TSTP Solution File: SWC048+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWC048+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n025.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 20:15:55 EDT 2022
% Result : Theorem 21.13s 6.41s
% Output : Proof 24.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC048+1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 12 23:58:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.51/0.60 ____ _
% 0.51/0.60 ___ / __ \_____(_)___ ________ __________
% 0.51/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.60
% 0.51/0.60 A Theorem Prover for First-Order Logic
% 0.51/0.60 (ePrincess v.1.0)
% 0.51/0.60
% 0.51/0.60 (c) Philipp Rümmer, 2009-2015
% 0.51/0.60 (c) Peter Backeman, 2014-2015
% 0.51/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.51/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.51/0.60 Bug reports to peter@backeman.se
% 0.51/0.60
% 0.51/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.51/0.60
% 0.51/0.60 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.71/0.65 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.34/1.12 Prover 0: Preprocessing ...
% 4.78/1.72 Prover 0: Constructing countermodel ...
% 18.95/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.55/6.05 Prover 1: Preprocessing ...
% 20.42/6.27 Prover 1: Constructing countermodel ...
% 21.13/6.41 Prover 1: proved (466ms)
% 21.13/6.41 Prover 0: stopped
% 21.13/6.41
% 21.13/6.41 No countermodel exists, formula is valid
% 21.13/6.41 % SZS status Theorem for theBenchmark
% 21.13/6.41
% 21.13/6.41 Generating proof ... found it (size 86)
% 23.56/6.98
% 23.56/6.98 % SZS output start Proof for theBenchmark
% 23.56/6.98 Assumed formulas after preprocessing and simplification:
% 23.56/6.98 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v6) & ~ (v0 = 0) & equalelemsP(nil) = 0 & duplicatefreeP(nil) = 0 & strictorderedP(nil) = 0 & totalorderedP(nil) = 0 & strictorderP(nil) = 0 & totalorderP(nil) = 0 & cyclefreeP(nil) = 0 & rearsegP(v2, v1) = v5 & singletonP(nil) = v0 & ssList(v2) = 0 & ssList(v1) = 0 & ssList(nil) = 0 & neq(v2, nil) = v3 & neq(v1, nil) = v4 & ssItem(v7) = 0 & ssItem(v6) = 0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v11 = 0 | ~ (strictorderedP(v8) = 0) | ~ (lt(v9, v10) = v11) | ~ (ssList(v12) = 0) | ~ (cons(v10, v16) = v17) | ~ (cons(v9, v13) = v14) | ~ (app(v15, v17) = v8) | ~ (app(v12, v14) = v15) | ~ (ssItem(v9) = 0) | ? [v18] : (( ~ (v18 = 0) & ssList(v16) = v18) | ( ~ (v18 = 0) & ssList(v13) = v18) | ( ~ (v18 = 0) & ssList(v8) = v18) | ( ~ (v18 = 0) & ssItem(v10) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v11 = 0 | ~ (totalorderedP(v8) = 0) | ~ (leq(v9, v10) = v11) | ~ (ssList(v12) = 0) | ~ (cons(v10, v16) = v17) | ~ (cons(v9, v13) = v14) | ~ (app(v15, v17) = v8) | ~ (app(v12, v14) = v15) | ~ (ssItem(v9) = 0) | ? [v18] : (( ~ (v18 = 0) & ssList(v16) = v18) | ( ~ (v18 = 0) & ssList(v13) = v18) | ( ~ (v18 = 0) & ssList(v8) = v18) | ( ~ (v18 = 0) & ssItem(v10) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (duplicatefreeP(v8) = 0) | ~ (ssList(v10) = 0) | ~ (cons(v9, v14) = v15) | ~ (cons(v9, v11) = v12) | ~ (app(v13, v15) = v8) | ~ (app(v10, v12) = v13) | ~ (ssItem(v9) = 0) | ? [v16] : (( ~ (v16 = 0) & ssList(v14) = v16) | ( ~ (v16 = 0) & ssList(v11) = v16) | ( ~ (v16 = 0) & ssList(v8) = v16))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (segmentP(v13, v9) = v14) | ~ (segmentP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ~ (app(v11, v12) = v13) | ~ (app(v10, v8) = v11) | ? [v15] : (( ~ (v15 = 0) & ssList(v12) = v15) | ( ~ (v15 = 0) & ssList(v10) = v15) | ( ~ (v15 = 0) & ssList(v9) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (equalelemsP(v8) = 0) | ~ (ssList(v11) = 0) | ~ (cons(v10, v12) = v13) | ~ (cons(v9, v13) = v14) | ~ (app(v11, v14) = v8) | ~ (ssItem(v10) = 0) | ~ (ssItem(v9) = 0) | ? [v15] : (( ~ (v15 = 0) & ssList(v12) = v15) | ( ~ (v15 = 0) & ssList(v8) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (frontsegP(v11, v13) = v14) | ~ (cons(v9, v12) = v13) | ~ (cons(v8, v10) = v11) | ~ (ssItem(v9) = 0) | ~ (ssItem(v8) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssList(v10) = v15) | (frontsegP(v10, v12) = v16 & ssList(v12) = v15 & ( ~ (v15 = 0) | (( ~ (v16 = 0) | ~ (v9 = v8) | v14 = 0) & ( ~ (v14 = 0) | (v16 = 0 & v9 = v8))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = 0 | ~ (segmentP(v8, v9) = v10) | ~ (ssList(v8) = 0) | ~ (app(v12, v13) = v8) | ~ (app(v11, v9) = v12) | ? [v14] : (( ~ (v14 = 0) & ssList(v13) = v14) | ( ~ (v14 = 0) & ssList(v11) = v14) | ( ~ (v14 = 0) & ssList(v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = 0 | ~ (memberP(v8, v9) = v10) | ~ (ssList(v11) = 0) | ~ (ssList(v8) = 0) | ~ (cons(v9, v12) = v13) | ~ (app(v11, v13) = v8) | ? [v14] : (( ~ (v14 = 0) & ssList(v12) = v14) | ( ~ (v14 = 0) & ssItem(v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (memberP(v12, v8) = v13) | ~ (memberP(v9, v8) = v10) | ~ (app(v9, v11) = v12) | ~ (ssItem(v8) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssList(v9) = v14) | (memberP(v11, v8) = v15 & ssList(v11) = v14 & ( ~ (v14 = 0) | (( ~ (v13 = 0) | v15 = 0 | v10 = 0) & (v13 = 0 | ( ~ (v15 = 0) & ~ (v10 = 0)))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (ssList(v8) = 0) | ~ (cons(v11, v9) = v12) | ~ (app(v12, v8) = v13) | ~ (app(v9, v8) = v10) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssList(v9) = v14) | (cons(v11, v10) = v15 & ssItem(v11) = v14 & ( ~ (v14 = 0) | v15 = v13)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (ssList(v9) = 0) | ~ (ssList(v8) = 0) | ~ (cons(v12, v9) = v11) | ~ (cons(v10, v8) = v11) | ? [v13] : (( ~ (v13 = 0) & ssItem(v12) = v13) | ( ~ (v13 = 0) & ssItem(v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (rearsegP(v11, v9) = v12) | ~ (rearsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ~ (app(v10, v8) = v11) | ? [v13] : (( ~ (v13 = 0) & ssList(v10) = v13) | ( ~ (v13 = 0) & ssList(v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (frontsegP(v11, v9) = v12) | ~ (frontsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ~ (app(v8, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & ssList(v10) = v13) | ( ~ (v13 = 0) & ssList(v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (ssList(v9) = 0) | ~ (ssList(v8) = 0) | ~ (cons(v12, v9) = v11) | ~ (cons(v10, v8) = v11) | ? [v13] : (( ~ (v13 = 0) & ssItem(v12) = v13) | ( ~ (v13 = 0) & ssItem(v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (memberP(v11, v8) = v12) | ~ (cons(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ~ (ssItem(v8) = 0) | ? [v13] : ? [v14] : (memberP(v10, v8) = v14 & ssList(v10) = v13 & ( ~ (v13 = 0) | (( ~ (v12 = 0) | v14 = 0 | v9 = v8) & (v12 = 0 | ( ~ (v14 = 0) & ~ (v9 = v8))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (ssList(v8) = 0) | ~ (app(v10, v11) = v12) | ~ (app(v8, v9) = v10) | ? [v13] : ? [v14] : ? [v15] : (( ~ (v13 = 0) & ssList(v9) = v13) | (ssList(v11) = v13 & app(v9, v11) = v14 & app(v8, v14) = v15 & ( ~ (v13 = 0) | v15 = v12)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | v8 = nil | ~ (tl(v8) = v10) | ~ (hd(v8) = v9) | ~ (cons(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & ssList(v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (ssList(v8) = 0) | ~ (app(v11, v9) = v10) | ~ (app(v8, v9) = v10) | ? [v12] : (( ~ (v12 = 0) & ssList(v11) = v12) | ( ~ (v12 = 0) & ssList(v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (ssList(v8) = 0) | ~ (app(v9, v11) = v10) | ~ (app(v9, v8) = v10) | ? [v12] : (( ~ (v12 = 0) & ssList(v11) = v12) | ( ~ (v12 = 0) & ssList(v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (gt(v8, v10) = v11) | ~ (gt(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssItem(v9) = v12) | (gt(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (geq(v8, v10) = v11) | ~ (geq(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssItem(v9) = v12) | (geq(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (lt(v8, v10) = v11) | ~ (lt(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssItem(v9) = v12) | (lt(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (lt(v8, v10) = v11) | ~ (leq(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssItem(v9) = v12) | (lt(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (leq(v8, v10) = v11) | ~ (leq(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssItem(v9) = v12) | (leq(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (segmentP(v8, v10) = v11) | ~ (segmentP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v9) = v12) | (segmentP(v9, v10) = v13 & ssList(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (rearsegP(v8, v10) = v11) | ~ (rearsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v9) = v12) | (rearsegP(v9, v10) = v13 & ssList(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (frontsegP(v8, v10) = v11) | ~ (frontsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v9) = v12) | (frontsegP(v9, v10) = v13 & ssList(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (rearsegP(v8, v9) = v10) | ~ (ssList(v8) = 0) | ~ (app(v11, v9) = v8) | ? [v12] : (( ~ (v12 = 0) & ssList(v11) = v12) | ( ~ (v12 = 0) & ssList(v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (frontsegP(v8, v9) = v10) | ~ (ssList(v8) = 0) | ~ (app(v9, v11) = v8) | ? [v12] : (( ~ (v12 = 0) & ssList(v11) = v12) | ( ~ (v12 = 0) & ssList(v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (gt(v11, v10) = v9) | ~ (gt(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (geq(v11, v10) = v9) | ~ (geq(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (lt(v11, v10) = v9) | ~ (lt(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (leq(v11, v10) = v9) | ~ (leq(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (segmentP(v11, v10) = v9) | ~ (segmentP(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (rearsegP(v11, v10) = v9) | ~ (rearsegP(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (frontsegP(v11, v10) = v9) | ~ (frontsegP(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (memberP(v11, v10) = v9) | ~ (memberP(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (cons(v11, v10) = v9) | ~ (cons(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (app(v11, v10) = v9) | ~ (app(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (neq(v11, v10) = v9) | ~ (neq(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = nil | ~ (tl(v8) = v9) | ~ (app(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (( ~ (v12 = 0) & ssList(v8) = v12) | (tl(v13) = v14 & ssList(v10) = v12 & app(v8, v10) = v13 & ( ~ (v12 = 0) | v14 = v11)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = nil | ~ (hd(v8) = v9) | ~ (app(v8, v10) = v11) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v8) = v12) | (hd(v11) = v13 & ssList(v10) = v12 & ( ~ (v12 = 0) | v13 = v9)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (hd(v9) = v10) | ~ (lt(v8, v10) = v11) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (strictorderedP(v13) = v14 & strictorderedP(v9) = v15 & ssList(v9) = v12 & cons(v8, v9) = v13 & ( ~ (v12 = 0) | (( ~ (v14 = 0) | v9 = nil | (v15 = 0 & v11 = 0)) & (v14 = 0 | ( ~ (v9 = nil) & ( ~ (v15 = 0) | ~ (v11 = 0)))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (hd(v9) = v10) | ~ (leq(v8, v10) = v11) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (totalorderedP(v13) = v14 & totalorderedP(v9) = v15 & ssList(v9) = v12 & cons(v8, v9) = v13 & ( ~ (v12 = 0) | (( ~ (v14 = 0) | v9 = nil | (v15 = 0 & v11 = 0)) & (v14 = 0 | ( ~ (v9 = nil) & ( ~ (v15 = 0) | ~ (v11 = 0)))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (strictorderP(v8) = 0) | ~ (lt(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v8) = v12) | (lt(v10, v9) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v13 = 0 | v11 = 0 | ~ (ssList(v14) = 0) | ~ (cons(v10, v18) = v19) | ~ (cons(v9, v15) = v16) | ~ (app(v17, v19) = v8) | ~ (app(v14, v16) = v17) | ? [v20] : (( ~ (v20 = 0) & ssList(v18) = v20) | ( ~ (v20 = 0) & ssList(v15) = v20))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (totalorderP(v8) = 0) | ~ (leq(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v8) = v12) | (leq(v10, v9) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v13 = 0 | v11 = 0 | ~ (ssList(v14) = 0) | ~ (cons(v10, v18) = v19) | ~ (cons(v9, v15) = v16) | ~ (app(v17, v19) = v8) | ~ (app(v14, v16) = v17) | ? [v20] : (( ~ (v20 = 0) & ssList(v18) = v20) | ( ~ (v20 = 0) & ssList(v15) = v20))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (cyclefreeP(v8) = 0) | ~ (leq(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v8) = v12) | (leq(v10, v9) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (v13 = 0) | ~ (v11 = 0) | ~ (ssList(v14) = 0) | ~ (cons(v10, v18) = v19) | ~ (cons(v9, v15) = v16) | ~ (app(v17, v19) = v8) | ~ (app(v14, v16) = v17) | ? [v20] : (( ~ (v20 = 0) & ssList(v18) = v20) | ( ~ (v20 = 0) & ssList(v15) = v20))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, nil) = v10) | ~ (app(v10, v8) = v11) | ? [v12] : ? [v13] : (cons(v9, v8) = v13 & ssItem(v9) = v12 & ( ~ (v12 = 0) | v13 = v11))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = v8 | ~ (lt(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (leq(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = v8 | ~ (ssList(v8) = 0) | ~ (neq(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & ssList(v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = v8 | ~ (neq(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ( ~ (v11 = 0) & ssItem(v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (tl(v10) = v9) | ~ (tl(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (hd(v10) = v9) | ~ (hd(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (equalelemsP(v10) = v9) | ~ (equalelemsP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (duplicatefreeP(v10) = v9) | ~ (duplicatefreeP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (strictorderedP(v10) = v9) | ~ (strictorderedP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (totalorderedP(v10) = v9) | ~ (totalorderedP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (strictorderP(v10) = v9) | ~ (strictorderP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (totalorderP(v10) = v9) | ~ (totalorderP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (cyclefreeP(v10) = v9) | ~ (cyclefreeP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singletonP(v10) = v9) | ~ (singletonP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (ssList(v10) = v9) | ~ (ssList(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (ssItem(v10) = v9) | ~ (ssItem(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (singletonP(v8) = v9) | ~ (cons(v10, nil) = v8) | ? [v11] : (( ~ (v11 = 0) & ssList(v8) = v11) | ( ~ (v11 = 0) & ssItem(v10) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (gt(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (lt(v9, v8) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | (( ~ (v12 = 0) | v10 = 0) & ( ~ (v10 = 0) | v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (geq(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (leq(v9, v8) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | (( ~ (v12 = 0) | v10 = 0) & ( ~ (v10 = 0) | v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (lt(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (leq(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | (( ~ (v12 = 0) | v10 = 0 | v9 = v8) & ( ~ (v10 = 0) | (v12 = 0 & ~ (v9 = v8))))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, v8) = v10) | ? [v11] : ? [v12] : (tl(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = v8))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, v8) = v10) | ? [v11] : ? [v12] : (hd(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = v9))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, v8) = v10) | ? [v11] : ? [v12] : (ssList(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ssList(v8) = 0) | ~ (app(v8, v9) = v10) | ? [v11] : ? [v12] : (ssList(v10) = v12 & ssList(v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (geq(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v10] : ? [v11] : (geq(v9, v8) = v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (leq(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v10] : ? [v11] : (leq(v9, v8) = v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (segmentP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : (segmentP(v9, v8) = v11 & ssList(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (rearsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : (rearsegP(v9, v8) = v11 & ssList(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (frontsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : (frontsegP(v9, v8) = v11 & ssList(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (app(v8, nil) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (app(nil, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = nil | ~ (ssList(v8) = 0) | ~ (app(v8, v9) = nil) | ? [v10] : ( ~ (v10 = 0) & ssList(v9) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (geq(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssItem(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (equalelemsP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v20 = v8 & v17 = 0 & v15 = 0 & v13 = 0 & v11 = 0 & ~ (v12 = v10) & ssList(v16) = 0 & ssList(v14) = 0 & cons(v12, v16) = v18 & cons(v10, v18) = v19 & app(v14, v19) = v8 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (duplicatefreeP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v23 = v8 & v21 = 0 & v17 = 0 & v15 = 0 & v13 = 0 & v12 = v10 & v11 = 0 & ssList(v20) = 0 & ssList(v16) = 0 & ssList(v14) = 0 & cons(v10, v20) = v22 & cons(v10, v16) = v18 & app(v19, v22) = v8 & app(v14, v18) = v19 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (strictorderedP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v24 = v8 & v22 = 0 & v18 = 0 & v16 = 0 & v13 = 0 & v11 = 0 & ~ (v14 = 0) & lt(v10, v12) = v14 & ssList(v21) = 0 & ssList(v17) = 0 & ssList(v15) = 0 & cons(v12, v21) = v23 & cons(v10, v17) = v19 & app(v20, v23) = v8 & app(v15, v19) = v20 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (totalorderedP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v24 = v8 & v22 = 0 & v18 = 0 & v16 = 0 & v13 = 0 & v11 = 0 & ~ (v14 = 0) & leq(v10, v12) = v14 & ssList(v21) = 0 & ssList(v17) = 0 & ssList(v15) = 0 & cons(v12, v21) = v23 & cons(v10, v17) = v19 & app(v20, v23) = v8 & app(v15, v19) = v20 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (strictorderP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = v8 & v23 = 0 & v19 = 0 & v17 = 0 & v13 = 0 & v11 = 0 & ~ (v15 = 0) & ~ (v14 = 0) & lt(v12, v10) = v15 & lt(v10, v12) = v14 & ssList(v22) = 0 & ssList(v18) = 0 & ssList(v16) = 0 & cons(v12, v22) = v24 & cons(v10, v18) = v20 & app(v21, v24) = v8 & app(v16, v20) = v21 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (totalorderP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = v8 & v23 = 0 & v19 = 0 & v17 = 0 & v13 = 0 & v11 = 0 & ~ (v15 = 0) & ~ (v14 = 0) & leq(v12, v10) = v15 & leq(v10, v12) = v14 & ssList(v22) = 0 & ssList(v18) = 0 & ssList(v16) = 0 & cons(v12, v22) = v24 & cons(v10, v18) = v20 & app(v21, v24) = v8 & app(v16, v20) = v21 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (cyclefreeP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = v8 & v23 = 0 & v19 = 0 & v17 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & v11 = 0 & leq(v12, v10) = 0 & leq(v10, v12) = 0 & ssList(v22) = 0 & ssList(v18) = 0 & ssList(v16) = 0 & cons(v12, v22) = v24 & cons(v10, v18) = v20 & app(v21, v24) = v8 & app(v16, v20) = v21 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (leq(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssItem(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (segmentP(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (segmentP(v8, nil) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (rearsegP(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (rearsegP(v8, nil) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (frontsegP(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (frontsegP(v8, nil) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v8 = nil | ~ (tl(v8) = v9) | ? [v10] : ? [v11] : (ssList(v9) = v11 & ssList(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : (v8 = nil | ~ (tl(v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = v9 & ssList(v9) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v8 = nil | ~ (hd(v8) = v9) | ? [v10] : ? [v11] : (ssList(v8) = v10 & ssItem(v9) = v11 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : (v8 = nil | ~ (hd(v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = v9 & ssItem(v9) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v8 = nil | ~ (ssList(v8) = 0) | ~ (app(v8, v9) = nil) | ? [v10] : ( ~ (v10 = 0) & ssList(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (gt(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v10] : ? [v11] : (gt(v9, v8) = v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : ( ~ (tl(v8) = v9) | ? [v10] : ? [v11] : (hd(v8) = v11 & ssList(v8) = v10 & ( ~ (v10 = 0) | ! [v12] : (v12 = v8 | v12 = nil | v8 = nil | ~ (tl(v12) = v9) | ? [v13] : ? [v14] : (hd(v12) = v14 & ssList(v12) = v13 & ( ~ (v14 = v11) | ~ (v13 = 0))))))) & ! [v8] : ! [v9] : ( ~ (lt(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v10] : ? [v11] : (lt(v9, v8) = v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : ( ~ (segmentP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v15 = v8 & v14 = 0 & v11 = 0 & ssList(v13) = 0 & ssList(v10) = 0 & app(v12, v13) = v8 & app(v10, v9) = v12) | ( ~ (v10 = 0) & ssList(v9) = v10))) & ! [v8] : ! [v9] : ( ~ (rearsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v8 & v11 = 0 & ssList(v10) = 0 & app(v10, v9) = v8) | ( ~ (v10 = 0) & ssList(v9) = v10))) & ! [v8] : ! [v9] : ( ~ (frontsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v8 & v11 = 0 & ssList(v10) = 0 & app(v9, v10) = v8) | ( ~ (v10 = 0) & ssList(v9) = v10))) & ! [v8] : ! [v9] : ( ~ (memberP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v15 = v8 & v13 = 0 & v11 = 0 & ssList(v12) = 0 & ssList(v10) = 0 & cons(v9, v12) = v14 & app(v10, v14) = v8) | ( ~ (v10 = 0) & ssItem(v9) = v10))) & ! [v8] : ! [v9] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, v8) = v8) | ? [v10] : ( ~ (v10 = 0) & ssItem(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, v8) = nil) | ? [v10] : ( ~ (v10 = 0) & ssItem(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (equalelemsP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (duplicatefreeP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (strictorderedP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (totalorderedP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (strictorderP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (totalorderP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (cyclefreeP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : (v8 = nil | ~ (segmentP(nil, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & ssList(v8) = v9)) & ! [v8] : (v8 = nil | ~ (rearsegP(nil, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & ssList(v8) = v9)) & ! [v8] : (v8 = nil | ~ (frontsegP(nil, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & ssList(v8) = v9)) & ! [v8] : (v8 = nil | ~ (ssList(v8) = 0) | ? [v9] : ? [v10] : (ssList(v9) = 0 & cons(v10, v9) = v8 & ssItem(v10) = 0)) & ! [v8] : (v8 = nil | ~ (app(nil, nil) = v8)) & ! [v8] : (v8 = 0 | ~ (segmentP(nil, nil) = v8)) & ! [v8] : (v8 = 0 | ~ (rearsegP(nil, nil) = v8)) & ! [v8] : (v8 = 0 | ~ (frontsegP(nil, nil) = v8)) & ! [v8] : ( ~ (lt(v8, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & ssItem(v8) = v9)) & ! [v8] : ( ~ (singletonP(v8) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v10 = 0 & cons(v9, nil) = v8 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v8) = v9))) & ! [v8] : ( ~ (memberP(nil, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & ssItem(v8) = v9)) & ! [v8] : ( ~ (ssList(v8) = 0) | ~ (neq(v8, v8) = 0)) & ! [v8] : ( ~ (neq(v8, v8) = 0) | ~ (ssItem(v8) = 0)) & ((v5 = 0 & v4 = 0) | (v2 = nil & v1 = nil)) & ((v3 = 0 & ! [v8] : ( ~ (neq(v8, nil) = 0) | ? [v9] : ? [v10] : ? [v11] : (rearsegP(v2, v8) = v10 & rearsegP(v1, v8) = v11 & ssList(v8) = v9 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0))))) | (v2 = nil & ~ (v1 = nil))))
% 23.91/7.05 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 23.91/7.05 | (1) ~ (all_0_0_0 = all_0_1_1) & ~ (all_0_7_7 = 0) & equalelemsP(nil) = 0 & duplicatefreeP(nil) = 0 & strictorderedP(nil) = 0 & totalorderedP(nil) = 0 & strictorderP(nil) = 0 & totalorderP(nil) = 0 & cyclefreeP(nil) = 0 & rearsegP(all_0_5_5, all_0_6_6) = all_0_2_2 & singletonP(nil) = all_0_7_7 & ssList(all_0_5_5) = 0 & ssList(all_0_6_6) = 0 & ssList(nil) = 0 & neq(all_0_5_5, nil) = all_0_4_4 & neq(all_0_6_6, nil) = all_0_3_3 & ssItem(all_0_0_0) = 0 & ssItem(all_0_1_1) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v3 = 0 | ~ (strictorderedP(v0) = 0) | ~ (lt(v1, v2) = v3) | ~ (ssList(v4) = 0) | ~ (cons(v2, v8) = v9) | ~ (cons(v1, v5) = v6) | ~ (app(v7, v9) = v0) | ~ (app(v4, v6) = v7) | ~ (ssItem(v1) = 0) | ? [v10] : (( ~ (v10 = 0) & ssList(v8) = v10) | ( ~ (v10 = 0) & ssList(v5) = v10) | ( ~ (v10 = 0) & ssList(v0) = v10) | ( ~ (v10 = 0) & ssItem(v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v3 = 0 | ~ (totalorderedP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssList(v4) = 0) | ~ (cons(v2, v8) = v9) | ~ (cons(v1, v5) = v6) | ~ (app(v7, v9) = v0) | ~ (app(v4, v6) = v7) | ~ (ssItem(v1) = 0) | ? [v10] : (( ~ (v10 = 0) & ssList(v8) = v10) | ( ~ (v10 = 0) & ssList(v5) = v10) | ( ~ (v10 = 0) & ssList(v0) = v10) | ( ~ (v10 = 0) & ssItem(v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (duplicatefreeP(v0) = 0) | ~ (ssList(v2) = 0) | ~ (cons(v1, v6) = v7) | ~ (cons(v1, v3) = v4) | ~ (app(v5, v7) = v0) | ~ (app(v2, v4) = v5) | ~ (ssItem(v1) = 0) | ? [v8] : (( ~ (v8 = 0) & ssList(v6) = v8) | ( ~ (v8 = 0) & ssList(v3) = v8) | ( ~ (v8 = 0) & ssList(v0) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (segmentP(v5, v1) = v6) | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v3, v4) = v5) | ~ (app(v2, v0) = v3) | ? [v7] : (( ~ (v7 = 0) & ssList(v4) = v7) | ( ~ (v7 = 0) & ssList(v2) = v7) | ( ~ (v7 = 0) & ssList(v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (equalelemsP(v0) = 0) | ~ (ssList(v3) = 0) | ~ (cons(v2, v4) = v5) | ~ (cons(v1, v5) = v6) | ~ (app(v3, v6) = v0) | ~ (ssItem(v2) = 0) | ~ (ssItem(v1) = 0) | ? [v7] : (( ~ (v7 = 0) & ssList(v4) = v7) | ( ~ (v7 = 0) & ssList(v0) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (frontsegP(v3, v5) = v6) | ~ (cons(v1, v4) = v5) | ~ (cons(v0, v2) = v3) | ~ (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ? [v7] : ? [v8] : (( ~ (v7 = 0) & ssList(v2) = v7) | (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 = 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = 0 | ~ (segmentP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v4, v5) = v0) | ~ (app(v3, v1) = v4) | ? [v6] : (( ~ (v6 = 0) & ssList(v5) = v6) | ( ~ (v6 = 0) & ssList(v3) = v6) | ( ~ (v6 = 0) & ssList(v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = 0 | ~ (memberP(v0, v1) = v2) | ~ (ssList(v3) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v1, v4) = v5) | ~ (app(v3, v5) = v0) | ? [v6] : (( ~ (v6 = 0) & ssList(v4) = v6) | ( ~ (v6 = 0) & ssItem(v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (memberP(v4, v0) = v5) | ~ (memberP(v1, v0) = v2) | ~ (app(v1, v3) = v4) | ~ (ssItem(v0) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & ssList(v1) = v6) | (memberP(v3, v0) = v7 & ssList(v3) = v6 & ( ~ (v6 = 0) | (( ~ (v5 = 0) | v7 = 0 | v2 = 0) & (v5 = 0 | ( ~ (v7 = 0) & ~ (v2 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ssList(v0) = 0) | ~ (cons(v3, v1) = v4) | ~ (app(v4, v0) = v5) | ~ (app(v1, v0) = v2) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & ssList(v1) = v6) | (cons(v3, v2) = v7 & ssItem(v3) = v6 & ( ~ (v6 = 0) | v7 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssItem(v4) = v5) | ( ~ (v5 = 0) & ssItem(v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (rearsegP(v3, v1) = v4) | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssList(v2) = v5) | ( ~ (v5 = 0) & ssList(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (frontsegP(v3, v1) = v4) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v0, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & ssList(v2) = v5) | ( ~ (v5 = 0) & ssList(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssItem(v4) = v5) | ( ~ (v5 = 0) & ssItem(v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (memberP(v3, v0) = v4) | ~ (cons(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ? [v5] : ? [v6] : (memberP(v2, v0) = v6 & ssList(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | v6 = 0 | v1 = v0) & (v4 = 0 | ( ~ (v6 = 0) & ~ (v1 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ssList(v0) = 0) | ~ (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & ssList(v1) = v5) | (ssList(v3) = v5 & app(v1, v3) = v6 & app(v0, v6) = v7 & ( ~ (v5 = 0) | v7 = v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & ssList(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ssList(v0) = 0) | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (gt(v0, v2) = v3) | ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (gt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (geq(v0, v2) = v3) | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (geq(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lt(v0, v2) = v3) | ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (lt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lt(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (lt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (leq(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (segmentP(v0, v2) = v3) | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (segmentP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (rearsegP(v0, v2) = v3) | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (rearsegP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (frontsegP(v0, v2) = v3) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (frontsegP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (rearsegP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v3, v1) = v0) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (frontsegP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v0) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & ssList(v0) = v4) | (tl(v5) = v6 & ssList(v2) = v4 & app(v0, v2) = v5 & ( ~ (v4 = 0) | v6 = v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (hd(v3) = v5 & ssList(v2) = v4 & ( ~ (v4 = 0) | v5 = v1)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (hd(v1) = v2) | ~ (lt(v0, v2) = v3) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (strictorderedP(v5) = v6 & strictorderedP(v1) = v7 & ssList(v1) = v4 & cons(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v1 = nil | (v7 = 0 & v3 = 0)) & (v6 = 0 | ( ~ (v1 = nil) & ( ~ (v7 = 0) | ~ (v3 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (hd(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (totalorderedP(v5) = v6 & totalorderedP(v1) = v7 & ssList(v1) = v4 & cons(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v1 = nil | (v7 = 0 & v3 = 0)) & (v6 = 0 | ( ~ (v1 = nil) & ( ~ (v7 = 0) | ~ (v3 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (strictorderP(v0) = 0) | ~ (lt(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (lt(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v5 = 0 | v3 = 0 | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (totalorderP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (leq(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v5 = 0 | v3 = 0 | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cyclefreeP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (leq(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (v5 = 0) | ~ (v3 = 0) | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ? [v4] : ? [v5] : (cons(v1, v0) = v5 & ssItem(v1) = v4 & ( ~ (v4 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (lt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v0, v1) = v4 & ssItem(v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (ssList(v0) = 0) | ~ (neq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & ssList(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (neq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & ssItem(v1) = v3)) & ! [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] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | ~ (equalelemsP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | ~ (duplicatefreeP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderP(v2) = v1) | ~ (strictorderP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ (totalorderP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ (cyclefreeP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (singletonP(v0) = v1) | ~ (cons(v2, nil) = v0) | ? [v3] : (( ~ (v3 = 0) & ssList(v0) = v3) | ( ~ (v3 = 0) & ssItem(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (gt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (lt(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (geq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (lt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v0, v1) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0 | v1 = v0) & ( ~ (v2 = 0) | (v4 = 0 & ~ (v1 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (tl(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (app(v0, v1) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (geq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (leq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (frontsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (equalelemsP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v0 & v9 = 0 & v7 = 0 & v5 = 0 & v3 = 0 & ~ (v4 = v2) & ssList(v8) = 0 & ssList(v6) = 0 & cons(v4, v8) = v10 & cons(v2, v10) = v11 & app(v6, v11) = v0 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (duplicatefreeP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v15 = v0 & v13 = 0 & v9 = 0 & v7 = 0 & v5 = 0 & v4 = v2 & v3 = 0 & ssList(v12) = 0 & ssList(v8) = 0 & ssList(v6) = 0 & cons(v2, v12) = v14 & cons(v2, v8) = v10 & app(v11, v14) = v0 & app(v6, v10) = v11 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (strictorderedP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v0 & v14 = 0 & v10 = 0 & v8 = 0 & v5 = 0 & v3 = 0 & ~ (v6 = 0) & lt(v2, v4) = v6 & ssList(v13) = 0 & ssList(v9) = 0 & ssList(v7) = 0 & cons(v4, v13) = v15 & cons(v2, v9) = v11 & app(v12, v15) = v0 & app(v7, v11) = v12 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (totalorderedP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v0 & v14 = 0 & v10 = 0 & v8 = 0 & v5 = 0 & v3 = 0 & ~ (v6 = 0) & leq(v2, v4) = v6 & ssList(v13) = 0 & ssList(v9) = 0 & ssList(v7) = 0 & cons(v4, v13) = v15 & cons(v2, v9) = v11 & app(v12, v15) = v0 & app(v7, v11) = v12 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (strictorderP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v5 = 0 & v3 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & lt(v4, v2) = v7 & lt(v2, v4) = v6 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (totalorderP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v5 = 0 & v3 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & leq(v4, v2) = v7 & leq(v2, v4) = v6 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cyclefreeP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & v3 = 0 & leq(v4, v2) = 0 & leq(v2, v4) = 0 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (ssList(v1) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssList(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : (ssList(v0) = v2 & ssItem(v1) = v3 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssItem(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v0 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (gt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (hd(v0) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : (v4 = v0 | v4 = nil | v0 = nil | ~ (tl(v4) = v1) | ? [v5] : ? [v6] : (hd(v4) = v6 & ssList(v4) = v5 & ( ~ (v6 = v3) | ~ (v5 = 0))))))) & ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (lt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v0 & v6 = 0 & v3 = 0 & ssList(v5) = 0 & ssList(v2) = 0 & app(v4, v5) = v0 & app(v2, v1) = v4) | ( ~ (v2 = 0) & ssList(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & v3 = 0 & ssList(v2) = 0 & app(v2, v1) = v0) | ( ~ (v2 = 0) & ssList(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & v3 = 0 & ssList(v2) = 0 & app(v1, v2) = v0) | ( ~ (v2 = 0) & ssList(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (memberP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v0 & v5 = 0 & v3 = 0 & ssList(v4) = 0 & ssList(v2) = 0 & cons(v1, v4) = v6 & app(v2, v6) = v0) | ( ~ (v2 = 0) & ssItem(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v0) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = nil) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : (v0 = nil | ~ (segmentP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1)) & ! [v0] : (v0 = nil | ~ (rearsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1)) & ! [v0] : (v0 = nil | ~ (frontsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1)) & ! [v0] : (v0 = nil | ~ (ssList(v0) = 0) | ? [v1] : ? [v2] : (ssList(v1) = 0 & cons(v2, v1) = v0 & ssItem(v2) = 0)) & ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0)) & ! [v0] : (v0 = 0 | ~ (segmentP(nil, nil) = v0)) & ! [v0] : (v0 = 0 | ~ (rearsegP(nil, nil) = v0)) & ! [v0] : (v0 = 0 | ~ (frontsegP(nil, nil) = v0)) & ! [v0] : ( ~ (lt(v0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1)) & ! [v0] : ( ~ (singletonP(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v0 & v2 = 0 & cons(v1, nil) = v0 & ssItem(v1) = 0) | ( ~ (v1 = 0) & ssList(v0) = v1))) & ! [v0] : ( ~ (memberP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1)) & ! [v0] : ( ~ (ssList(v0) = 0) | ~ (neq(v0, v0) = 0)) & ! [v0] : ( ~ (neq(v0, v0) = 0) | ~ (ssItem(v0) = 0)) & ((all_0_2_2 = 0 & all_0_3_3 = 0) | (all_0_5_5 = nil & all_0_6_6 = nil)) & ((all_0_4_4 = 0 & ! [v0] : ( ~ (neq(v0, nil) = 0) | ? [v1] : ? [v2] : ? [v3] : (rearsegP(all_0_5_5, v0) = v2 & rearsegP(all_0_6_6, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))) | (all_0_5_5 = nil & ~ (all_0_6_6 = nil)))
% 24.26/7.08 |
% 24.26/7.08 | Applying alpha-rule on (1) yields:
% 24.26/7.08 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (totalorderP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (leq(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v5 = 0 | v3 = 0 | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12)))))))
% 24.26/7.08 | (3) ! [v0] : (v0 = 0 | ~ (frontsegP(nil, nil) = v0))
% 24.26/7.08 | (4) ! [v0] : ( ~ (lt(v0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 24.26/7.08 | (5) ! [v0] : ! [v1] : (v1 = v0 | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 24.26/7.08 | (6) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 24.26/7.08 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 24.26/7.08 | (8) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 24.26/7.08 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0))
% 24.26/7.08 | (10) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lt(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (lt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 24.26/7.08 | (11) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 24.26/7.08 | (12) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4)))
% 24.26/7.08 | (13) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cyclefreeP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (leq(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (v5 = 0) | ~ (v3 = 0) | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12)))))))
% 24.26/7.08 | (14) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 24.26/7.08 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (memberP(v3, v0) = v4) | ~ (cons(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ? [v5] : ? [v6] : (memberP(v2, v0) = v6 & ssList(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | v6 = 0 | v1 = v0) & (v4 = 0 | ( ~ (v6 = 0) & ~ (v1 = v0)))))))
% 24.26/7.08 | (16) ! [v0] : ! [v1] : (v1 = v0 | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 24.26/7.08 | (17) ! [v0] : ! [v1] : (v1 = 0 | ~ (totalorderedP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v0 & v14 = 0 & v10 = 0 & v8 = 0 & v5 = 0 & v3 = 0 & ~ (v6 = 0) & leq(v2, v4) = v6 & ssList(v13) = 0 & ssList(v9) = 0 & ssList(v7) = 0 & cons(v4, v13) = v15 & cons(v2, v9) = v11 & app(v12, v15) = v0 & app(v7, v11) = v12 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 24.26/7.08 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderP(v2) = v1) | ~ (strictorderP(v2) = v0))
% 24.26/7.08 | (19) totalorderedP(nil) = 0
% 24.26/7.08 | (20) cyclefreeP(nil) = 0
% 24.26/7.08 | (21) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ? [v4] : ? [v5] : (cons(v1, v0) = v5 & ssItem(v1) = v4 & ( ~ (v4 = 0) | v5 = v3)))
% 24.26/7.08 | (22) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : (ssList(v0) = v2 & ssItem(v1) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 24.26/7.08 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = 0 | ~ (segmentP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v4, v5) = v0) | ~ (app(v3, v1) = v4) | ? [v6] : (( ~ (v6 = 0) & ssList(v5) = v6) | ( ~ (v6 = 0) & ssList(v3) = v6) | ( ~ (v6 = 0) & ssList(v1) = v6)))
% 24.26/7.08 | (24) ! [v0] : ! [v1] : (v1 = 0 | ~ (duplicatefreeP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v15 = v0 & v13 = 0 & v9 = 0 & v7 = 0 & v5 = 0 & v4 = v2 & v3 = 0 & ssList(v12) = 0 & ssList(v8) = 0 & ssList(v6) = 0 & cons(v2, v12) = v14 & cons(v2, v8) = v10 & app(v11, v14) = v0 & app(v6, v10) = v11 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 24.26/7.08 | (25) ! [v0] : ! [v1] : (v1 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 24.26/7.08 | (26) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 24.26/7.08 | (27) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 24.26/7.08 | (28) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0))
% 24.26/7.08 | (29) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (frontsegP(v0, v2) = v3) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (frontsegP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 24.26/7.09 | (30) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (rearsegP(v3, v1) = v4) | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssList(v2) = v5) | ( ~ (v5 = 0) & ssList(v1) = v5)))
% 24.26/7.09 | (31) ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0))
% 24.26/7.09 | (32) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (strictorderP(v0) = 0) | ~ (lt(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (lt(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v5 = 0 | v3 = 0 | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12)))))))
% 24.26/7.09 | (33) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0))
% 24.26/7.09 | (34) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0))
% 24.26/7.09 | (35) ! [v0] : ! [v1] : (v1 = 0 | ~ (cyclefreeP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & v3 = 0 & leq(v4, v2) = 0 & leq(v2, v4) = 0 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 24.26/7.09 | (36) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ (cyclefreeP(v2) = v0))
% 24.26/7.09 | (37) ! [v0] : (v0 = nil | ~ (segmentP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 24.26/7.09 | (38) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 24.26/7.09 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0))
% 24.26/7.09 | (40) ! [v0] : ! [v1] : ( ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & v3 = 0 & ssList(v2) = 0 & app(v2, v1) = v0) | ( ~ (v2 = 0) & ssList(v1) = v2)))
% 24.26/7.09 | (41) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = nil) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 24.26/7.09 | (42) ssList(nil) = 0
% 24.26/7.09 | (43) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (memberP(v4, v0) = v5) | ~ (memberP(v1, v0) = v2) | ~ (app(v1, v3) = v4) | ~ (ssItem(v0) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & ssList(v1) = v6) | (memberP(v3, v0) = v7 & ssList(v3) = v6 & ( ~ (v6 = 0) | (( ~ (v5 = 0) | v7 = 0 | v2 = 0) & (v5 = 0 | ( ~ (v7 = 0) & ~ (v2 = 0))))))))
% 24.26/7.09 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (segmentP(v0, v2) = v3) | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (segmentP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 24.26/7.09 | (45) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssList(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 24.26/7.09 | (46) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 24.26/7.09 | (47) ~ (all_0_7_7 = 0)
% 24.26/7.09 | (48) ! [v0] : ( ~ (singletonP(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v0 & v2 = 0 & cons(v1, nil) = v0 & ssItem(v1) = 0) | ( ~ (v1 = 0) & ssList(v0) = v1)))
% 24.26/7.09 | (49) strictorderedP(nil) = 0
% 24.26/7.09 | (50) ~ (all_0_0_0 = all_0_1_1)
% 24.26/7.09 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssItem(v4) = v5) | ( ~ (v5 = 0) & ssItem(v2) = v5)))
% 24.26/7.09 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 24.26/7.09 | (53) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = v0))
% 24.26/7.09 | (54) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (lt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v0, v1) = v4 & ssItem(v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 24.26/7.09 | (55) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 24.26/7.09 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ssList(v0) = 0) | ~ (cons(v3, v1) = v4) | ~ (app(v4, v0) = v5) | ~ (app(v1, v0) = v2) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & ssList(v1) = v6) | (cons(v3, v2) = v7 & ssItem(v3) = v6 & ( ~ (v6 = 0) | v7 = v5))))
% 24.26/7.09 | (57) ! [v0] : (v0 = 0 | ~ (rearsegP(nil, nil) = v0))
% 24.26/7.09 | (58) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 24.26/7.09 | (59) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 24.26/7.09 | (60) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (tl(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v0)))
% 24.26/7.09 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v3 = 0 | ~ (strictorderedP(v0) = 0) | ~ (lt(v1, v2) = v3) | ~ (ssList(v4) = 0) | ~ (cons(v2, v8) = v9) | ~ (cons(v1, v5) = v6) | ~ (app(v7, v9) = v0) | ~ (app(v4, v6) = v7) | ~ (ssItem(v1) = 0) | ? [v10] : (( ~ (v10 = 0) & ssList(v8) = v10) | ( ~ (v10 = 0) & ssList(v5) = v10) | ( ~ (v10 = 0) & ssList(v0) = v10) | ( ~ (v10 = 0) & ssItem(v2) = v10)))
% 24.26/7.09 | (62) ! [v0] : (v0 = nil | ~ (rearsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 24.26/7.09 | (63) ! [v0] : ! [v1] : (v1 = 0 | ~ (strictorderP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v5 = 0 & v3 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & lt(v4, v2) = v7 & lt(v2, v4) = v6 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 24.26/7.09 | (64) ! [v0] : ! [v1] : ( ~ (memberP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v0 & v5 = 0 & v3 = 0 & ssList(v4) = 0 & ssList(v2) = 0 & cons(v1, v4) = v6 & app(v2, v6) = v0) | ( ~ (v2 = 0) & ssItem(v1) = v2)))
% 24.26/7.09 | (65) ! [v0] : ! [v1] : ! [v2] : ( ~ (geq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))))
% 24.26/7.09 | (66) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssItem(v4) = v5) | ( ~ (v5 = 0) & ssItem(v2) = v5)))
% 24.26/7.09 | (67) totalorderP(nil) = 0
% 24.26/7.10 | (68) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = 0 | ~ (memberP(v0, v1) = v2) | ~ (ssList(v3) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v1, v4) = v5) | ~ (app(v3, v5) = v0) | ? [v6] : (( ~ (v6 = 0) & ssList(v4) = v6) | ( ~ (v6 = 0) & ssItem(v1) = v6)))
% 24.26/7.10 | (69) (all_0_4_4 = 0 & ! [v0] : ( ~ (neq(v0, nil) = 0) | ? [v1] : ? [v2] : ? [v3] : (rearsegP(all_0_5_5, v0) = v2 & rearsegP(all_0_6_6, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))) | (all_0_5_5 = nil & ~ (all_0_6_6 = nil))
% 24.26/7.10 | (70) ssItem(all_0_0_0) = 0
% 24.26/7.10 | (71) ! [v0] : ! [v1] : (v1 = v0 | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (frontsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 24.26/7.10 | (72) ssList(all_0_5_5) = 0
% 24.26/7.10 | (73) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v1)))
% 24.26/7.10 | (74) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (singletonP(v0) = v1) | ~ (cons(v2, nil) = v0) | ? [v3] : (( ~ (v3 = 0) & ssList(v0) = v3) | ( ~ (v3 = 0) & ssItem(v2) = v3)))
% 24.26/7.10 | (75) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 24.26/7.10 | (76) ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 24.26/7.10 | (77) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0))
% 24.26/7.10 | (78) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ssList(v0) = 0) | ~ (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & ssList(v1) = v5) | (ssList(v3) = v5 & app(v1, v3) = v6 & app(v0, v6) = v7 & ( ~ (v5 = 0) | v7 = v4))))
% 24.26/7.10 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 24.26/7.10 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & ssList(v0) = v4) | (tl(v5) = v6 & ssList(v2) = v4 & app(v0, v2) = v5 & ( ~ (v4 = 0) | v6 = v3))))
% 24.26/7.10 | (81) ! [v0] : ! [v1] : ! [v2] : ( ~ (gt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (lt(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))))
% 24.26/7.10 | (82) ! [v0] : ! [v1] : ( ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (gt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 24.26/7.10 | (83) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (rearsegP(v0, v2) = v3) | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (rearsegP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 24.26/7.10 | (84) (all_0_2_2 = 0 & all_0_3_3 = 0) | (all_0_5_5 = nil & all_0_6_6 = nil)
% 24.26/7.10 | (85) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0))
% 24.26/7.10 | (86) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (ssList(v1) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 24.26/7.10 | (87) ! [v0] : ! [v1] : (v1 = 0 | ~ (totalorderP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v5 = 0 & v3 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & leq(v4, v2) = v7 & leq(v2, v4) = v6 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 24.26/7.10 | (88) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (frontsegP(v3, v1) = v4) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v0, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & ssList(v2) = v5) | ( ~ (v5 = 0) & ssList(v1) = v5)))
% 24.26/7.10 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (equalelemsP(v0) = 0) | ~ (ssList(v3) = 0) | ~ (cons(v2, v4) = v5) | ~ (cons(v1, v5) = v6) | ~ (app(v3, v6) = v0) | ~ (ssItem(v2) = 0) | ~ (ssItem(v1) = 0) | ? [v7] : (( ~ (v7 = 0) & ssList(v4) = v7) | ( ~ (v7 = 0) & ssList(v0) = v7)))
% 24.26/7.10 | (90) ! [v0] : ! [v1] : ! [v2] : ( ~ (lt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v0, v1) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0 | v1 = v0) & ( ~ (v2 = 0) | (v4 = 0 & ~ (v1 = v0)))))))
% 24.26/7.10 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & ssList(v0) = v4))
% 24.26/7.10 | (92) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v0) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 24.26/7.10 | (93) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0))
% 24.26/7.10 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (segmentP(v5, v1) = v6) | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v3, v4) = v5) | ~ (app(v2, v0) = v3) | ? [v7] : (( ~ (v7 = 0) & ssList(v4) = v7) | ( ~ (v7 = 0) & ssList(v2) = v7) | ( ~ (v7 = 0) & ssList(v1) = v7)))
% 24.26/7.10 | (95) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (frontsegP(v3, v5) = v6) | ~ (cons(v1, v4) = v5) | ~ (cons(v0, v2) = v3) | ~ (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ? [v7] : ? [v8] : (( ~ (v7 = 0) & ssList(v2) = v7) | (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 = 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 = v0)))))))
% 24.26/7.10 | (96) ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (lt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 24.26/7.10 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (rearsegP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v3, v1) = v0) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4)))
% 24.26/7.10 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (geq(v0, v2) = v3) | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (geq(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 24.26/7.10 | (99) ssItem(all_0_1_1) = 0
% 24.26/7.10 | (100) ! [v0] : ! [v1] : (v1 = 0 | ~ (strictorderedP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v0 & v14 = 0 & v10 = 0 & v8 = 0 & v5 = 0 & v3 = 0 & ~ (v6 = 0) & lt(v2, v4) = v6 & ssList(v13) = 0 & ssList(v9) = 0 & ssList(v7) = 0 & cons(v4, v13) = v15 & cons(v2, v9) = v11 & app(v12, v15) = v0 & app(v7, v11) = v12 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 24.26/7.10 | (101) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (hd(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (totalorderedP(v5) = v6 & totalorderedP(v1) = v7 & ssList(v1) = v4 & cons(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v1 = nil | (v7 = 0 & v3 = 0)) & (v6 = 0 | ( ~ (v1 = nil) & ( ~ (v7 = 0) | ~ (v3 = 0))))))))
% 24.26/7.10 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lt(v0, v2) = v3) | ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (lt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 24.26/7.10 | (103) strictorderP(nil) = 0
% 24.26/7.10 | (104) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssItem(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 24.26/7.10 | (105) ! [v0] : ! [v1] : (v0 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 24.26/7.11 | (106) duplicatefreeP(nil) = 0
% 24.26/7.11 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (frontsegP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v0) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4)))
% 24.26/7.11 | (108) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) = v0))
% 24.26/7.11 | (109) ! [v0] : ! [v1] : ( ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (hd(v0) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : (v4 = v0 | v4 = nil | v0 = nil | ~ (tl(v4) = v1) | ? [v5] : ? [v6] : (hd(v4) = v6 & ssList(v4) = v5 & ( ~ (v6 = v3) | ~ (v5 = 0)))))))
% 24.26/7.11 | (110) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 24.26/7.11 | (111) ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (leq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 24.26/7.11 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 24.26/7.11 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (gt(v0, v2) = v3) | ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (gt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 24.26/7.11 | (114) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 24.26/7.11 | (115) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (neq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & ssItem(v1) = v3))
% 24.26/7.11 | (116) ! [v0] : ! [v1] : ( ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & v3 = 0 & ssList(v2) = 0 & app(v1, v2) = v0) | ( ~ (v2 = 0) & ssList(v1) = v2)))
% 24.26/7.11 | (117) neq(all_0_5_5, nil) = all_0_4_4
% 24.26/7.11 | (118) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (hd(v1) = v2) | ~ (lt(v0, v2) = v3) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (strictorderedP(v5) = v6 & strictorderedP(v1) = v7 & ssList(v1) = v4 & cons(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v1 = nil | (v7 = 0 & v3 = 0)) & (v6 = 0 | ( ~ (v1 = nil) & ( ~ (v7 = 0) | ~ (v3 = 0))))))))
% 24.26/7.11 | (119) ! [v0] : (v0 = 0 | ~ (segmentP(nil, nil) = v0))
% 24.26/7.11 | (120) ! [v0] : ( ~ (memberP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 24.26/7.11 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ssList(v0) = 0) | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4)))
% 24.26/7.11 | (122) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | ~ (duplicatefreeP(v2) = v0))
% 24.26/7.11 | (123) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0))
% 24.26/7.11 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0))
% 24.26/7.11 | (125) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v3 = 0 | ~ (totalorderedP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssList(v4) = 0) | ~ (cons(v2, v8) = v9) | ~ (cons(v1, v5) = v6) | ~ (app(v7, v9) = v0) | ~ (app(v4, v6) = v7) | ~ (ssItem(v1) = 0) | ? [v10] : (( ~ (v10 = 0) & ssList(v8) = v10) | ( ~ (v10 = 0) & ssList(v5) = v10) | ( ~ (v10 = 0) & ssList(v0) = v10) | ( ~ (v10 = 0) & ssItem(v2) = v10)))
% 24.26/7.11 | (126) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 24.26/7.11 | (127) neq(all_0_6_6, nil) = all_0_3_3
% 24.26/7.11 | (128) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (leq(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 24.26/7.11 | (129) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 24.26/7.11 | (130) ! [v0] : ( ~ (ssList(v0) = 0) | ~ (neq(v0, v0) = 0))
% 24.26/7.11 | (131) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 24.26/7.11 | (132) ! [v0] : ( ~ (neq(v0, v0) = 0) | ~ (ssItem(v0) = 0))
% 24.26/7.11 | (133) ! [v0] : (v0 = nil | ~ (frontsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 24.26/7.11 | (134) ! [v0] : (v0 = nil | ~ (ssList(v0) = 0) | ? [v1] : ? [v2] : (ssList(v1) = 0 & cons(v2, v1) = v0 & ssItem(v2) = 0))
% 24.26/7.11 | (135) ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (geq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 24.26/7.11 | (136) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 24.26/7.11 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (duplicatefreeP(v0) = 0) | ~ (ssList(v2) = 0) | ~ (cons(v1, v6) = v7) | ~ (cons(v1, v3) = v4) | ~ (app(v5, v7) = v0) | ~ (app(v2, v4) = v5) | ~ (ssItem(v1) = 0) | ? [v8] : (( ~ (v8 = 0) & ssList(v6) = v8) | ( ~ (v8 = 0) & ssList(v3) = v8) | ( ~ (v8 = 0) & ssList(v0) = v8)))
% 24.26/7.11 | (138) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (ssList(v0) = 0) | ~ (neq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & ssList(v1) = v3))
% 24.26/7.11 | (139) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 24.26/7.11 | (140) equalelemsP(nil) = 0
% 24.26/7.11 | (141) ssList(all_0_6_6) = 0
% 24.26/7.11 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (hd(v3) = v5 & ssList(v2) = v4 & ( ~ (v4 = 0) | v5 = v1))))
% 24.26/7.11 | (143) ! [v0] : ! [v1] : ( ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v0 & v6 = 0 & v3 = 0 & ssList(v5) = 0 & ssList(v2) = 0 & app(v4, v5) = v0 & app(v2, v1) = v4) | ( ~ (v2 = 0) & ssList(v1) = v2)))
% 24.26/7.11 | (144) rearsegP(all_0_5_5, all_0_6_6) = all_0_2_2
% 24.26/7.11 | (145) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (app(v0, v1) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 24.26/7.11 | (146) ! [v0] : ! [v1] : (v1 = 0 | ~ (equalelemsP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v0 & v9 = 0 & v7 = 0 & v5 = 0 & v3 = 0 & ~ (v4 = v2) & ssList(v8) = 0 & ssList(v6) = 0 & cons(v4, v8) = v10 & cons(v2, v10) = v11 & app(v6, v11) = v0 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 24.26/7.11 | (147) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ (totalorderP(v2) = v0))
% 24.26/7.11 | (148) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | ~ (equalelemsP(v2) = v0))
% 24.26/7.11 | (149) singletonP(nil) = all_0_7_7
% 24.26/7.11 |
% 24.26/7.11 | Instantiating formula (28) with all_0_6_6, nil, all_0_3_3, all_0_4_4 and discharging atoms neq(all_0_6_6, nil) = all_0_3_3, yields:
% 24.26/7.11 | (150) all_0_3_3 = all_0_4_4 | ~ (neq(all_0_6_6, nil) = all_0_4_4)
% 24.26/7.11 |
% 24.26/7.11 | Instantiating formula (134) with all_0_6_6 and discharging atoms ssList(all_0_6_6) = 0, yields:
% 24.26/7.11 | (151) all_0_6_6 = nil | ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_6_6 & ssItem(v1) = 0)
% 24.26/7.11 |
% 24.26/7.11 +-Applying beta-rule and splitting (69), into two cases.
% 24.26/7.11 |-Branch one:
% 24.26/7.11 | (152) all_0_4_4 = 0 & ! [v0] : ( ~ (neq(v0, nil) = 0) | ? [v1] : ? [v2] : ? [v3] : (rearsegP(all_0_5_5, v0) = v2 & rearsegP(all_0_6_6, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))
% 24.26/7.11 |
% 24.26/7.11 | Applying alpha-rule on (152) yields:
% 24.26/7.11 | (153) all_0_4_4 = 0
% 24.26/7.11 | (154) ! [v0] : ( ~ (neq(v0, nil) = 0) | ? [v1] : ? [v2] : ? [v3] : (rearsegP(all_0_5_5, v0) = v2 & rearsegP(all_0_6_6, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))
% 24.26/7.11 |
% 24.26/7.11 | Instantiating formula (154) with all_0_5_5 yields:
% 24.26/7.11 | (155) ~ (neq(all_0_5_5, nil) = 0) | ? [v0] : ? [v1] : ? [v2] : (rearsegP(all_0_5_5, all_0_5_5) = v1 & rearsegP(all_0_6_6, all_0_5_5) = v2 & ssList(all_0_5_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 24.26/7.11 |
% 24.26/7.11 | Instantiating formula (154) with all_0_6_6 yields:
% 24.26/7.11 | (156) ~ (neq(all_0_6_6, nil) = 0) | ? [v0] : ? [v1] : ? [v2] : (rearsegP(all_0_5_5, all_0_6_6) = v1 & rearsegP(all_0_6_6, all_0_6_6) = v2 & ssList(all_0_6_6) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 24.26/7.11 |
% 24.26/7.11 | From (153) and (117) follows:
% 24.26/7.11 | (157) neq(all_0_5_5, nil) = 0
% 24.26/7.11 |
% 24.26/7.11 +-Applying beta-rule and splitting (155), into two cases.
% 24.26/7.11 |-Branch one:
% 24.26/7.11 | (158) ~ (neq(all_0_5_5, nil) = 0)
% 24.26/7.11 |
% 24.26/7.11 | Using (157) and (158) yields:
% 24.26/7.11 | (159) $false
% 24.26/7.11 |
% 24.26/7.12 |-The branch is then unsatisfiable
% 24.26/7.12 |-Branch two:
% 24.26/7.12 | (157) neq(all_0_5_5, nil) = 0
% 24.26/7.12 | (161) ? [v0] : ? [v1] : ? [v2] : (rearsegP(all_0_5_5, all_0_5_5) = v1 & rearsegP(all_0_6_6, all_0_5_5) = v2 & ssList(all_0_5_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 24.26/7.12 |
% 24.26/7.12 +-Applying beta-rule and splitting (84), into two cases.
% 24.26/7.12 |-Branch one:
% 24.26/7.12 | (162) all_0_2_2 = 0 & all_0_3_3 = 0
% 24.26/7.12 |
% 24.26/7.12 | Applying alpha-rule on (162) yields:
% 24.26/7.12 | (163) all_0_2_2 = 0
% 24.26/7.12 | (164) all_0_3_3 = 0
% 24.26/7.12 |
% 24.26/7.12 | From (163) and (144) follows:
% 24.26/7.12 | (165) rearsegP(all_0_5_5, all_0_6_6) = 0
% 24.26/7.12 |
% 24.26/7.12 | From (164) and (127) follows:
% 24.26/7.12 | (166) neq(all_0_6_6, nil) = 0
% 24.26/7.12 |
% 24.26/7.12 +-Applying beta-rule and splitting (156), into two cases.
% 24.26/7.12 |-Branch one:
% 24.26/7.12 | (167) ~ (neq(all_0_6_6, nil) = 0)
% 24.26/7.12 |
% 24.26/7.12 | Using (166) and (167) yields:
% 24.26/7.12 | (159) $false
% 24.26/7.12 |
% 24.26/7.12 |-The branch is then unsatisfiable
% 24.26/7.12 |-Branch two:
% 24.26/7.12 | (166) neq(all_0_6_6, nil) = 0
% 24.26/7.12 | (170) ? [v0] : ? [v1] : ? [v2] : (rearsegP(all_0_5_5, all_0_6_6) = v1 & rearsegP(all_0_6_6, all_0_6_6) = v2 & ssList(all_0_6_6) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 24.26/7.12 |
% 24.26/7.12 | Instantiating (170) with all_35_0_11, all_35_1_12, all_35_2_13 yields:
% 24.26/7.12 | (171) rearsegP(all_0_5_5, all_0_6_6) = all_35_1_12 & rearsegP(all_0_6_6, all_0_6_6) = all_35_0_11 & ssList(all_0_6_6) = all_35_2_13 & ( ~ (all_35_0_11 = 0) | ~ (all_35_1_12 = 0) | ~ (all_35_2_13 = 0))
% 24.26/7.12 |
% 24.26/7.12 | Applying alpha-rule on (171) yields:
% 24.26/7.12 | (172) rearsegP(all_0_5_5, all_0_6_6) = all_35_1_12
% 24.26/7.12 | (173) rearsegP(all_0_6_6, all_0_6_6) = all_35_0_11
% 24.26/7.12 | (174) ssList(all_0_6_6) = all_35_2_13
% 24.26/7.12 | (175) ~ (all_35_0_11 = 0) | ~ (all_35_1_12 = 0) | ~ (all_35_2_13 = 0)
% 24.26/7.12 |
% 24.26/7.12 | Instantiating formula (33) with all_0_5_5, all_0_6_6, 0, all_35_1_12 and discharging atoms rearsegP(all_0_5_5, all_0_6_6) = all_35_1_12, rearsegP(all_0_5_5, all_0_6_6) = 0, yields:
% 24.26/7.12 | (176) all_35_1_12 = 0
% 24.26/7.12 |
% 24.26/7.12 | Instantiating formula (79) with all_0_6_6, all_35_2_13, 0 and discharging atoms ssList(all_0_6_6) = all_35_2_13, ssList(all_0_6_6) = 0, yields:
% 24.26/7.12 | (177) all_35_2_13 = 0
% 24.26/7.12 |
% 24.26/7.12 | From (177) and (174) follows:
% 24.26/7.12 | (141) ssList(all_0_6_6) = 0
% 24.26/7.12 |
% 24.26/7.12 +-Applying beta-rule and splitting (175), into two cases.
% 24.26/7.12 |-Branch one:
% 24.26/7.12 | (179) ~ (all_35_0_11 = 0)
% 24.26/7.12 |
% 24.26/7.12 | Instantiating formula (136) with all_35_0_11, all_0_6_6 and discharging atoms rearsegP(all_0_6_6, all_0_6_6) = all_35_0_11, yields:
% 24.26/7.12 | (180) all_35_0_11 = 0 | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 24.26/7.12 |
% 24.26/7.12 +-Applying beta-rule and splitting (180), into two cases.
% 24.26/7.12 |-Branch one:
% 24.26/7.12 | (181) all_35_0_11 = 0
% 24.26/7.12 |
% 24.26/7.12 | Equations (181) can reduce 179 to:
% 24.26/7.12 | (182) $false
% 24.26/7.12 |
% 24.26/7.12 |-The branch is then unsatisfiable
% 24.26/7.12 |-Branch two:
% 24.26/7.12 | (179) ~ (all_35_0_11 = 0)
% 24.26/7.12 | (184) ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 24.26/7.12 |
% 24.26/7.12 | Instantiating (184) with all_86_0_26 yields:
% 24.26/7.12 | (185) ~ (all_86_0_26 = 0) & ssList(all_0_6_6) = all_86_0_26
% 24.26/7.12 |
% 24.26/7.12 | Applying alpha-rule on (185) yields:
% 24.26/7.12 | (186) ~ (all_86_0_26 = 0)
% 24.26/7.12 | (187) ssList(all_0_6_6) = all_86_0_26
% 24.26/7.12 |
% 24.26/7.12 | Instantiating formula (79) with all_0_6_6, all_86_0_26, 0 and discharging atoms ssList(all_0_6_6) = all_86_0_26, ssList(all_0_6_6) = 0, yields:
% 24.26/7.12 | (188) all_86_0_26 = 0
% 24.26/7.12 |
% 24.26/7.12 | Equations (188) can reduce 186 to:
% 24.26/7.12 | (182) $false
% 24.26/7.12 |
% 24.26/7.12 |-The branch is then unsatisfiable
% 24.26/7.12 |-Branch two:
% 24.26/7.12 | (181) all_35_0_11 = 0
% 24.26/7.12 | (191) ~ (all_35_1_12 = 0) | ~ (all_35_2_13 = 0)
% 24.26/7.12 |
% 24.26/7.12 +-Applying beta-rule and splitting (191), into two cases.
% 24.26/7.12 |-Branch one:
% 24.26/7.12 | (192) ~ (all_35_1_12 = 0)
% 24.26/7.12 |
% 24.26/7.12 | Equations (176) can reduce 192 to:
% 24.26/7.12 | (182) $false
% 24.26/7.12 |
% 24.26/7.12 |-The branch is then unsatisfiable
% 24.26/7.12 |-Branch two:
% 24.26/7.12 | (176) all_35_1_12 = 0
% 24.26/7.12 | (195) ~ (all_35_2_13 = 0)
% 24.26/7.12 |
% 24.26/7.12 | Equations (177) can reduce 195 to:
% 24.26/7.12 | (182) $false
% 24.26/7.12 |
% 24.26/7.12 |-The branch is then unsatisfiable
% 24.26/7.12 |-Branch two:
% 24.26/7.12 | (197) all_0_5_5 = nil & all_0_6_6 = nil
% 24.26/7.12 |
% 24.26/7.12 | Applying alpha-rule on (197) yields:
% 24.26/7.12 | (198) all_0_5_5 = nil
% 24.26/7.12 | (199) all_0_6_6 = nil
% 24.26/7.12 |
% 24.26/7.12 | From (199) and (141) follows:
% 24.26/7.12 | (42) ssList(nil) = 0
% 24.26/7.12 |
% 24.26/7.12 | From (198) and (157) follows:
% 24.26/7.12 | (201) neq(nil, nil) = 0
% 24.26/7.12 |
% 24.26/7.12 | From (199) and (127) follows:
% 24.26/7.12 | (202) neq(nil, nil) = all_0_3_3
% 24.26/7.12 |
% 24.26/7.12 +-Applying beta-rule and splitting (150), into two cases.
% 24.26/7.12 |-Branch one:
% 24.26/7.12 | (203) ~ (neq(all_0_6_6, nil) = all_0_4_4)
% 24.26/7.12 |
% 24.26/7.12 | From (199)(153) and (203) follows:
% 24.26/7.12 | (204) ~ (neq(nil, nil) = 0)
% 24.26/7.12 |
% 24.26/7.12 | Using (201) and (204) yields:
% 24.26/7.12 | (159) $false
% 24.26/7.12 |
% 24.26/7.12 |-The branch is then unsatisfiable
% 24.26/7.12 |-Branch two:
% 24.26/7.12 | (206) neq(all_0_6_6, nil) = all_0_4_4
% 24.26/7.12 | (207) all_0_3_3 = all_0_4_4
% 24.26/7.12 |
% 24.26/7.12 | Combining equations (153,207) yields a new equation:
% 24.26/7.12 | (164) all_0_3_3 = 0
% 24.26/7.12 |
% 24.26/7.12 | From (164) and (202) follows:
% 24.26/7.12 | (201) neq(nil, nil) = 0
% 24.26/7.12 |
% 24.26/7.12 +-Applying beta-rule and splitting (156), into two cases.
% 24.26/7.12 |-Branch one:
% 24.26/7.12 | (167) ~ (neq(all_0_6_6, nil) = 0)
% 24.26/7.12 |
% 24.26/7.12 | From (199) and (167) follows:
% 24.26/7.12 | (204) ~ (neq(nil, nil) = 0)
% 24.26/7.12 |
% 24.26/7.12 | Using (201) and (204) yields:
% 24.26/7.12 | (159) $false
% 24.26/7.12 |
% 24.26/7.12 |-The branch is then unsatisfiable
% 24.26/7.12 |-Branch two:
% 24.26/7.12 | (166) neq(all_0_6_6, nil) = 0
% 24.26/7.12 | (170) ? [v0] : ? [v1] : ? [v2] : (rearsegP(all_0_5_5, all_0_6_6) = v1 & rearsegP(all_0_6_6, all_0_6_6) = v2 & ssList(all_0_6_6) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 24.26/7.12 |
% 24.26/7.12 | From (199) and (166) follows:
% 24.26/7.12 | (201) neq(nil, nil) = 0
% 24.26/7.12 |
% 24.26/7.12 | Instantiating formula (130) with nil and discharging atoms ssList(nil) = 0, neq(nil, nil) = 0, yields:
% 24.26/7.12 | (159) $false
% 24.26/7.12 |
% 24.26/7.12 |-The branch is then unsatisfiable
% 24.26/7.12 |-Branch two:
% 24.26/7.12 | (217) all_0_5_5 = nil & ~ (all_0_6_6 = nil)
% 24.26/7.12 |
% 24.26/7.12 | Applying alpha-rule on (217) yields:
% 24.26/7.12 | (198) all_0_5_5 = nil
% 24.26/7.12 | (219) ~ (all_0_6_6 = nil)
% 24.26/7.12 |
% 24.26/7.12 | From (198) and (144) follows:
% 24.26/7.12 | (220) rearsegP(nil, all_0_6_6) = all_0_2_2
% 24.26/7.12 |
% 24.26/7.12 | From (198) and (72) follows:
% 24.26/7.12 | (42) ssList(nil) = 0
% 24.26/7.12 |
% 24.26/7.12 +-Applying beta-rule and splitting (84), into two cases.
% 24.26/7.12 |-Branch one:
% 24.26/7.12 | (162) all_0_2_2 = 0 & all_0_3_3 = 0
% 24.26/7.12 |
% 24.26/7.12 | Applying alpha-rule on (162) yields:
% 24.26/7.12 | (163) all_0_2_2 = 0
% 24.26/7.12 | (164) all_0_3_3 = 0
% 24.26/7.12 |
% 24.26/7.12 | From (163) and (220) follows:
% 24.26/7.12 | (225) rearsegP(nil, all_0_6_6) = 0
% 24.26/7.12 |
% 24.26/7.12 +-Applying beta-rule and splitting (151), into two cases.
% 24.26/7.12 |-Branch one:
% 24.26/7.12 | (199) all_0_6_6 = nil
% 24.26/7.12 |
% 24.26/7.12 | Equations (199) can reduce 219 to:
% 24.26/7.12 | (182) $false
% 24.26/7.12 |
% 24.26/7.12 |-The branch is then unsatisfiable
% 24.26/7.12 |-Branch two:
% 24.26/7.12 | (219) ~ (all_0_6_6 = nil)
% 24.26/7.12 | (229) ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_6_6 & ssItem(v1) = 0)
% 24.26/7.12 |
% 24.26/7.12 | Instantiating formula (16) with all_0_6_6, nil and discharging atoms rearsegP(nil, all_0_6_6) = 0, ssList(nil) = 0, yields:
% 24.26/7.12 | (230) all_0_6_6 = nil | ? [v0] : ? [v1] : (rearsegP(all_0_6_6, nil) = v1 & ssList(all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 24.26/7.12 |
% 24.26/7.12 | Instantiating formula (62) with all_0_6_6 and discharging atoms rearsegP(nil, all_0_6_6) = 0, yields:
% 24.26/7.12 | (231) all_0_6_6 = nil | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 24.26/7.12 |
% 24.26/7.12 +-Applying beta-rule and splitting (231), into two cases.
% 24.26/7.12 |-Branch one:
% 24.26/7.12 | (199) all_0_6_6 = nil
% 24.26/7.12 |
% 24.26/7.12 | Equations (199) can reduce 219 to:
% 24.26/7.12 | (182) $false
% 24.26/7.12 |
% 24.26/7.12 |-The branch is then unsatisfiable
% 24.26/7.12 |-Branch two:
% 24.26/7.12 | (219) ~ (all_0_6_6 = nil)
% 24.26/7.12 | (184) ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 24.26/7.12 |
% 24.26/7.12 | Instantiating (184) with all_34_0_40 yields:
% 24.26/7.12 | (236) ~ (all_34_0_40 = 0) & ssList(all_0_6_6) = all_34_0_40
% 24.26/7.12 |
% 24.26/7.12 | Applying alpha-rule on (236) yields:
% 24.26/7.12 | (237) ~ (all_34_0_40 = 0)
% 24.26/7.12 | (238) ssList(all_0_6_6) = all_34_0_40
% 24.26/7.12 |
% 24.26/7.12 +-Applying beta-rule and splitting (230), into two cases.
% 24.26/7.12 |-Branch one:
% 24.26/7.12 | (199) all_0_6_6 = nil
% 24.26/7.12 |
% 24.26/7.12 | Equations (199) can reduce 219 to:
% 24.26/7.12 | (182) $false
% 24.26/7.12 |
% 24.26/7.12 |-The branch is then unsatisfiable
% 24.26/7.12 |-Branch two:
% 24.26/7.12 | (219) ~ (all_0_6_6 = nil)
% 24.26/7.12 | (242) ? [v0] : ? [v1] : (rearsegP(all_0_6_6, nil) = v1 & ssList(all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 24.26/7.12 |
% 24.26/7.12 | Instantiating (242) with all_39_0_41, all_39_1_42 yields:
% 24.26/7.12 | (243) rearsegP(all_0_6_6, nil) = all_39_0_41 & ssList(all_0_6_6) = all_39_1_42 & ( ~ (all_39_0_41 = 0) | ~ (all_39_1_42 = 0))
% 24.26/7.12 |
% 24.26/7.12 | Applying alpha-rule on (243) yields:
% 24.26/7.12 | (244) rearsegP(all_0_6_6, nil) = all_39_0_41
% 24.26/7.12 | (245) ssList(all_0_6_6) = all_39_1_42
% 24.26/7.12 | (246) ~ (all_39_0_41 = 0) | ~ (all_39_1_42 = 0)
% 24.26/7.12 |
% 24.26/7.12 | Instantiating formula (79) with all_0_6_6, all_39_1_42, 0 and discharging atoms ssList(all_0_6_6) = all_39_1_42, ssList(all_0_6_6) = 0, yields:
% 24.26/7.12 | (247) all_39_1_42 = 0
% 24.26/7.12 |
% 24.26/7.12 | Instantiating formula (79) with all_0_6_6, all_34_0_40, all_39_1_42 and discharging atoms ssList(all_0_6_6) = all_39_1_42, ssList(all_0_6_6) = all_34_0_40, yields:
% 24.26/7.12 | (248) all_39_1_42 = all_34_0_40
% 24.26/7.12 |
% 24.26/7.13 | Combining equations (248,247) yields a new equation:
% 24.26/7.13 | (249) all_34_0_40 = 0
% 24.26/7.13 |
% 24.26/7.13 | Simplifying 249 yields:
% 24.26/7.13 | (250) all_34_0_40 = 0
% 24.26/7.13 |
% 24.26/7.13 | Equations (250) can reduce 237 to:
% 24.26/7.13 | (182) $false
% 24.26/7.13 |
% 24.26/7.13 |-The branch is then unsatisfiable
% 24.26/7.13 |-Branch two:
% 24.26/7.13 | (197) all_0_5_5 = nil & all_0_6_6 = nil
% 24.26/7.13 |
% 24.26/7.13 | Applying alpha-rule on (197) yields:
% 24.26/7.13 | (198) all_0_5_5 = nil
% 24.26/7.13 | (199) all_0_6_6 = nil
% 24.26/7.13 |
% 24.26/7.13 | Equations (199) can reduce 219 to:
% 24.26/7.13 | (182) $false
% 24.26/7.13 |
% 24.26/7.13 |-The branch is then unsatisfiable
% 24.26/7.13 % SZS output end Proof for theBenchmark
% 24.26/7.13
% 24.26/7.13 6515ms
%------------------------------------------------------------------------------