta-rule and splitting (224), into two cases. % 273.34/191.99 |-Branch one: % 273.34/191.99 | (230) ~ ssList(all_119_1_27) % 273.34/191.99 | % 273.34/191.99 | Using (223) and (230) yields: % 273.34/191.99 | (158) $false % 273.34/191.99 | % 273.34/191.99 |-The branch is then unsatisfiable % 273.34/191.99 |-Branch two: % 273.34/191.99 | (223) ssList(all_119_1_27) % 273.34/191.99 | (253) rearsegP(all_0_3_3, all_119_0_26) % 273.34/191.99 | % 273.34/191.99 +-Applying beta-rule and splitting (227), into two cases. % 273.34/191.99 |-Branch one: % 273.34/191.99 | (230) ~ ssList(all_119_1_27) % 273.34/191.99 | % 273.34/191.99 | Using (223) and (230) yields: % 273.34/191.99 | (158) $false % 273.34/191.99 | % 273.34/191.99 |-The branch is then unsatisfiable % 273.34/191.99 |-Branch two: % 273.34/191.99 | (223) ssList(all_119_1_27) % 273.34/191.99 | (257) ? [v0] : (app(all_119_0_26, nil) = v0 & app(all_119_1_27, v0) = all_0_3_3) % 273.34/191.99 | % 273.34/191.99 | Instantiating (257) with all_454_0_145 yields: % 273.34/191.99 | (258) app(all_119_0_26, nil) = all_454_0_145 & app(all_119_1_27, all_454_0_145) = all_0_3_3 % 273.34/191.99 | % 273.34/191.99 | Applying alpha-rule on (258) yields: % 273.34/191.99 | (259) app(all_119_0_26, nil) = all_454_0_145 % 273.34/191.99 | (260) app(all_119_1_27, all_454_0_145) = all_0_3_3 % 273.34/191.99 | % 273.34/191.99 | Instantiating formula (9) with all_454_0_145, all_119_0_26 and discharging atoms app(all_119_0_26, nil) = all_454_0_145, ssList(all_119_0_26), yields: % 273.34/191.99 | (261) all_454_0_145 = all_119_0_26 % 273.34/191.99 | % 273.34/191.99 | Instantiating formula (52) with all_0_2_2, all_21_0_5, all_381_0_132, all_21_1_6, all_381_1_133 and discharging atoms cons(all_381_0_132, all_381_1_133) = all_21_0_5, cons(all_0_2_2, all_21_1_6) = all_21_0_5, ssList(all_381_1_133), ssList(all_21_1_6), ssItem(all_381_0_132), ssItem(all_0_2_2), yields: % 273.34/191.99 | (262) all_381_0_132 = all_0_2_2 % 273.34/191.99 | % 273.34/191.99 | From (261) and (260) follows: % 273.34/191.99 | (198) app(all_119_1_27, all_119_0_26) = all_0_3_3 % 273.34/191.99 | % 273.34/191.99 | From (262) and (245) follows: % 273.34/191.99 | (130) ssItem(all_0_2_2) % 273.34/191.99 | % 273.34/191.99 | Instantiating formula (64) with all_0_3_3, all_119_0_26, all_119_1_27, all_0_2_2 and discharging atoms app(all_119_1_27, all_119_0_26) = all_0_3_3, memberP(all_119_1_27, all_0_2_2), ssList(all_119_0_26), ssList(all_119_1_27), ssItem(all_0_2_2), ~ memberP(all_0_3_3, all_0_2_2), yields: % 273.34/191.99 | (158) $false % 273.34/191.99 | % 273.34/191.99 |-The branch is then unsatisfiable % 273.34/191.99 |-Branch two: % 273.34/191.99 | (157) ~ neq(all_0_3_3, nil) % 273.34/191.99 | (267) all_0_3_3 = nil % 273.34/191.99 | % 273.34/191.99 | Equations (267) can reduce 138 to: % 273.34/191.99 | (239) $false % 273.34/191.99 | % 273.34/191.99 |-The branch is then unsatisfiable % 273.34/191.99 |-Branch two: % 273.34/191.99 | (267) all_0_3_3 = nil % 273.34/191.99 | (270) all_0_4_4 = nil % 273.34/191.99 | % 273.34/191.99 | Equations (270) can reduce 137 to: % 273.34/191.99 | (239) $false % 273.34/191.99 | % 273.34/191.99 |-The branch is then unsatisfiable % 273.34/191.99 % SZS output end Proof for theBenchmark % 273.34/191.99 % 273.34/191.99 191401ms %------------------------------------------------------------------------------