TSTP Solution File: SWC020+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWC020+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n018.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 20:15:46 EDT 2022
% Result : Theorem 20.52s 6.35s
% Output : Proof 23.89s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWC020+1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 12 18:47:56 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.51/0.59 ____ _
% 0.51/0.59 ___ / __ \_____(_)___ ________ __________
% 0.51/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.51/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.51/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.51/0.59
% 0.51/0.59 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/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.30/1.06 Prover 0: Preprocessing ...
% 4.53/1.65 Prover 0: Constructing countermodel ...
% 18.69/5.94 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.15/6.03 Prover 1: Preprocessing ...
% 20.24/6.27 Prover 1: Constructing countermodel ...
% 20.52/6.35 Prover 1: proved (412ms)
% 20.52/6.35 Prover 0: stopped
% 20.52/6.35
% 20.52/6.35 No countermodel exists, formula is valid
% 20.52/6.35 % SZS status Theorem for theBenchmark
% 20.52/6.35
% 20.52/6.35 Generating proof ... found it (size 74)
% 23.18/6.91
% 23.18/6.91 % SZS output start Proof for theBenchmark
% 23.18/6.91 Assumed formulas after preprocessing and simplification:
% 23.18/6.91 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v0 = 0) & equalelemsP(nil) = 0 & duplicatefreeP(nil) = 0 & strictorderedP(nil) = 0 & totalorderedP(nil) = 0 & strictorderP(nil) = 0 & totalorderP(nil) = 0 & cyclefreeP(nil) = 0 & frontsegP(v2, v1) = v4 & singletonP(nil) = v0 & ssList(v2) = 0 & ssList(v1) = 0 & ssList(nil) = 0 & neq(v1, nil) = v3 & ssItem(v6) = 0 & ssItem(v5) = 0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v10 = 0 | ~ (strictorderedP(v7) = 0) | ~ (lt(v8, v9) = v10) | ~ (ssList(v11) = 0) | ~ (cons(v9, v15) = v16) | ~ (cons(v8, v12) = v13) | ~ (app(v14, v16) = v7) | ~ (app(v11, v13) = v14) | ~ (ssItem(v8) = 0) | ? [v17] : (( ~ (v17 = 0) & ssList(v15) = v17) | ( ~ (v17 = 0) & ssList(v12) = v17) | ( ~ (v17 = 0) & ssList(v7) = v17) | ( ~ (v17 = 0) & ssItem(v9) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v10 = 0 | ~ (totalorderedP(v7) = 0) | ~ (leq(v8, v9) = v10) | ~ (ssList(v11) = 0) | ~ (cons(v9, v15) = v16) | ~ (cons(v8, v12) = v13) | ~ (app(v14, v16) = v7) | ~ (app(v11, v13) = v14) | ~ (ssItem(v8) = 0) | ? [v17] : (( ~ (v17 = 0) & ssList(v15) = v17) | ( ~ (v17 = 0) & ssList(v12) = v17) | ( ~ (v17 = 0) & ssList(v7) = v17) | ( ~ (v17 = 0) & ssItem(v9) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (duplicatefreeP(v7) = 0) | ~ (ssList(v9) = 0) | ~ (cons(v8, v13) = v14) | ~ (cons(v8, v10) = v11) | ~ (app(v12, v14) = v7) | ~ (app(v9, v11) = v12) | ~ (ssItem(v8) = 0) | ? [v15] : (( ~ (v15 = 0) & ssList(v13) = v15) | ( ~ (v15 = 0) & ssList(v10) = v15) | ( ~ (v15 = 0) & ssList(v7) = v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (segmentP(v12, v8) = v13) | ~ (segmentP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ~ (app(v10, v11) = v12) | ~ (app(v9, v7) = v10) | ? [v14] : (( ~ (v14 = 0) & ssList(v11) = v14) | ( ~ (v14 = 0) & ssList(v9) = v14) | ( ~ (v14 = 0) & ssList(v8) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (equalelemsP(v7) = 0) | ~ (ssList(v10) = 0) | ~ (cons(v9, v11) = v12) | ~ (cons(v8, v12) = v13) | ~ (app(v10, v13) = v7) | ~ (ssItem(v9) = 0) | ~ (ssItem(v8) = 0) | ? [v14] : (( ~ (v14 = 0) & ssList(v11) = v14) | ( ~ (v14 = 0) & ssList(v7) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (frontsegP(v10, v12) = v13) | ~ (cons(v8, v11) = v12) | ~ (cons(v7, v9) = v10) | ~ (ssItem(v8) = 0) | ~ (ssItem(v7) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssList(v9) = v14) | (frontsegP(v9, v11) = v15 & ssList(v11) = v14 & ( ~ (v14 = 0) | (( ~ (v15 = 0) | ~ (v8 = v7) | v13 = 0) & ( ~ (v13 = 0) | (v15 = 0 & v8 = v7))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = 0 | ~ (segmentP(v7, v8) = v9) | ~ (ssList(v7) = 0) | ~ (app(v11, v12) = v7) | ~ (app(v10, v8) = v11) | ? [v13] : (( ~ (v13 = 0) & ssList(v12) = v13) | ( ~ (v13 = 0) & ssList(v10) = v13) | ( ~ (v13 = 0) & ssList(v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = 0 | ~ (memberP(v7, v8) = v9) | ~ (ssList(v10) = 0) | ~ (ssList(v7) = 0) | ~ (cons(v8, v11) = v12) | ~ (app(v10, v12) = v7) | ? [v13] : (( ~ (v13 = 0) & ssList(v11) = v13) | ( ~ (v13 = 0) & ssItem(v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (memberP(v11, v7) = v12) | ~ (memberP(v8, v7) = v9) | ~ (app(v8, v10) = v11) | ~ (ssItem(v7) = 0) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssList(v8) = v13) | (memberP(v10, v7) = v14 & ssList(v10) = v13 & ( ~ (v13 = 0) | (( ~ (v12 = 0) | v14 = 0 | v9 = 0) & (v12 = 0 | ( ~ (v14 = 0) & ~ (v9 = 0)))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (ssList(v7) = 0) | ~ (cons(v10, v8) = v11) | ~ (app(v11, v7) = v12) | ~ (app(v8, v7) = v9) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssList(v8) = v13) | (cons(v10, v9) = v14 & ssItem(v10) = v13 & ( ~ (v13 = 0) | v14 = v12)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (ssList(v8) = 0) | ~ (ssList(v7) = 0) | ~ (cons(v11, v8) = v10) | ~ (cons(v9, v7) = v10) | ? [v12] : (( ~ (v12 = 0) & ssItem(v11) = v12) | ( ~ (v12 = 0) & ssItem(v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (rearsegP(v10, v8) = v11) | ~ (rearsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ~ (app(v9, v7) = v10) | ? [v12] : (( ~ (v12 = 0) & ssList(v9) = v12) | ( ~ (v12 = 0) & ssList(v8) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (frontsegP(v10, v8) = v11) | ~ (frontsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ~ (app(v7, v9) = v10) | ? [v12] : (( ~ (v12 = 0) & ssList(v9) = v12) | ( ~ (v12 = 0) & ssList(v8) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (ssList(v8) = 0) | ~ (ssList(v7) = 0) | ~ (cons(v11, v8) = v10) | ~ (cons(v9, v7) = v10) | ? [v12] : (( ~ (v12 = 0) & ssItem(v11) = v12) | ( ~ (v12 = 0) & ssItem(v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (memberP(v10, v7) = v11) | ~ (cons(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ~ (ssItem(v7) = 0) | ? [v12] : ? [v13] : (memberP(v9, v7) = v13 & ssList(v9) = v12 & ( ~ (v12 = 0) | (( ~ (v11 = 0) | v13 = 0 | v8 = v7) & (v11 = 0 | ( ~ (v13 = 0) & ~ (v8 = v7))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (ssList(v7) = 0) | ~ (app(v9, v10) = v11) | ~ (app(v7, v8) = v9) | ? [v12] : ? [v13] : ? [v14] : (( ~ (v12 = 0) & ssList(v8) = v12) | (ssList(v10) = v12 & app(v8, v10) = v13 & app(v7, v13) = v14 & ( ~ (v12 = 0) | v14 = v11)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | v7 = nil | ~ (tl(v7) = v9) | ~ (hd(v7) = v8) | ~ (cons(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & ssList(v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (ssList(v7) = 0) | ~ (app(v10, v8) = v9) | ~ (app(v7, v8) = v9) | ? [v11] : (( ~ (v11 = 0) & ssList(v10) = v11) | ( ~ (v11 = 0) & ssList(v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (ssList(v7) = 0) | ~ (app(v8, v10) = v9) | ~ (app(v8, v7) = v9) | ? [v11] : (( ~ (v11 = 0) & ssList(v10) = v11) | ( ~ (v11 = 0) & ssList(v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (gt(v7, v9) = v10) | ~ (gt(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssItem(v8) = v11) | (gt(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (geq(v7, v9) = v10) | ~ (geq(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssItem(v8) = v11) | (geq(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (lt(v7, v9) = v10) | ~ (lt(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssItem(v8) = v11) | (lt(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (lt(v7, v9) = v10) | ~ (leq(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssItem(v8) = v11) | (lt(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (leq(v7, v9) = v10) | ~ (leq(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssItem(v8) = v11) | (leq(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (segmentP(v7, v9) = v10) | ~ (segmentP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssList(v8) = v11) | (segmentP(v8, v9) = v12 & ssList(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (rearsegP(v7, v9) = v10) | ~ (rearsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssList(v8) = v11) | (rearsegP(v8, v9) = v12 & ssList(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (frontsegP(v7, v9) = v10) | ~ (frontsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssList(v8) = v11) | (frontsegP(v8, v9) = v12 & ssList(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (rearsegP(v7, v8) = v9) | ~ (ssList(v7) = 0) | ~ (app(v10, v8) = v7) | ? [v11] : (( ~ (v11 = 0) & ssList(v10) = v11) | ( ~ (v11 = 0) & ssList(v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (frontsegP(v7, v8) = v9) | ~ (ssList(v7) = 0) | ~ (app(v8, v10) = v7) | ? [v11] : (( ~ (v11 = 0) & ssList(v10) = v11) | ( ~ (v11 = 0) & ssList(v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (gt(v10, v9) = v8) | ~ (gt(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (geq(v10, v9) = v8) | ~ (geq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (lt(v10, v9) = v8) | ~ (lt(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (leq(v10, v9) = v8) | ~ (leq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (segmentP(v10, v9) = v8) | ~ (segmentP(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (rearsegP(v10, v9) = v8) | ~ (rearsegP(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (frontsegP(v10, v9) = v8) | ~ (frontsegP(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (memberP(v10, v9) = v8) | ~ (memberP(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (cons(v10, v9) = v8) | ~ (cons(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (app(v10, v9) = v8) | ~ (app(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (neq(v10, v9) = v8) | ~ (neq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = nil | ~ (tl(v7) = v8) | ~ (app(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (( ~ (v11 = 0) & ssList(v7) = v11) | (tl(v12) = v13 & ssList(v9) = v11 & app(v7, v9) = v12 & ( ~ (v11 = 0) | v13 = v10)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = nil | ~ (hd(v7) = v8) | ~ (app(v7, v9) = v10) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssList(v7) = v11) | (hd(v10) = v12 & ssList(v9) = v11 & ( ~ (v11 = 0) | v12 = v8)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (hd(v8) = v9) | ~ (lt(v7, v9) = v10) | ~ (ssItem(v7) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (strictorderedP(v12) = v13 & strictorderedP(v8) = v14 & ssList(v8) = v11 & cons(v7, v8) = v12 & ( ~ (v11 = 0) | (( ~ (v13 = 0) | v8 = nil | (v14 = 0 & v10 = 0)) & (v13 = 0 | ( ~ (v8 = nil) & ( ~ (v14 = 0) | ~ (v10 = 0)))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (hd(v8) = v9) | ~ (leq(v7, v9) = v10) | ~ (ssItem(v7) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (totalorderedP(v12) = v13 & totalorderedP(v8) = v14 & ssList(v8) = v11 & cons(v7, v8) = v12 & ( ~ (v11 = 0) | (( ~ (v13 = 0) | v8 = nil | (v14 = 0 & v10 = 0)) & (v13 = 0 | ( ~ (v8 = nil) & ( ~ (v14 = 0) | ~ (v10 = 0)))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (strictorderP(v7) = 0) | ~ (lt(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssList(v7) = v11) | (lt(v9, v8) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v12 = 0 | v10 = 0 | ~ (ssList(v13) = 0) | ~ (cons(v9, v17) = v18) | ~ (cons(v8, v14) = v15) | ~ (app(v16, v18) = v7) | ~ (app(v13, v15) = v16) | ? [v19] : (( ~ (v19 = 0) & ssList(v17) = v19) | ( ~ (v19 = 0) & ssList(v14) = v19))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (totalorderP(v7) = 0) | ~ (leq(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssList(v7) = v11) | (leq(v9, v8) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v12 = 0 | v10 = 0 | ~ (ssList(v13) = 0) | ~ (cons(v9, v17) = v18) | ~ (cons(v8, v14) = v15) | ~ (app(v16, v18) = v7) | ~ (app(v13, v15) = v16) | ? [v19] : (( ~ (v19 = 0) & ssList(v17) = v19) | ( ~ (v19 = 0) & ssList(v14) = v19))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (cyclefreeP(v7) = 0) | ~ (leq(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssList(v7) = v11) | (leq(v9, v8) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (v12 = 0) | ~ (v10 = 0) | ~ (ssList(v13) = 0) | ~ (cons(v9, v17) = v18) | ~ (cons(v8, v14) = v15) | ~ (app(v16, v18) = v7) | ~ (app(v13, v15) = v16) | ? [v19] : (( ~ (v19 = 0) & ssList(v17) = v19) | ( ~ (v19 = 0) & ssList(v14) = v19))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (ssList(v7) = 0) | ~ (cons(v8, nil) = v9) | ~ (app(v9, v7) = v10) | ? [v11] : ? [v12] : (cons(v8, v7) = v12 & ssItem(v8) = v11 & ( ~ (v11 = 0) | v12 = v10))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = v7 | ~ (lt(v7, v8) = v9) | ~ (ssItem(v7) = 0) | ? [v10] : ? [v11] : (leq(v7, v8) = v11 & ssItem(v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = v7 | ~ (ssList(v7) = 0) | ~ (neq(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = v7 | ~ (neq(v7, v8) = v9) | ~ (ssItem(v7) = 0) | ? [v10] : ( ~ (v10 = 0) & ssItem(v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (tl(v9) = v8) | ~ (tl(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (hd(v9) = v8) | ~ (hd(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (equalelemsP(v9) = v8) | ~ (equalelemsP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (duplicatefreeP(v9) = v8) | ~ (duplicatefreeP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (strictorderedP(v9) = v8) | ~ (strictorderedP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (totalorderedP(v9) = v8) | ~ (totalorderedP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (strictorderP(v9) = v8) | ~ (strictorderP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (totalorderP(v9) = v8) | ~ (totalorderP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (cyclefreeP(v9) = v8) | ~ (cyclefreeP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singletonP(v9) = v8) | ~ (singletonP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (ssList(v9) = v8) | ~ (ssList(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (ssItem(v9) = v8) | ~ (ssItem(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (singletonP(v7) = v8) | ~ (cons(v9, nil) = v7) | ? [v10] : (( ~ (v10 = 0) & ssList(v7) = v10) | ( ~ (v10 = 0) & ssItem(v9) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (gt(v7, v8) = v9) | ~ (ssItem(v7) = 0) | ? [v10] : ? [v11] : (lt(v8, v7) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | (( ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (geq(v7, v8) = v9) | ~ (ssItem(v7) = 0) | ? [v10] : ? [v11] : (leq(v8, v7) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | (( ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (lt(v7, v8) = v9) | ~ (ssItem(v7) = 0) | ? [v10] : ? [v11] : (leq(v7, v8) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | (( ~ (v11 = 0) | v9 = 0 | v8 = v7) & ( ~ (v9 = 0) | (v11 = 0 & ~ (v8 = v7))))))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ssList(v7) = 0) | ~ (cons(v8, v7) = v9) | ? [v10] : ? [v11] : (tl(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = v7))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ssList(v7) = 0) | ~ (cons(v8, v7) = v9) | ? [v10] : ? [v11] : (hd(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = v8))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ssList(v7) = 0) | ~ (cons(v8, v7) = v9) | ? [v10] : ? [v11] : (ssList(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ssList(v7) = 0) | ~ (app(v7, v8) = v9) | ? [v10] : ? [v11] : (ssList(v9) = v11 & ssList(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (geq(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v9] : ? [v10] : (geq(v8, v7) = v10 & ssItem(v8) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (leq(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v9] : ? [v10] : (leq(v8, v7) = v10 & ssItem(v8) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (segmentP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v9] : ? [v10] : (segmentP(v8, v7) = v10 & ssList(v8) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (rearsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v9] : ? [v10] : (rearsegP(v8, v7) = v10 & ssList(v8) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (frontsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v9] : ? [v10] : (frontsegP(v8, v7) = v10 & ssList(v8) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (app(v7, nil) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (app(nil, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v8 = nil | ~ (ssList(v7) = 0) | ~ (app(v7, v8) = nil) | ? [v9] : ( ~ (v9 = 0) & ssList(v8) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (geq(v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & ssItem(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (equalelemsP(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = v7 & v16 = 0 & v14 = 0 & v12 = 0 & v10 = 0 & ~ (v11 = v9) & ssList(v15) = 0 & ssList(v13) = 0 & cons(v11, v15) = v17 & cons(v9, v17) = v18 & app(v13, v18) = v7 & ssItem(v11) = 0 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (duplicatefreeP(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ((v22 = v7 & v20 = 0 & v16 = 0 & v14 = 0 & v12 = 0 & v11 = v9 & v10 = 0 & ssList(v19) = 0 & ssList(v15) = 0 & ssList(v13) = 0 & cons(v9, v19) = v21 & cons(v9, v15) = v17 & app(v18, v21) = v7 & app(v13, v17) = v18 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (strictorderedP(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v23 = v7 & v21 = 0 & v17 = 0 & v15 = 0 & v12 = 0 & v10 = 0 & ~ (v13 = 0) & lt(v9, v11) = v13 & ssList(v20) = 0 & ssList(v16) = 0 & ssList(v14) = 0 & cons(v11, v20) = v22 & cons(v9, v16) = v18 & app(v19, v22) = v7 & app(v14, v18) = v19 & ssItem(v11) = 0 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (totalorderedP(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v23 = v7 & v21 = 0 & v17 = 0 & v15 = 0 & v12 = 0 & v10 = 0 & ~ (v13 = 0) & leq(v9, v11) = v13 & ssList(v20) = 0 & ssList(v16) = 0 & ssList(v14) = 0 & cons(v11, v20) = v22 & cons(v9, v16) = v18 & app(v19, v22) = v7 & app(v14, v18) = v19 & ssItem(v11) = 0 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (strictorderP(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v24 = v7 & v22 = 0 & v18 = 0 & v16 = 0 & v12 = 0 & v10 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & lt(v11, v9) = v14 & lt(v9, v11) = v13 & ssList(v21) = 0 & ssList(v17) = 0 & ssList(v15) = 0 & cons(v11, v21) = v23 & cons(v9, v17) = v19 & app(v20, v23) = v7 & app(v15, v19) = v20 & ssItem(v11) = 0 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (totalorderP(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v24 = v7 & v22 = 0 & v18 = 0 & v16 = 0 & v12 = 0 & v10 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & leq(v11, v9) = v14 & leq(v9, v11) = v13 & ssList(v21) = 0 & ssList(v17) = 0 & ssList(v15) = 0 & cons(v11, v21) = v23 & cons(v9, v17) = v19 & app(v20, v23) = v7 & app(v15, v19) = v20 & ssItem(v11) = 0 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (cyclefreeP(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v24 = v7 & v22 = 0 & v18 = 0 & v16 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & v10 = 0 & leq(v11, v9) = 0 & leq(v9, v11) = 0 & ssList(v21) = 0 & ssList(v17) = 0 & ssList(v15) = 0 & cons(v11, v21) = v23 & cons(v9, v17) = v19 & app(v20, v23) = v7 & app(v15, v19) = v20 & ssItem(v11) = 0 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (leq(v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & ssItem(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (segmentP(v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (segmentP(v7, nil) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (rearsegP(v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (rearsegP(v7, nil) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (frontsegP(v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (frontsegP(v7, nil) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v7 = nil | ~ (tl(v7) = v8) | ? [v9] : ? [v10] : (ssList(v8) = v10 & ssList(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : (v7 = nil | ~ (tl(v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = v8 & ssList(v8) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v7 = nil | ~ (hd(v7) = v8) | ? [v9] : ? [v10] : (ssList(v7) = v9 & ssItem(v8) = v10 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : (v7 = nil | ~ (hd(v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = v8 & ssItem(v8) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v7 = nil | ~ (ssList(v7) = 0) | ~ (app(v7, v8) = nil) | ? [v9] : ( ~ (v9 = 0) & ssList(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (gt(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v9] : ? [v10] : (gt(v8, v7) = v10 & ssItem(v8) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : ( ~ (tl(v7) = v8) | ? [v9] : ? [v10] : (hd(v7) = v10 & ssList(v7) = v9 & ( ~ (v9 = 0) | ! [v11] : (v11 = v7 | v11 = nil | v7 = nil | ~ (tl(v11) = v8) | ? [v12] : ? [v13] : (hd(v11) = v13 & ssList(v11) = v12 & ( ~ (v13 = v10) | ~ (v12 = 0))))))) & ! [v7] : ! [v8] : ( ~ (lt(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v9] : ? [v10] : (lt(v8, v7) = v10 & ssItem(v8) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : ( ~ (segmentP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = v7 & v13 = 0 & v10 = 0 & ssList(v12) = 0 & ssList(v9) = 0 & app(v11, v12) = v7 & app(v9, v8) = v11) | ( ~ (v9 = 0) & ssList(v8) = v9))) & ! [v7] : ! [v8] : ( ~ (rearsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = v7 & v10 = 0 & ssList(v9) = 0 & app(v9, v8) = v7) | ( ~ (v9 = 0) & ssList(v8) = v9))) & ! [v7] : ! [v8] : ( ~ (frontsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = v7 & v10 = 0 & ssList(v9) = 0 & app(v8, v9) = v7) | ( ~ (v9 = 0) & ssList(v8) = v9))) & ! [v7] : ! [v8] : ( ~ (memberP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = v7 & v12 = 0 & v10 = 0 & ssList(v11) = 0 & ssList(v9) = 0 & cons(v8, v11) = v13 & app(v9, v13) = v7) | ( ~ (v9 = 0) & ssItem(v8) = v9))) & ! [v7] : ! [v8] : ( ~ (ssList(v7) = 0) | ~ (cons(v8, v7) = v7) | ? [v9] : ( ~ (v9 = 0) & ssItem(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (ssList(v7) = 0) | ~ (cons(v8, v7) = nil) | ? [v9] : ( ~ (v9 = 0) & ssItem(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (cons(v7, nil) = v8) | ? [v9] : ? [v10] : (equalelemsP(v8) = v10 & ssItem(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : ( ~ (cons(v7, nil) = v8) | ? [v9] : ? [v10] : (duplicatefreeP(v8) = v10 & ssItem(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : ( ~ (cons(v7, nil) = v8) | ? [v9] : ? [v10] : (strictorderedP(v8) = v10 & ssItem(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : ( ~ (cons(v7, nil) = v8) | ? [v9] : ? [v10] : (totalorderedP(v8) = v10 & ssItem(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : ( ~ (cons(v7, nil) = v8) | ? [v9] : ? [v10] : (strictorderP(v8) = v10 & ssItem(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : ( ~ (cons(v7, nil) = v8) | ? [v9] : ? [v10] : (totalorderP(v8) = v10 & ssItem(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : ( ~ (cons(v7, nil) = v8) | ? [v9] : ? [v10] : (cyclefreeP(v8) = v10 & ssItem(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : (v7 = nil | ~ (segmentP(nil, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & ssList(v7) = v8)) & ! [v7] : (v7 = nil | ~ (rearsegP(nil, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & ssList(v7) = v8)) & ! [v7] : (v7 = nil | ~ (frontsegP(nil, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & ssList(v7) = v8)) & ! [v7] : (v7 = nil | ~ (ssList(v7) = 0) | ? [v8] : ? [v9] : (ssList(v8) = 0 & cons(v9, v8) = v7 & ssItem(v9) = 0)) & ! [v7] : (v7 = nil | ~ (app(nil, nil) = v7)) & ! [v7] : (v7 = 0 | ~ (segmentP(nil, nil) = v7)) & ! [v7] : (v7 = 0 | ~ (rearsegP(nil, nil) = v7)) & ! [v7] : (v7 = 0 | ~ (frontsegP(nil, nil) = v7)) & ! [v7] : ( ~ (lt(v7, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & ssItem(v7) = v8)) & ! [v7] : ( ~ (singletonP(v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v10 = v7 & v9 = 0 & cons(v8, nil) = v7 & ssItem(v8) = 0) | ( ~ (v8 = 0) & ssList(v7) = v8))) & ! [v7] : ( ~ (memberP(nil, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & ssItem(v7) = v8)) & ! [v7] : ( ~ (ssList(v7) = 0) | ~ (neq(v7, v7) = 0)) & ! [v7] : ( ~ (neq(v7, v7) = 0) | ~ (ssItem(v7) = 0)) & ! [v7] : ( ~ (neq(v7, nil) = 0) | ? [v8] : ? [v9] : ? [v10] : (frontsegP(v2, v7) = v9 & frontsegP(v1, v7) = v10 & ssList(v7) = v8 & ( ~ (v10 = 0) | ~ (v9 = 0) | ~ (v8 = 0)))) & ( ~ (v2 = nil) | ~ (v1 = nil)) & ((v4 = 0 & v3 = 0) | (v2 = nil & v1 = nil)))
% 23.37/7.00 | 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 yields:
% 23.37/7.00 | (1) ~ (all_0_0_0 = all_0_1_1) & ~ (all_0_6_6 = 0) & equalelemsP(nil) = 0 & duplicatefreeP(nil) = 0 & strictorderedP(nil) = 0 & totalorderedP(nil) = 0 & strictorderP(nil) = 0 & totalorderP(nil) = 0 & cyclefreeP(nil) = 0 & frontsegP(all_0_4_4, all_0_5_5) = all_0_2_2 & singletonP(nil) = all_0_6_6 & ssList(all_0_4_4) = 0 & ssList(all_0_5_5) = 0 & ssList(nil) = 0 & neq(all_0_5_5, 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)) & ! [v0] : ( ~ (neq(v0, nil) = 0) | ? [v1] : ? [v2] : ? [v3] : (frontsegP(all_0_4_4, v0) = v2 & frontsegP(all_0_5_5, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0)))) & ( ~ (all_0_4_4 = nil) | ~ (all_0_5_5 = nil)) & ((all_0_2_2 = 0 & all_0_3_3 = 0) | (all_0_4_4 = nil & all_0_5_5 = nil))
% 23.37/7.03 |
% 23.37/7.03 | Applying alpha-rule on (1) yields:
% 23.37/7.03 | (2) ! [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)))))
% 23.37/7.03 | (3) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | ~ (duplicatefreeP(v2) = v0))
% 23.37/7.03 | (4) ! [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)))
% 23.37/7.03 | (5) (all_0_2_2 = 0 & all_0_3_3 = 0) | (all_0_4_4 = nil & all_0_5_5 = nil)
% 23.37/7.03 | (6) totalorderedP(nil) = 0
% 23.37/7.03 | (7) ! [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)))
% 23.37/7.03 | (8) ! [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)))))))
% 23.37/7.03 | (9) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0))
% 23.37/7.03 | (10) ! [v0] : ! [v1] : (v1 = v0 | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (frontsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 23.37/7.03 | (11) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssItem(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 23.37/7.03 | (12) ! [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)))
% 23.37/7.03 | (13) ! [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)))
% 23.37/7.03 | (14) ! [v0] : ! [v1] : (v1 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 23.37/7.03 | (15) duplicatefreeP(nil) = 0
% 23.37/7.03 | (16) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssList(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 23.37/7.03 | (17) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0))
% 23.37/7.03 | (18) neq(all_0_5_5, nil) = all_0_3_3
% 23.37/7.03 | (19) ! [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)))))
% 23.37/7.03 | (20) ! [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)))
% 23.37/7.03 | (21) strictorderP(nil) = 0
% 23.37/7.03 | (22) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & ssList(v0) = v4))
% 23.37/7.03 | (23) ! [v0] : ! [v1] : ( ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (gt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 23.37/7.04 | (24) ! [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)))
% 23.37/7.04 | (25) ! [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)))
% 23.37/7.04 | (26) ! [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))))
% 23.37/7.04 | (27) ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (leq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 23.37/7.04 | (28) ! [v0] : ! [v1] : (v1 = v0 | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 23.37/7.04 | (29) ! [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)))
% 23.37/7.04 | (30) ! [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)))
% 23.37/7.04 | (31) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.37/7.04 | (32) ! [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)))))))
% 23.37/7.04 | (33) ~ (all_0_0_0 = all_0_1_1)
% 23.37/7.04 | (34) ! [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))))))))
% 23.37/7.04 | (35) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.37/7.04 | (36) ! [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)))
% 23.37/7.04 | (37) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = v0))
% 23.37/7.04 | (38) ! [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)))
% 23.37/7.04 | (39) ssList(nil) = 0
% 23.37/7.04 | (40) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.37/7.04 | (41) ! [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))))))))
% 23.37/7.04 | (42) ! [v0] : (v0 = 0 | ~ (rearsegP(nil, nil) = v0))
% 23.37/7.04 | (43) ! [v0] : ( ~ (singletonP(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v0 & v2 = 0 & cons(v1, nil) = v0 & ssItem(v1) = 0) | ( ~ (v1 = 0) & ssList(v0) = v1)))
% 23.37/7.04 | (44) ! [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)))
% 23.37/7.04 | (45) ! [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)))))))
% 23.37/7.04 | (46) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : (ssList(v0) = v2 & ssItem(v1) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 23.37/7.04 | (47) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 23.37/7.04 | (48) ! [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)))
% 23.37/7.04 | (49) ! [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))))
% 23.37/7.04 | (50) ! [v0] : ( ~ (neq(v0, nil) = 0) | ? [v1] : ? [v2] : ? [v3] : (frontsegP(all_0_4_4, v0) = v2 & frontsegP(all_0_5_5, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))
% 23.37/7.04 | (51) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.37/7.05 | (52) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v0) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 23.37/7.05 | (53) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.37/7.05 | (54) ! [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)))
% 23.37/7.05 | (55) ! [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)))))))
% 23.37/7.05 | (56) ! [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)))))))
% 23.37/7.05 | (57) ! [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)))))
% 23.37/7.05 | (58) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.37/7.05 | (59) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.37/7.05 | (60) equalelemsP(nil) = 0
% 23.37/7.05 | (61) ! [v0] : ( ~ (neq(v0, v0) = 0) | ~ (ssItem(v0) = 0))
% 23.37/7.05 | (62) ! [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)))
% 23.37/7.05 | (63) ! [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)))))
% 23.37/7.05 | (64) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ (totalorderP(v2) = v0))
% 23.37/7.05 | (65) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 23.37/7.05 | (66) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.37/7.05 | (67) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.37/7.05 | (68) ssItem(all_0_1_1) = 0
% 23.37/7.05 | (69) ! [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))))
% 23.37/7.05 | (70) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = nil) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 23.37/7.05 | (71) ! [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)))))))
% 23.37/7.05 | (72) cyclefreeP(nil) = 0
% 23.37/7.05 | (73) ! [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)))
% 23.37/7.05 | (74) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderP(v2) = v1) | ~ (strictorderP(v2) = v0))
% 23.37/7.05 | (75) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) = v0))
% 23.37/7.05 | (76) ! [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)))))))
% 23.37/7.05 | (77) ! [v0] : (v0 = nil | ~ (frontsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 23.37/7.05 | (78) ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0))
% 23.37/7.05 | (79) ! [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)))
% 23.37/7.05 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0))
% 23.37/7.05 | (81) ~ (all_0_6_6 = 0)
% 23.37/7.05 | (82) frontsegP(all_0_4_4, all_0_5_5) = all_0_2_2
% 23.37/7.05 | (83) ! [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)))))
% 23.37/7.05 | (84) ! [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))))
% 23.37/7.05 | (85) ! [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)))
% 23.37/7.06 | (86) ! [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)))
% 23.37/7.06 | (87) ssList(all_0_4_4) = 0
% 23.37/7.06 | (88) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (neq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & ssItem(v1) = v3))
% 23.37/7.06 | (89) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 23.89/7.06 | (90) ~ (all_0_4_4 = nil) | ~ (all_0_5_5 = nil)
% 23.89/7.06 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0))
% 23.89/7.06 | (92) ! [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)))))
% 23.89/7.06 | (93) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.89/7.06 | (94) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 23.89/7.06 | (95) ! [v0] : ! [v1] : (v0 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 23.89/7.06 | (96) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (ssList(v0) = 0) | ~ (neq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & ssList(v1) = v3))
% 23.89/7.06 | (97) ! [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)))))
% 23.89/7.06 | (98) ! [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)))
% 23.89/7.06 | (99) ! [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)))
% 23.89/7.06 | (100) ! [v0] : (v0 = nil | ~ (ssList(v0) = 0) | ? [v1] : ? [v2] : (ssList(v1) = 0 & cons(v2, v1) = v0 & ssItem(v2) = 0))
% 23.89/7.06 | (101) ! [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)))))
% 23.89/7.06 | (102) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 23.89/7.06 | (103) ! [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)))
% 23.89/7.06 | (104) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | ~ (equalelemsP(v2) = v0))
% 23.89/7.06 | (105) ! [v0] : ( ~ (lt(v0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 23.89/7.06 | (106) ! [v0] : (v0 = nil | ~ (rearsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 23.89/7.06 | (107) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v1)))
% 23.89/7.06 | (108) ! [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)))
% 23.89/7.06 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0))
% 23.89/7.06 | (110) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 23.89/7.06 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0))
% 23.89/7.06 | (112) ! [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)))
% 23.89/7.06 | (113) ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 23.89/7.06 | (114) ! [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)))))
% 23.89/7.06 | (115) ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (lt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 23.89/7.06 | (116) ! [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)))))
% 23.89/7.06 | (117) ! [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))))))))
% 23.89/7.06 | (118) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.89/7.06 | (119) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.89/7.06 | (120) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.89/7.06 | (121) ! [v0] : ( ~ (memberP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 23.89/7.06 | (122) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ (cyclefreeP(v2) = v0))
% 23.89/7.06 | (123) ssList(all_0_5_5) = 0
% 23.89/7.06 | (124) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0))
% 23.89/7.06 | (125) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 23.89/7.07 | (126) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0))
% 23.89/7.07 | (127) strictorderedP(nil) = 0
% 23.89/7.07 | (128) totalorderP(nil) = 0
% 23.89/7.07 | (129) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (ssList(v1) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.89/7.07 | (130) ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (geq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 23.89/7.07 | (131) ! [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)))
% 23.89/7.07 | (132) ! [v0] : (v0 = 0 | ~ (frontsegP(nil, nil) = v0))
% 23.89/7.07 | (133) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0))
% 23.89/7.07 | (134) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (singletonP(v0) = v1) | ~ (cons(v2, nil) = v0) | ? [v3] : (( ~ (v3 = 0) & ssList(v0) = v3) | ( ~ (v3 = 0) & ssItem(v2) = v3)))
% 23.89/7.07 | (135) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (tl(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v0)))
% 23.89/7.07 | (136) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 23.89/7.07 | (137) singletonP(nil) = all_0_6_6
% 23.89/7.07 | (138) ! [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))))
% 23.89/7.07 | (139) ! [v0] : ! [v1] : (v1 = v0 | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 23.89/7.07 | (140) ! [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)))
% 23.89/7.07 | (141) ! [v0] : (v0 = nil | ~ (segmentP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 23.89/7.07 | (142) ! [v0] : ( ~ (ssList(v0) = 0) | ~ (neq(v0, v0) = 0))
% 23.89/7.07 | (143) ! [v0] : (v0 = 0 | ~ (segmentP(nil, nil) = v0))
% 23.89/7.07 | (144) ! [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)))
% 23.89/7.07 | (145) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (app(v0, v1) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 23.89/7.07 | (146) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.89/7.07 | (147) ssItem(all_0_0_0) = 0
% 23.89/7.07 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0))
% 23.89/7.07 | (149) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.89/7.07 |
% 23.89/7.07 | Instantiating formula (100) with all_0_5_5 and discharging atoms ssList(all_0_5_5) = 0, yields:
% 23.89/7.07 | (150) all_0_5_5 = nil | ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_5_5 & ssItem(v1) = 0)
% 23.89/7.07 |
% 23.89/7.07 | Instantiating formula (50) with all_0_5_5 yields:
% 23.89/7.07 | (151) ~ (neq(all_0_5_5, nil) = 0) | ? [v0] : ? [v1] : ? [v2] : (frontsegP(all_0_4_4, all_0_5_5) = v1 & frontsegP(all_0_5_5, all_0_5_5) = v2 & ssList(all_0_5_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 23.89/7.07 |
% 23.89/7.07 +-Applying beta-rule and splitting (90), into two cases.
% 23.89/7.07 |-Branch one:
% 23.89/7.07 | (152) ~ (all_0_4_4 = nil)
% 23.89/7.07 |
% 23.89/7.07 +-Applying beta-rule and splitting (5), into two cases.
% 23.89/7.07 |-Branch one:
% 23.89/7.07 | (153) all_0_2_2 = 0 & all_0_3_3 = 0
% 23.89/7.07 |
% 23.89/7.07 | Applying alpha-rule on (153) yields:
% 23.89/7.07 | (154) all_0_2_2 = 0
% 23.89/7.07 | (155) all_0_3_3 = 0
% 23.89/7.07 |
% 23.89/7.07 | From (154) and (82) follows:
% 23.89/7.07 | (156) frontsegP(all_0_4_4, all_0_5_5) = 0
% 23.89/7.07 |
% 23.89/7.07 | From (155) and (18) follows:
% 23.89/7.07 | (157) neq(all_0_5_5, nil) = 0
% 23.89/7.07 |
% 23.89/7.07 +-Applying beta-rule and splitting (151), into two cases.
% 23.89/7.07 |-Branch one:
% 23.89/7.07 | (158) ~ (neq(all_0_5_5, nil) = 0)
% 23.89/7.07 |
% 23.89/7.07 | Using (157) and (158) yields:
% 23.89/7.07 | (159) $false
% 23.89/7.07 |
% 23.89/7.07 |-The branch is then unsatisfiable
% 23.89/7.07 |-Branch two:
% 23.89/7.07 | (157) neq(all_0_5_5, nil) = 0
% 23.89/7.07 | (161) ? [v0] : ? [v1] : ? [v2] : (frontsegP(all_0_4_4, all_0_5_5) = v1 & frontsegP(all_0_5_5, all_0_5_5) = v2 & ssList(all_0_5_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 23.89/7.07 |
% 23.89/7.07 | Instantiating (161) with all_18_0_7, all_18_1_8, all_18_2_9 yields:
% 23.89/7.07 | (162) frontsegP(all_0_4_4, all_0_5_5) = all_18_1_8 & frontsegP(all_0_5_5, all_0_5_5) = all_18_0_7 & ssList(all_0_5_5) = all_18_2_9 & ( ~ (all_18_0_7 = 0) | ~ (all_18_1_8 = 0) | ~ (all_18_2_9 = 0))
% 23.89/7.07 |
% 23.89/7.07 | Applying alpha-rule on (162) yields:
% 23.89/7.07 | (163) frontsegP(all_0_4_4, all_0_5_5) = all_18_1_8
% 23.89/7.07 | (164) frontsegP(all_0_5_5, all_0_5_5) = all_18_0_7
% 23.89/7.07 | (165) ssList(all_0_5_5) = all_18_2_9
% 23.89/7.07 | (166) ~ (all_18_0_7 = 0) | ~ (all_18_1_8 = 0) | ~ (all_18_2_9 = 0)
% 23.89/7.07 |
% 23.89/7.07 | Instantiating formula (65) with all_0_4_4, all_0_5_5, 0, all_18_1_8 and discharging atoms frontsegP(all_0_4_4, all_0_5_5) = all_18_1_8, frontsegP(all_0_4_4, all_0_5_5) = 0, yields:
% 23.89/7.07 | (167) all_18_1_8 = 0
% 23.89/7.07 |
% 23.89/7.07 | Instantiating formula (136) with all_0_5_5, all_18_2_9, 0 and discharging atoms ssList(all_0_5_5) = all_18_2_9, ssList(all_0_5_5) = 0, yields:
% 23.89/7.07 | (168) all_18_2_9 = 0
% 23.89/7.08 |
% 23.89/7.08 | From (168) and (165) follows:
% 23.89/7.08 | (123) ssList(all_0_5_5) = 0
% 23.89/7.08 |
% 23.89/7.08 +-Applying beta-rule and splitting (166), into two cases.
% 23.89/7.08 |-Branch one:
% 23.89/7.08 | (170) ~ (all_18_0_7 = 0)
% 23.89/7.08 |
% 23.89/7.08 | Instantiating formula (53) with all_18_0_7, all_0_5_5 and discharging atoms frontsegP(all_0_5_5, all_0_5_5) = all_18_0_7, yields:
% 23.89/7.08 | (171) all_18_0_7 = 0 | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_5_5) = v0)
% 23.89/7.08 |
% 23.89/7.08 +-Applying beta-rule and splitting (171), into two cases.
% 23.89/7.08 |-Branch one:
% 23.89/7.08 | (172) all_18_0_7 = 0
% 23.89/7.08 |
% 23.89/7.08 | Equations (172) can reduce 170 to:
% 23.89/7.08 | (173) $false
% 23.89/7.08 |
% 23.89/7.08 |-The branch is then unsatisfiable
% 23.89/7.08 |-Branch two:
% 23.89/7.08 | (170) ~ (all_18_0_7 = 0)
% 23.89/7.08 | (175) ? [v0] : ( ~ (v0 = 0) & ssList(all_0_5_5) = v0)
% 23.89/7.08 |
% 23.89/7.08 | Instantiating (175) with all_55_0_19 yields:
% 23.89/7.08 | (176) ~ (all_55_0_19 = 0) & ssList(all_0_5_5) = all_55_0_19
% 23.89/7.08 |
% 23.89/7.08 | Applying alpha-rule on (176) yields:
% 23.89/7.08 | (177) ~ (all_55_0_19 = 0)
% 23.89/7.08 | (178) ssList(all_0_5_5) = all_55_0_19
% 23.89/7.08 |
% 23.89/7.08 | Instantiating formula (136) with all_0_5_5, all_55_0_19, 0 and discharging atoms ssList(all_0_5_5) = all_55_0_19, ssList(all_0_5_5) = 0, yields:
% 23.89/7.08 | (179) all_55_0_19 = 0
% 23.89/7.08 |
% 23.89/7.08 | Equations (179) can reduce 177 to:
% 23.89/7.08 | (173) $false
% 23.89/7.08 |
% 23.89/7.08 |-The branch is then unsatisfiable
% 23.89/7.08 |-Branch two:
% 23.89/7.08 | (172) all_18_0_7 = 0
% 23.89/7.08 | (182) ~ (all_18_1_8 = 0) | ~ (all_18_2_9 = 0)
% 23.89/7.08 |
% 23.89/7.08 +-Applying beta-rule and splitting (182), into two cases.
% 23.89/7.08 |-Branch one:
% 23.89/7.08 | (183) ~ (all_18_1_8 = 0)
% 23.89/7.08 |
% 23.89/7.08 | Equations (167) can reduce 183 to:
% 23.89/7.08 | (173) $false
% 23.89/7.08 |
% 23.89/7.08 |-The branch is then unsatisfiable
% 23.89/7.08 |-Branch two:
% 23.89/7.08 | (167) all_18_1_8 = 0
% 23.89/7.08 | (186) ~ (all_18_2_9 = 0)
% 23.89/7.08 |
% 23.89/7.08 | Equations (168) can reduce 186 to:
% 23.89/7.08 | (173) $false
% 23.89/7.08 |
% 23.89/7.08 |-The branch is then unsatisfiable
% 23.89/7.08 |-Branch two:
% 23.89/7.08 | (188) all_0_4_4 = nil & all_0_5_5 = nil
% 23.89/7.08 |
% 23.89/7.08 | Applying alpha-rule on (188) yields:
% 23.89/7.08 | (189) all_0_4_4 = nil
% 23.89/7.08 | (190) all_0_5_5 = nil
% 23.89/7.08 |
% 23.89/7.08 | Equations (189) can reduce 152 to:
% 23.89/7.08 | (173) $false
% 23.89/7.08 |
% 23.89/7.08 |-The branch is then unsatisfiable
% 23.89/7.08 |-Branch two:
% 23.89/7.08 | (189) all_0_4_4 = nil
% 23.89/7.08 | (193) ~ (all_0_5_5 = nil)
% 23.89/7.08 |
% 23.89/7.08 | From (189) and (82) follows:
% 23.89/7.08 | (194) frontsegP(nil, all_0_5_5) = all_0_2_2
% 23.89/7.08 |
% 23.89/7.08 | From (189) and (87) follows:
% 23.89/7.08 | (39) ssList(nil) = 0
% 23.89/7.08 |
% 23.89/7.08 +-Applying beta-rule and splitting (5), into two cases.
% 23.89/7.08 |-Branch one:
% 23.89/7.08 | (153) all_0_2_2 = 0 & all_0_3_3 = 0
% 23.89/7.08 |
% 23.89/7.08 | Applying alpha-rule on (153) yields:
% 23.89/7.08 | (154) all_0_2_2 = 0
% 23.89/7.08 | (155) all_0_3_3 = 0
% 23.89/7.08 |
% 23.89/7.08 | From (154) and (194) follows:
% 23.89/7.08 | (199) frontsegP(nil, all_0_5_5) = 0
% 23.89/7.08 |
% 23.89/7.08 | From (155) and (18) follows:
% 23.89/7.08 | (157) neq(all_0_5_5, nil) = 0
% 23.89/7.08 |
% 23.89/7.08 +-Applying beta-rule and splitting (151), into two cases.
% 23.89/7.08 |-Branch one:
% 23.89/7.08 | (158) ~ (neq(all_0_5_5, nil) = 0)
% 23.89/7.08 |
% 23.89/7.08 | Using (157) and (158) yields:
% 23.89/7.08 | (159) $false
% 23.89/7.08 |
% 23.89/7.08 |-The branch is then unsatisfiable
% 23.89/7.08 |-Branch two:
% 23.89/7.08 | (157) neq(all_0_5_5, nil) = 0
% 23.89/7.08 | (161) ? [v0] : ? [v1] : ? [v2] : (frontsegP(all_0_4_4, all_0_5_5) = v1 & frontsegP(all_0_5_5, all_0_5_5) = v2 & ssList(all_0_5_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 23.89/7.08 |
% 23.89/7.08 | Instantiating (161) with all_18_0_20, all_18_1_21, all_18_2_22 yields:
% 23.89/7.08 | (205) frontsegP(all_0_4_4, all_0_5_5) = all_18_1_21 & frontsegP(all_0_5_5, all_0_5_5) = all_18_0_20 & ssList(all_0_5_5) = all_18_2_22 & ( ~ (all_18_0_20 = 0) | ~ (all_18_1_21 = 0) | ~ (all_18_2_22 = 0))
% 23.89/7.08 |
% 23.89/7.08 | Applying alpha-rule on (205) yields:
% 23.89/7.08 | (206) frontsegP(all_0_4_4, all_0_5_5) = all_18_1_21
% 23.89/7.08 | (207) frontsegP(all_0_5_5, all_0_5_5) = all_18_0_20
% 23.89/7.08 | (208) ssList(all_0_5_5) = all_18_2_22
% 23.89/7.08 | (209) ~ (all_18_0_20 = 0) | ~ (all_18_1_21 = 0) | ~ (all_18_2_22 = 0)
% 23.89/7.08 |
% 23.89/7.08 | From (189) and (206) follows:
% 23.89/7.08 | (210) frontsegP(nil, all_0_5_5) = all_18_1_21
% 23.89/7.08 |
% 23.89/7.08 +-Applying beta-rule and splitting (150), into two cases.
% 23.89/7.08 |-Branch one:
% 23.89/7.08 | (190) all_0_5_5 = nil
% 23.89/7.08 |
% 23.89/7.08 | Equations (190) can reduce 193 to:
% 23.89/7.08 | (173) $false
% 23.89/7.08 |
% 23.89/7.08 |-The branch is then unsatisfiable
% 23.89/7.08 |-Branch two:
% 23.89/7.08 | (193) ~ (all_0_5_5 = nil)
% 23.89/7.08 | (214) ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_5_5 & ssItem(v1) = 0)
% 23.89/7.08 |
% 23.89/7.08 | Instantiating formula (65) with nil, all_0_5_5, 0, all_18_1_21 and discharging atoms frontsegP(nil, all_0_5_5) = all_18_1_21, frontsegP(nil, all_0_5_5) = 0, yields:
% 23.89/7.08 | (215) all_18_1_21 = 0
% 23.89/7.08 |
% 23.89/7.08 | Instantiating formula (136) with all_0_5_5, all_18_2_22, 0 and discharging atoms ssList(all_0_5_5) = all_18_2_22, ssList(all_0_5_5) = 0, yields:
% 23.89/7.08 | (216) all_18_2_22 = 0
% 23.89/7.08 |
% 23.89/7.08 | From (215) and (210) follows:
% 23.89/7.08 | (199) frontsegP(nil, all_0_5_5) = 0
% 23.89/7.08 |
% 23.89/7.08 | From (216) and (208) follows:
% 23.89/7.08 | (123) ssList(all_0_5_5) = 0
% 23.89/7.08 |
% 23.89/7.08 | Instantiating formula (10) with all_0_5_5, nil and discharging atoms frontsegP(nil, all_0_5_5) = 0, ssList(nil) = 0, yields:
% 23.89/7.08 | (219) all_0_5_5 = nil | ? [v0] : ? [v1] : (frontsegP(all_0_5_5, nil) = v1 & ssList(all_0_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 23.89/7.08 |
% 23.89/7.08 | Instantiating formula (77) with all_0_5_5 and discharging atoms frontsegP(nil, all_0_5_5) = 0, yields:
% 23.89/7.08 | (220) all_0_5_5 = nil | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_5_5) = v0)
% 23.89/7.08 |
% 23.89/7.08 +-Applying beta-rule and splitting (220), into two cases.
% 23.89/7.08 |-Branch one:
% 23.89/7.08 | (190) all_0_5_5 = nil
% 23.89/7.08 |
% 23.89/7.08 | Equations (190) can reduce 193 to:
% 23.89/7.08 | (173) $false
% 23.89/7.08 |
% 23.89/7.08 |-The branch is then unsatisfiable
% 23.89/7.08 |-Branch two:
% 23.89/7.08 | (193) ~ (all_0_5_5 = nil)
% 23.89/7.08 | (175) ? [v0] : ( ~ (v0 = 0) & ssList(all_0_5_5) = v0)
% 23.89/7.08 |
% 23.89/7.08 | Instantiating (175) with all_48_0_34 yields:
% 23.89/7.08 | (225) ~ (all_48_0_34 = 0) & ssList(all_0_5_5) = all_48_0_34
% 23.89/7.08 |
% 23.89/7.08 | Applying alpha-rule on (225) yields:
% 23.89/7.08 | (226) ~ (all_48_0_34 = 0)
% 23.89/7.08 | (227) ssList(all_0_5_5) = all_48_0_34
% 23.89/7.08 |
% 23.89/7.08 +-Applying beta-rule and splitting (219), into two cases.
% 23.89/7.08 |-Branch one:
% 23.89/7.08 | (190) all_0_5_5 = nil
% 23.89/7.08 |
% 23.89/7.08 | Equations (190) can reduce 193 to:
% 23.89/7.08 | (173) $false
% 23.89/7.08 |
% 23.89/7.08 |-The branch is then unsatisfiable
% 23.89/7.08 |-Branch two:
% 23.89/7.08 | (193) ~ (all_0_5_5 = nil)
% 23.89/7.08 | (231) ? [v0] : ? [v1] : (frontsegP(all_0_5_5, nil) = v1 & ssList(all_0_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 23.89/7.08 |
% 23.89/7.08 | Instantiating (231) with all_57_0_37, all_57_1_38 yields:
% 23.89/7.08 | (232) frontsegP(all_0_5_5, nil) = all_57_0_37 & ssList(all_0_5_5) = all_57_1_38 & ( ~ (all_57_0_37 = 0) | ~ (all_57_1_38 = 0))
% 23.89/7.08 |
% 23.89/7.08 | Applying alpha-rule on (232) yields:
% 23.89/7.08 | (233) frontsegP(all_0_5_5, nil) = all_57_0_37
% 23.89/7.08 | (234) ssList(all_0_5_5) = all_57_1_38
% 23.89/7.08 | (235) ~ (all_57_0_37 = 0) | ~ (all_57_1_38 = 0)
% 23.89/7.08 |
% 23.89/7.08 | Instantiating formula (136) with all_0_5_5, all_57_1_38, 0 and discharging atoms ssList(all_0_5_5) = all_57_1_38, ssList(all_0_5_5) = 0, yields:
% 23.89/7.08 | (236) all_57_1_38 = 0
% 23.89/7.08 |
% 23.89/7.08 | Instantiating formula (136) with all_0_5_5, all_48_0_34, all_57_1_38 and discharging atoms ssList(all_0_5_5) = all_57_1_38, ssList(all_0_5_5) = all_48_0_34, yields:
% 23.89/7.08 | (237) all_57_1_38 = all_48_0_34
% 23.89/7.08 |
% 23.89/7.08 | Combining equations (236,237) yields a new equation:
% 23.89/7.08 | (238) all_48_0_34 = 0
% 23.89/7.08 |
% 23.89/7.08 | Equations (238) can reduce 226 to:
% 23.89/7.08 | (173) $false
% 23.89/7.08 |
% 23.89/7.08 |-The branch is then unsatisfiable
% 23.89/7.08 |-Branch two:
% 23.89/7.08 | (188) all_0_4_4 = nil & all_0_5_5 = nil
% 23.89/7.08 |
% 23.89/7.08 | Applying alpha-rule on (188) yields:
% 23.89/7.08 | (189) all_0_4_4 = nil
% 23.89/7.08 | (190) all_0_5_5 = nil
% 23.89/7.08 |
% 23.89/7.08 | Equations (190) can reduce 193 to:
% 23.89/7.08 | (173) $false
% 23.89/7.08 |
% 23.89/7.08 |-The branch is then unsatisfiable
% 23.89/7.08 % SZS output end Proof for theBenchmark
% 23.89/7.08
% 23.89/7.08 6477ms
%------------------------------------------------------------------------------