TSTP Solution File: SWC294+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWC294+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 20:17:19 EDT 2022
% Result : Theorem 23.03s 6.92s
% Output : Proof 30.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWC294+1 : TPTP v8.1.0. Released v2.4.0.
% 0.11/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 11 23:15:21 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.61/0.60 ____ _
% 0.61/0.60 ___ / __ \_____(_)___ ________ __________
% 0.61/0.60 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.61/0.60 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.61/0.60 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.61/0.60
% 0.61/0.60 A Theorem Prover for First-Order Logic
% 0.61/0.60 (ePrincess v.1.0)
% 0.61/0.60
% 0.61/0.60 (c) Philipp Rümmer, 2009-2015
% 0.61/0.60 (c) Peter Backeman, 2014-2015
% 0.61/0.60 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.61/0.60 Free software under GNU Lesser General Public License (LGPL).
% 0.61/0.60 Bug reports to peter@backeman.se
% 0.61/0.60
% 0.61/0.60 For more information, visit http://user.uu.se/~petba168/breu/
% 0.61/0.60
% 0.61/0.60 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.70/0.67 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.13/1.06 Prover 0: Preprocessing ...
% 4.57/1.70 Prover 0: Constructing countermodel ...
% 18.89/5.96 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.18/6.10 Prover 1: Preprocessing ...
% 20.47/6.31 Prover 1: Constructing countermodel ...
% 23.03/6.91 Prover 1: proved (952ms)
% 23.03/6.92 Prover 0: stopped
% 23.03/6.92
% 23.03/6.92 No countermodel exists, formula is valid
% 23.03/6.92 % SZS status Theorem for theBenchmark
% 23.03/6.92
% 23.03/6.92 Generating proof ... found it (size 171)
% 29.94/8.57
% 29.94/8.57 % SZS output start Proof for theBenchmark
% 29.94/8.58 Assumed formulas after preprocessing and simplification:
% 29.94/8.58 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v6) & ~ (v2 = 0) & ~ (v0 = 0) & equalelemsP(nil) = 0 & duplicatefreeP(nil) = 0 & strictorderedP(v1) = v2 & strictorderedP(nil) = 0 & totalorderedP(nil) = 0 & strictorderP(nil) = 0 & totalorderP(nil) = 0 & cyclefreeP(nil) = 0 & segmentP(v3, v1) = 0 & singletonP(v1) = v4 & singletonP(nil) = v0 & ssList(v3) = 0 & ssList(v1) = 0 & ssList(nil) = 0 & neq(v3, nil) = v5 & ssItem(v7) = 0 & ssItem(v6) = 0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v11 = 0 | ~ (strictorderedP(v8) = 0) | ~ (lt(v9, v10) = v11) | ~ (ssList(v12) = 0) | ~ (cons(v10, v16) = v17) | ~ (cons(v9, v13) = v14) | ~ (app(v15, v17) = v8) | ~ (app(v12, v14) = v15) | ~ (ssItem(v9) = 0) | ? [v18] : (( ~ (v18 = 0) & ssList(v16) = v18) | ( ~ (v18 = 0) & ssList(v13) = v18) | ( ~ (v18 = 0) & ssList(v8) = v18) | ( ~ (v18 = 0) & ssItem(v10) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v11 = 0 | ~ (totalorderedP(v8) = 0) | ~ (leq(v9, v10) = v11) | ~ (ssList(v12) = 0) | ~ (cons(v10, v16) = v17) | ~ (cons(v9, v13) = v14) | ~ (app(v15, v17) = v8) | ~ (app(v12, v14) = v15) | ~ (ssItem(v9) = 0) | ? [v18] : (( ~ (v18 = 0) & ssList(v16) = v18) | ( ~ (v18 = 0) & ssList(v13) = v18) | ( ~ (v18 = 0) & ssList(v8) = v18) | ( ~ (v18 = 0) & ssItem(v10) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (duplicatefreeP(v8) = 0) | ~ (ssList(v10) = 0) | ~ (cons(v9, v14) = v15) | ~ (cons(v9, v11) = v12) | ~ (app(v13, v15) = v8) | ~ (app(v10, v12) = v13) | ~ (ssItem(v9) = 0) | ? [v16] : (( ~ (v16 = 0) & ssList(v14) = v16) | ( ~ (v16 = 0) & ssList(v11) = v16) | ( ~ (v16 = 0) & ssList(v8) = v16))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (segmentP(v13, v9) = v14) | ~ (segmentP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ~ (app(v11, v12) = v13) | ~ (app(v10, v8) = v11) | ? [v15] : (( ~ (v15 = 0) & ssList(v12) = v15) | ( ~ (v15 = 0) & ssList(v10) = v15) | ( ~ (v15 = 0) & ssList(v9) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (equalelemsP(v8) = 0) | ~ (ssList(v11) = 0) | ~ (cons(v10, v12) = v13) | ~ (cons(v9, v13) = v14) | ~ (app(v11, v14) = v8) | ~ (ssItem(v10) = 0) | ~ (ssItem(v9) = 0) | ? [v15] : (( ~ (v15 = 0) & ssList(v12) = v15) | ( ~ (v15 = 0) & ssList(v8) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (frontsegP(v11, v13) = v14) | ~ (cons(v9, v12) = v13) | ~ (cons(v8, v10) = v11) | ~ (ssItem(v9) = 0) | ~ (ssItem(v8) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssList(v10) = v15) | (frontsegP(v10, v12) = v16 & ssList(v12) = v15 & ( ~ (v15 = 0) | (( ~ (v16 = 0) | ~ (v9 = v8) | v14 = 0) & ( ~ (v14 = 0) | (v16 = 0 & v9 = v8))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = 0 | ~ (segmentP(v8, v9) = v10) | ~ (ssList(v8) = 0) | ~ (app(v12, v13) = v8) | ~ (app(v11, v9) = v12) | ? [v14] : (( ~ (v14 = 0) & ssList(v13) = v14) | ( ~ (v14 = 0) & ssList(v11) = v14) | ( ~ (v14 = 0) & ssList(v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = 0 | ~ (memberP(v8, v9) = v10) | ~ (ssList(v11) = 0) | ~ (ssList(v8) = 0) | ~ (cons(v9, v12) = v13) | ~ (app(v11, v13) = v8) | ? [v14] : (( ~ (v14 = 0) & ssList(v12) = v14) | ( ~ (v14 = 0) & ssItem(v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (memberP(v12, v8) = v13) | ~ (memberP(v9, v8) = v10) | ~ (app(v9, v11) = v12) | ~ (ssItem(v8) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssList(v9) = v14) | (memberP(v11, v8) = v15 & ssList(v11) = v14 & ( ~ (v14 = 0) | (( ~ (v13 = 0) | v15 = 0 | v10 = 0) & (v13 = 0 | ( ~ (v15 = 0) & ~ (v10 = 0)))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (ssList(v8) = 0) | ~ (cons(v11, v9) = v12) | ~ (app(v12, v8) = v13) | ~ (app(v9, v8) = v10) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssList(v9) = v14) | (cons(v11, v10) = v15 & ssItem(v11) = v14 & ( ~ (v14 = 0) | v15 = v13)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (ssList(v9) = 0) | ~ (ssList(v8) = 0) | ~ (cons(v12, v9) = v11) | ~ (cons(v10, v8) = v11) | ? [v13] : (( ~ (v13 = 0) & ssItem(v12) = v13) | ( ~ (v13 = 0) & ssItem(v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (rearsegP(v11, v9) = v12) | ~ (rearsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ~ (app(v10, v8) = v11) | ? [v13] : (( ~ (v13 = 0) & ssList(v10) = v13) | ( ~ (v13 = 0) & ssList(v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (frontsegP(v11, v9) = v12) | ~ (frontsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ~ (app(v8, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & ssList(v10) = v13) | ( ~ (v13 = 0) & ssList(v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (ssList(v9) = 0) | ~ (ssList(v8) = 0) | ~ (cons(v12, v9) = v11) | ~ (cons(v10, v8) = v11) | ? [v13] : (( ~ (v13 = 0) & ssItem(v12) = v13) | ( ~ (v13 = 0) & ssItem(v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (memberP(v11, v8) = v12) | ~ (cons(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ~ (ssItem(v8) = 0) | ? [v13] : ? [v14] : (memberP(v10, v8) = v14 & ssList(v10) = v13 & ( ~ (v13 = 0) | (( ~ (v12 = 0) | v14 = 0 | v9 = v8) & (v12 = 0 | ( ~ (v14 = 0) & ~ (v9 = v8))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (ssList(v8) = 0) | ~ (app(v10, v11) = v12) | ~ (app(v8, v9) = v10) | ? [v13] : ? [v14] : ? [v15] : (( ~ (v13 = 0) & ssList(v9) = v13) | (ssList(v11) = v13 & app(v9, v11) = v14 & app(v8, v14) = v15 & ( ~ (v13 = 0) | v15 = v12)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | v8 = nil | ~ (tl(v8) = v10) | ~ (hd(v8) = v9) | ~ (cons(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & ssList(v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (ssList(v8) = 0) | ~ (app(v11, v9) = v10) | ~ (app(v8, v9) = v10) | ? [v12] : (( ~ (v12 = 0) & ssList(v11) = v12) | ( ~ (v12 = 0) & ssList(v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (ssList(v8) = 0) | ~ (app(v9, v11) = v10) | ~ (app(v9, v8) = v10) | ? [v12] : (( ~ (v12 = 0) & ssList(v11) = v12) | ( ~ (v12 = 0) & ssList(v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (gt(v8, v10) = v11) | ~ (gt(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssItem(v9) = v12) | (gt(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (geq(v8, v10) = v11) | ~ (geq(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssItem(v9) = v12) | (geq(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (lt(v8, v10) = v11) | ~ (lt(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssItem(v9) = v12) | (lt(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (lt(v8, v10) = v11) | ~ (leq(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssItem(v9) = v12) | (lt(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (leq(v8, v10) = v11) | ~ (leq(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssItem(v9) = v12) | (leq(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (segmentP(v8, v10) = v11) | ~ (segmentP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v9) = v12) | (segmentP(v9, v10) = v13 & ssList(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (rearsegP(v8, v10) = v11) | ~ (rearsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v9) = v12) | (rearsegP(v9, v10) = v13 & ssList(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (frontsegP(v8, v10) = v11) | ~ (frontsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v9) = v12) | (frontsegP(v9, v10) = v13 & ssList(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (rearsegP(v8, v9) = v10) | ~ (ssList(v8) = 0) | ~ (app(v11, v9) = v8) | ? [v12] : (( ~ (v12 = 0) & ssList(v11) = v12) | ( ~ (v12 = 0) & ssList(v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (frontsegP(v8, v9) = v10) | ~ (ssList(v8) = 0) | ~ (app(v9, v11) = v8) | ? [v12] : (( ~ (v12 = 0) & ssList(v11) = v12) | ( ~ (v12 = 0) & ssList(v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (gt(v11, v10) = v9) | ~ (gt(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (geq(v11, v10) = v9) | ~ (geq(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (lt(v11, v10) = v9) | ~ (lt(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (leq(v11, v10) = v9) | ~ (leq(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (segmentP(v11, v10) = v9) | ~ (segmentP(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (rearsegP(v11, v10) = v9) | ~ (rearsegP(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (frontsegP(v11, v10) = v9) | ~ (frontsegP(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (memberP(v11, v10) = v9) | ~ (memberP(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (cons(v11, v10) = v9) | ~ (cons(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (app(v11, v10) = v9) | ~ (app(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (neq(v11, v10) = v9) | ~ (neq(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = nil | ~ (tl(v8) = v9) | ~ (app(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (( ~ (v12 = 0) & ssList(v8) = v12) | (tl(v13) = v14 & ssList(v10) = v12 & app(v8, v10) = v13 & ( ~ (v12 = 0) | v14 = v11)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = nil | ~ (hd(v8) = v9) | ~ (app(v8, v10) = v11) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v8) = v12) | (hd(v11) = v13 & ssList(v10) = v12 & ( ~ (v12 = 0) | v13 = v9)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (hd(v9) = v10) | ~ (lt(v8, v10) = v11) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (strictorderedP(v13) = v14 & strictorderedP(v9) = v15 & ssList(v9) = v12 & cons(v8, v9) = v13 & ( ~ (v12 = 0) | (( ~ (v14 = 0) | v9 = nil | (v15 = 0 & v11 = 0)) & (v14 = 0 | ( ~ (v9 = nil) & ( ~ (v15 = 0) | ~ (v11 = 0)))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (hd(v9) = v10) | ~ (leq(v8, v10) = v11) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (totalorderedP(v13) = v14 & totalorderedP(v9) = v15 & ssList(v9) = v12 & cons(v8, v9) = v13 & ( ~ (v12 = 0) | (( ~ (v14 = 0) | v9 = nil | (v15 = 0 & v11 = 0)) & (v14 = 0 | ( ~ (v9 = nil) & ( ~ (v15 = 0) | ~ (v11 = 0)))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (strictorderP(v8) = 0) | ~ (lt(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v8) = v12) | (lt(v10, v9) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v13 = 0 | v11 = 0 | ~ (ssList(v14) = 0) | ~ (cons(v10, v18) = v19) | ~ (cons(v9, v15) = v16) | ~ (app(v17, v19) = v8) | ~ (app(v14, v16) = v17) | ? [v20] : (( ~ (v20 = 0) & ssList(v18) = v20) | ( ~ (v20 = 0) & ssList(v15) = v20))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (totalorderP(v8) = 0) | ~ (leq(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v8) = v12) | (leq(v10, v9) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v13 = 0 | v11 = 0 | ~ (ssList(v14) = 0) | ~ (cons(v10, v18) = v19) | ~ (cons(v9, v15) = v16) | ~ (app(v17, v19) = v8) | ~ (app(v14, v16) = v17) | ? [v20] : (( ~ (v20 = 0) & ssList(v18) = v20) | ( ~ (v20 = 0) & ssList(v15) = v20))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (cyclefreeP(v8) = 0) | ~ (leq(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v8) = v12) | (leq(v10, v9) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (v13 = 0) | ~ (v11 = 0) | ~ (ssList(v14) = 0) | ~ (cons(v10, v18) = v19) | ~ (cons(v9, v15) = v16) | ~ (app(v17, v19) = v8) | ~ (app(v14, v16) = v17) | ? [v20] : (( ~ (v20 = 0) & ssList(v18) = v20) | ( ~ (v20 = 0) & ssList(v15) = v20))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, nil) = v10) | ~ (app(v10, v8) = v11) | ? [v12] : ? [v13] : (cons(v9, v8) = v13 & ssItem(v9) = v12 & ( ~ (v12 = 0) | v13 = v11))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = v8 | ~ (lt(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (leq(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = v8 | ~ (ssList(v8) = 0) | ~ (neq(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & ssList(v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = v8 | ~ (neq(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ( ~ (v11 = 0) & ssItem(v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (tl(v10) = v9) | ~ (tl(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (hd(v10) = v9) | ~ (hd(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (equalelemsP(v10) = v9) | ~ (equalelemsP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (duplicatefreeP(v10) = v9) | ~ (duplicatefreeP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (strictorderedP(v10) = v9) | ~ (strictorderedP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (totalorderedP(v10) = v9) | ~ (totalorderedP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (strictorderP(v10) = v9) | ~ (strictorderP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (totalorderP(v10) = v9) | ~ (totalorderP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (cyclefreeP(v10) = v9) | ~ (cyclefreeP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singletonP(v10) = v9) | ~ (singletonP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (ssList(v10) = v9) | ~ (ssList(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (ssItem(v10) = v9) | ~ (ssItem(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (singletonP(v8) = v9) | ~ (cons(v10, nil) = v8) | ? [v11] : (( ~ (v11 = 0) & ssList(v8) = v11) | ( ~ (v11 = 0) & ssItem(v10) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (gt(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (lt(v9, v8) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | (( ~ (v12 = 0) | v10 = 0) & ( ~ (v10 = 0) | v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (geq(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (leq(v9, v8) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | (( ~ (v12 = 0) | v10 = 0) & ( ~ (v10 = 0) | v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (lt(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (leq(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | (( ~ (v12 = 0) | v10 = 0 | v9 = v8) & ( ~ (v10 = 0) | (v12 = 0 & ~ (v9 = v8))))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, v8) = v10) | ? [v11] : ? [v12] : (tl(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = v8))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, v8) = v10) | ? [v11] : ? [v12] : (hd(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = v9))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, v8) = v10) | ? [v11] : ? [v12] : (ssList(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ssList(v8) = 0) | ~ (app(v8, v9) = v10) | ? [v11] : ? [v12] : (ssList(v10) = v12 & ssList(v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (geq(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v10] : ? [v11] : (geq(v9, v8) = v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (leq(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v10] : ? [v11] : (leq(v9, v8) = v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (segmentP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : (segmentP(v9, v8) = v11 & ssList(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (rearsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : (rearsegP(v9, v8) = v11 & ssList(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (frontsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : (frontsegP(v9, v8) = v11 & ssList(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (app(v8, nil) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (app(nil, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = nil | ~ (ssList(v8) = 0) | ~ (app(v8, v9) = nil) | ? [v10] : ( ~ (v10 = 0) & ssList(v9) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (geq(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssItem(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (equalelemsP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v20 = v8 & v17 = 0 & v15 = 0 & v13 = 0 & v11 = 0 & ~ (v12 = v10) & ssList(v16) = 0 & ssList(v14) = 0 & cons(v12, v16) = v18 & cons(v10, v18) = v19 & app(v14, v19) = v8 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (duplicatefreeP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v23 = v8 & v21 = 0 & v17 = 0 & v15 = 0 & v13 = 0 & v12 = v10 & v11 = 0 & ssList(v20) = 0 & ssList(v16) = 0 & ssList(v14) = 0 & cons(v10, v20) = v22 & cons(v10, v16) = v18 & app(v19, v22) = v8 & app(v14, v18) = v19 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (strictorderedP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v24 = v8 & v22 = 0 & v18 = 0 & v16 = 0 & v13 = 0 & v11 = 0 & ~ (v14 = 0) & lt(v10, v12) = v14 & ssList(v21) = 0 & ssList(v17) = 0 & ssList(v15) = 0 & cons(v12, v21) = v23 & cons(v10, v17) = v19 & app(v20, v23) = v8 & app(v15, v19) = v20 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (totalorderedP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v24 = v8 & v22 = 0 & v18 = 0 & v16 = 0 & v13 = 0 & v11 = 0 & ~ (v14 = 0) & leq(v10, v12) = v14 & ssList(v21) = 0 & ssList(v17) = 0 & ssList(v15) = 0 & cons(v12, v21) = v23 & cons(v10, v17) = v19 & app(v20, v23) = v8 & app(v15, v19) = v20 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (strictorderP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = v8 & v23 = 0 & v19 = 0 & v17 = 0 & v13 = 0 & v11 = 0 & ~ (v15 = 0) & ~ (v14 = 0) & lt(v12, v10) = v15 & lt(v10, v12) = v14 & ssList(v22) = 0 & ssList(v18) = 0 & ssList(v16) = 0 & cons(v12, v22) = v24 & cons(v10, v18) = v20 & app(v21, v24) = v8 & app(v16, v20) = v21 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (totalorderP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = v8 & v23 = 0 & v19 = 0 & v17 = 0 & v13 = 0 & v11 = 0 & ~ (v15 = 0) & ~ (v14 = 0) & leq(v12, v10) = v15 & leq(v10, v12) = v14 & ssList(v22) = 0 & ssList(v18) = 0 & ssList(v16) = 0 & cons(v12, v22) = v24 & cons(v10, v18) = v20 & app(v21, v24) = v8 & app(v16, v20) = v21 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (cyclefreeP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = v8 & v23 = 0 & v19 = 0 & v17 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & v11 = 0 & leq(v12, v10) = 0 & leq(v10, v12) = 0 & ssList(v22) = 0 & ssList(v18) = 0 & ssList(v16) = 0 & cons(v12, v22) = v24 & cons(v10, v18) = v20 & app(v21, v24) = v8 & app(v16, v20) = v21 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (leq(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssItem(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (segmentP(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (segmentP(v8, nil) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (rearsegP(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (rearsegP(v8, nil) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (frontsegP(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (frontsegP(v8, nil) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v8 = nil | ~ (tl(v8) = v9) | ? [v10] : ? [v11] : (ssList(v9) = v11 & ssList(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : (v8 = nil | ~ (tl(v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = v9 & ssList(v9) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v8 = nil | ~ (hd(v8) = v9) | ? [v10] : ? [v11] : (ssList(v8) = v10 & ssItem(v9) = v11 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : (v8 = nil | ~ (hd(v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = v9 & ssItem(v9) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v8 = nil | ~ (ssList(v8) = 0) | ~ (app(v8, v9) = nil) | ? [v10] : ( ~ (v10 = 0) & ssList(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (gt(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v10] : ? [v11] : (gt(v9, v8) = v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : ( ~ (tl(v8) = v9) | ? [v10] : ? [v11] : (hd(v8) = v11 & ssList(v8) = v10 & ( ~ (v10 = 0) | ! [v12] : (v12 = v8 | v12 = nil | v8 = nil | ~ (tl(v12) = v9) | ? [v13] : ? [v14] : (hd(v12) = v14 & ssList(v12) = v13 & ( ~ (v14 = v11) | ~ (v13 = 0))))))) & ! [v8] : ! [v9] : ( ~ (lt(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v10] : ? [v11] : (lt(v9, v8) = v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : ( ~ (segmentP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v15 = v8 & v14 = 0 & v11 = 0 & ssList(v13) = 0 & ssList(v10) = 0 & app(v12, v13) = v8 & app(v10, v9) = v12) | ( ~ (v10 = 0) & ssList(v9) = v10))) & ! [v8] : ! [v9] : ( ~ (rearsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v8 & v11 = 0 & ssList(v10) = 0 & app(v10, v9) = v8) | ( ~ (v10 = 0) & ssList(v9) = v10))) & ! [v8] : ! [v9] : ( ~ (frontsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v8 & v11 = 0 & ssList(v10) = 0 & app(v9, v10) = v8) | ( ~ (v10 = 0) & ssList(v9) = v10))) & ! [v8] : ! [v9] : ( ~ (memberP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v15 = v8 & v13 = 0 & v11 = 0 & ssList(v12) = 0 & ssList(v10) = 0 & cons(v9, v12) = v14 & app(v10, v14) = v8) | ( ~ (v10 = 0) & ssItem(v9) = v10))) & ! [v8] : ! [v9] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, v8) = v8) | ? [v10] : ( ~ (v10 = 0) & ssItem(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, v8) = nil) | ? [v10] : ( ~ (v10 = 0) & ssItem(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (equalelemsP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (duplicatefreeP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (strictorderedP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (totalorderedP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (strictorderP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (totalorderP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (cyclefreeP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : (v8 = nil | ~ (segmentP(nil, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & ssList(v8) = v9)) & ! [v8] : (v8 = nil | ~ (rearsegP(nil, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & ssList(v8) = v9)) & ! [v8] : (v8 = nil | ~ (frontsegP(nil, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & ssList(v8) = v9)) & ! [v8] : (v8 = nil | ~ (ssList(v8) = 0) | ? [v9] : ? [v10] : (ssList(v9) = 0 & cons(v10, v9) = v8 & ssItem(v10) = 0)) & ! [v8] : (v8 = nil | ~ (app(nil, nil) = v8)) & ! [v8] : (v8 = 0 | ~ (segmentP(nil, nil) = v8)) & ! [v8] : (v8 = 0 | ~ (rearsegP(nil, nil) = v8)) & ! [v8] : (v8 = 0 | ~ (frontsegP(nil, nil) = v8)) & ! [v8] : ( ~ (lt(v8, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & ssItem(v8) = v9)) & ! [v8] : ( ~ (singletonP(v8) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v10 = 0 & cons(v9, nil) = v8 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v8) = v9))) & ! [v8] : ( ~ (memberP(nil, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & ssItem(v8) = v9)) & ! [v8] : ( ~ (ssList(v8) = 0) | ~ (neq(v8, v8) = 0)) & ! [v8] : ( ~ (neq(v8, v8) = 0) | ~ (ssItem(v8) = 0)) & ( ~ (v5 = 0) | v4 = 0))
% 30.28/8.67 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 30.28/8.67 | (1) ~ (all_0_0_0 = all_0_1_1) & ~ (all_0_5_5 = 0) & ~ (all_0_7_7 = 0) & equalelemsP(nil) = 0 & duplicatefreeP(nil) = 0 & strictorderedP(all_0_6_6) = all_0_5_5 & strictorderedP(nil) = 0 & totalorderedP(nil) = 0 & strictorderP(nil) = 0 & totalorderP(nil) = 0 & cyclefreeP(nil) = 0 & segmentP(all_0_4_4, all_0_6_6) = 0 & singletonP(all_0_6_6) = all_0_3_3 & singletonP(nil) = all_0_7_7 & ssList(all_0_4_4) = 0 & ssList(all_0_6_6) = 0 & ssList(nil) = 0 & neq(all_0_4_4, nil) = all_0_2_2 & ssItem(all_0_0_0) = 0 & ssItem(all_0_1_1) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v3 = 0 | ~ (strictorderedP(v0) = 0) | ~ (lt(v1, v2) = v3) | ~ (ssList(v4) = 0) | ~ (cons(v2, v8) = v9) | ~ (cons(v1, v5) = v6) | ~ (app(v7, v9) = v0) | ~ (app(v4, v6) = v7) | ~ (ssItem(v1) = 0) | ? [v10] : (( ~ (v10 = 0) & ssList(v8) = v10) | ( ~ (v10 = 0) & ssList(v5) = v10) | ( ~ (v10 = 0) & ssList(v0) = v10) | ( ~ (v10 = 0) & ssItem(v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v3 = 0 | ~ (totalorderedP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssList(v4) = 0) | ~ (cons(v2, v8) = v9) | ~ (cons(v1, v5) = v6) | ~ (app(v7, v9) = v0) | ~ (app(v4, v6) = v7) | ~ (ssItem(v1) = 0) | ? [v10] : (( ~ (v10 = 0) & ssList(v8) = v10) | ( ~ (v10 = 0) & ssList(v5) = v10) | ( ~ (v10 = 0) & ssList(v0) = v10) | ( ~ (v10 = 0) & ssItem(v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (duplicatefreeP(v0) = 0) | ~ (ssList(v2) = 0) | ~ (cons(v1, v6) = v7) | ~ (cons(v1, v3) = v4) | ~ (app(v5, v7) = v0) | ~ (app(v2, v4) = v5) | ~ (ssItem(v1) = 0) | ? [v8] : (( ~ (v8 = 0) & ssList(v6) = v8) | ( ~ (v8 = 0) & ssList(v3) = v8) | ( ~ (v8 = 0) & ssList(v0) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (segmentP(v5, v1) = v6) | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v3, v4) = v5) | ~ (app(v2, v0) = v3) | ? [v7] : (( ~ (v7 = 0) & ssList(v4) = v7) | ( ~ (v7 = 0) & ssList(v2) = v7) | ( ~ (v7 = 0) & ssList(v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (equalelemsP(v0) = 0) | ~ (ssList(v3) = 0) | ~ (cons(v2, v4) = v5) | ~ (cons(v1, v5) = v6) | ~ (app(v3, v6) = v0) | ~ (ssItem(v2) = 0) | ~ (ssItem(v1) = 0) | ? [v7] : (( ~ (v7 = 0) & ssList(v4) = v7) | ( ~ (v7 = 0) & ssList(v0) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (frontsegP(v3, v5) = v6) | ~ (cons(v1, v4) = v5) | ~ (cons(v0, v2) = v3) | ~ (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ? [v7] : ? [v8] : (( ~ (v7 = 0) & ssList(v2) = v7) | (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 = 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = 0 | ~ (segmentP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v4, v5) = v0) | ~ (app(v3, v1) = v4) | ? [v6] : (( ~ (v6 = 0) & ssList(v5) = v6) | ( ~ (v6 = 0) & ssList(v3) = v6) | ( ~ (v6 = 0) & ssList(v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = 0 | ~ (memberP(v0, v1) = v2) | ~ (ssList(v3) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v1, v4) = v5) | ~ (app(v3, v5) = v0) | ? [v6] : (( ~ (v6 = 0) & ssList(v4) = v6) | ( ~ (v6 = 0) & ssItem(v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (memberP(v4, v0) = v5) | ~ (memberP(v1, v0) = v2) | ~ (app(v1, v3) = v4) | ~ (ssItem(v0) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & ssList(v1) = v6) | (memberP(v3, v0) = v7 & ssList(v3) = v6 & ( ~ (v6 = 0) | (( ~ (v5 = 0) | v7 = 0 | v2 = 0) & (v5 = 0 | ( ~ (v7 = 0) & ~ (v2 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ssList(v0) = 0) | ~ (cons(v3, v1) = v4) | ~ (app(v4, v0) = v5) | ~ (app(v1, v0) = v2) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & ssList(v1) = v6) | (cons(v3, v2) = v7 & ssItem(v3) = v6 & ( ~ (v6 = 0) | v7 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssItem(v4) = v5) | ( ~ (v5 = 0) & ssItem(v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (rearsegP(v3, v1) = v4) | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssList(v2) = v5) | ( ~ (v5 = 0) & ssList(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (frontsegP(v3, v1) = v4) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v0, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & ssList(v2) = v5) | ( ~ (v5 = 0) & ssList(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssItem(v4) = v5) | ( ~ (v5 = 0) & ssItem(v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (memberP(v3, v0) = v4) | ~ (cons(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ? [v5] : ? [v6] : (memberP(v2, v0) = v6 & ssList(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | v6 = 0 | v1 = v0) & (v4 = 0 | ( ~ (v6 = 0) & ~ (v1 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ssList(v0) = 0) | ~ (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & ssList(v1) = v5) | (ssList(v3) = v5 & app(v1, v3) = v6 & app(v0, v6) = v7 & ( ~ (v5 = 0) | v7 = v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & ssList(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ssList(v0) = 0) | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (gt(v0, v2) = v3) | ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (gt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (geq(v0, v2) = v3) | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (geq(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lt(v0, v2) = v3) | ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (lt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lt(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (lt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (leq(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (segmentP(v0, v2) = v3) | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (segmentP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (rearsegP(v0, v2) = v3) | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (rearsegP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (frontsegP(v0, v2) = v3) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (frontsegP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (rearsegP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v3, v1) = v0) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (frontsegP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v0) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & ssList(v0) = v4) | (tl(v5) = v6 & ssList(v2) = v4 & app(v0, v2) = v5 & ( ~ (v4 = 0) | v6 = v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (hd(v3) = v5 & ssList(v2) = v4 & ( ~ (v4 = 0) | v5 = v1)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (hd(v1) = v2) | ~ (lt(v0, v2) = v3) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (strictorderedP(v5) = v6 & strictorderedP(v1) = v7 & ssList(v1) = v4 & cons(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v1 = nil | (v7 = 0 & v3 = 0)) & (v6 = 0 | ( ~ (v1 = nil) & ( ~ (v7 = 0) | ~ (v3 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (hd(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (totalorderedP(v5) = v6 & totalorderedP(v1) = v7 & ssList(v1) = v4 & cons(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v1 = nil | (v7 = 0 & v3 = 0)) & (v6 = 0 | ( ~ (v1 = nil) & ( ~ (v7 = 0) | ~ (v3 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (strictorderP(v0) = 0) | ~ (lt(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (lt(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v5 = 0 | v3 = 0 | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (totalorderP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (leq(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v5 = 0 | v3 = 0 | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cyclefreeP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (leq(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (v5 = 0) | ~ (v3 = 0) | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ? [v4] : ? [v5] : (cons(v1, v0) = v5 & ssItem(v1) = v4 & ( ~ (v4 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (lt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v0, v1) = v4 & ssItem(v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (ssList(v0) = 0) | ~ (neq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & ssList(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (neq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & ssItem(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | ~ (equalelemsP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | ~ (duplicatefreeP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderP(v2) = v1) | ~ (strictorderP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ (totalorderP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ (cyclefreeP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (singletonP(v0) = v1) | ~ (cons(v2, nil) = v0) | ? [v3] : (( ~ (v3 = 0) & ssList(v0) = v3) | ( ~ (v3 = 0) & ssItem(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (gt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (lt(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (geq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (lt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v0, v1) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0 | v1 = v0) & ( ~ (v2 = 0) | (v4 = 0 & ~ (v1 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (tl(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (app(v0, v1) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (geq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (leq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (frontsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (equalelemsP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v0 & v9 = 0 & v7 = 0 & v5 = 0 & v3 = 0 & ~ (v4 = v2) & ssList(v8) = 0 & ssList(v6) = 0 & cons(v4, v8) = v10 & cons(v2, v10) = v11 & app(v6, v11) = v0 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (duplicatefreeP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v15 = v0 & v13 = 0 & v9 = 0 & v7 = 0 & v5 = 0 & v4 = v2 & v3 = 0 & ssList(v12) = 0 & ssList(v8) = 0 & ssList(v6) = 0 & cons(v2, v12) = v14 & cons(v2, v8) = v10 & app(v11, v14) = v0 & app(v6, v10) = v11 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (strictorderedP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v0 & v14 = 0 & v10 = 0 & v8 = 0 & v5 = 0 & v3 = 0 & ~ (v6 = 0) & lt(v2, v4) = v6 & ssList(v13) = 0 & ssList(v9) = 0 & ssList(v7) = 0 & cons(v4, v13) = v15 & cons(v2, v9) = v11 & app(v12, v15) = v0 & app(v7, v11) = v12 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (totalorderedP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v0 & v14 = 0 & v10 = 0 & v8 = 0 & v5 = 0 & v3 = 0 & ~ (v6 = 0) & leq(v2, v4) = v6 & ssList(v13) = 0 & ssList(v9) = 0 & ssList(v7) = 0 & cons(v4, v13) = v15 & cons(v2, v9) = v11 & app(v12, v15) = v0 & app(v7, v11) = v12 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (strictorderP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v5 = 0 & v3 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & lt(v4, v2) = v7 & lt(v2, v4) = v6 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (totalorderP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v5 = 0 & v3 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & leq(v4, v2) = v7 & leq(v2, v4) = v6 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cyclefreeP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & v3 = 0 & leq(v4, v2) = 0 & leq(v2, v4) = 0 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (ssList(v1) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssList(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : (ssList(v0) = v2 & ssItem(v1) = v3 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssItem(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v0 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (gt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (hd(v0) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : (v4 = v0 | v4 = nil | v0 = nil | ~ (tl(v4) = v1) | ? [v5] : ? [v6] : (hd(v4) = v6 & ssList(v4) = v5 & ( ~ (v6 = v3) | ~ (v5 = 0))))))) & ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (lt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v0 & v6 = 0 & v3 = 0 & ssList(v5) = 0 & ssList(v2) = 0 & app(v4, v5) = v0 & app(v2, v1) = v4) | ( ~ (v2 = 0) & ssList(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & v3 = 0 & ssList(v2) = 0 & app(v2, v1) = v0) | ( ~ (v2 = 0) & ssList(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & v3 = 0 & ssList(v2) = 0 & app(v1, v2) = v0) | ( ~ (v2 = 0) & ssList(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (memberP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v0 & v5 = 0 & v3 = 0 & ssList(v4) = 0 & ssList(v2) = 0 & cons(v1, v4) = v6 & app(v2, v6) = v0) | ( ~ (v2 = 0) & ssItem(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v0) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = nil) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : (v0 = nil | ~ (segmentP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1)) & ! [v0] : (v0 = nil | ~ (rearsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1)) & ! [v0] : (v0 = nil | ~ (frontsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1)) & ! [v0] : (v0 = nil | ~ (ssList(v0) = 0) | ? [v1] : ? [v2] : (ssList(v1) = 0 & cons(v2, v1) = v0 & ssItem(v2) = 0)) & ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0)) & ! [v0] : (v0 = 0 | ~ (segmentP(nil, nil) = v0)) & ! [v0] : (v0 = 0 | ~ (rearsegP(nil, nil) = v0)) & ! [v0] : (v0 = 0 | ~ (frontsegP(nil, nil) = v0)) & ! [v0] : ( ~ (lt(v0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1)) & ! [v0] : ( ~ (singletonP(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v0 & v2 = 0 & cons(v1, nil) = v0 & ssItem(v1) = 0) | ( ~ (v1 = 0) & ssList(v0) = v1))) & ! [v0] : ( ~ (memberP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1)) & ! [v0] : ( ~ (ssList(v0) = 0) | ~ (neq(v0, v0) = 0)) & ! [v0] : ( ~ (neq(v0, v0) = 0) | ~ (ssItem(v0) = 0)) & ( ~ (all_0_2_2 = 0) | all_0_3_3 = 0)
% 30.82/8.71 |
% 30.82/8.71 | Applying alpha-rule on (1) yields:
% 30.82/8.71 | (2) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 30.82/8.71 | (3) ! [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)))
% 30.82/8.71 | (4) ! [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)))))
% 30.82/8.71 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 30.82/8.71 | (6) ! [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)))))))
% 30.82/8.72 | (7) ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (leq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 30.82/8.72 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0))
% 30.82/8.72 | (9) ! [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)))
% 30.82/8.72 | (10) ! [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)))))
% 30.82/8.72 | (11) ! [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)))))
% 30.82/8.72 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 30.82/8.72 | (13) ! [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))))
% 30.82/8.72 | (14) ! [v0] : ! [v1] : (v1 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 30.82/8.72 | (15) ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0))
% 30.82/8.72 | (16) ssList(nil) = 0
% 30.82/8.72 | (17) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (ssList(v0) = 0) | ~ (neq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & ssList(v1) = v3))
% 30.82/8.72 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0))
% 30.82/8.72 | (19) ! [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)))))
% 30.82/8.72 | (20) ! [v0] : ( ~ (neq(v0, v0) = 0) | ~ (ssItem(v0) = 0))
% 30.82/8.72 | (21) ! [v0] : ( ~ (ssList(v0) = 0) | ~ (neq(v0, v0) = 0))
% 30.82/8.72 | (22) ! [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)))))
% 30.82/8.72 | (23) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v0) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 30.82/8.72 | (24) ~ (all_0_0_0 = all_0_1_1)
% 30.82/8.72 | (25) ! [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)))
% 30.82/8.72 | (26) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 30.82/8.72 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0))
% 30.82/8.72 | (28) ssList(all_0_4_4) = 0
% 30.82/8.72 | (29) ! [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)))))))
% 30.82/8.72 | (30) ~ (all_0_5_5 = 0)
% 30.82/8.72 | (31) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = v0))
% 30.82/8.72 | (32) cyclefreeP(nil) = 0
% 30.82/8.72 | (33) ! [v0] : (v0 = nil | ~ (rearsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 30.82/8.72 | (34) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssItem(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 30.82/8.72 | (35) ! [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))))
% 30.82/8.72 | (36) ! [v0] : ( ~ (memberP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 30.82/8.72 | (37) strictorderP(nil) = 0
% 30.82/8.72 | (38) ! [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)))
% 30.82/8.72 | (39) ! [v0] : (v0 = nil | ~ (ssList(v0) = 0) | ? [v1] : ? [v2] : (ssList(v1) = 0 & cons(v2, v1) = v0 & ssItem(v2) = 0))
% 30.82/8.72 | (40) ! [v0] : ! [v1] : ( ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (gt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 30.82/8.72 | (41) segmentP(all_0_4_4, all_0_6_6) = 0
% 30.82/8.72 | (42) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 30.82/8.72 | (43) ! [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))))))))
% 30.82/8.72 | (44) ! [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)))))
% 30.82/8.73 | (45) ! [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)))
% 30.82/8.73 | (46) ! [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)))
% 30.82/8.73 | (47) ! [v0] : (v0 = 0 | ~ (segmentP(nil, nil) = v0))
% 30.82/8.73 | (48) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = nil) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 30.82/8.73 | (49) ! [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)))))))
% 30.82/8.73 | (50) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) = v0))
% 30.82/8.73 | (51) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0))
% 30.82/8.73 | (52) ! [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))))
% 30.82/8.73 | (53) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 30.82/8.73 | (54) ! [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)))
% 30.82/8.73 | (55) strictorderedP(nil) = 0
% 30.82/8.73 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0))
% 30.82/8.73 | (57) ! [v0] : ! [v1] : (v1 = v0 | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 30.82/8.73 | (58) singletonP(nil) = all_0_7_7
% 30.82/8.73 | (59) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 30.82/8.73 | (60) ! [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)))
% 30.82/8.73 | (61) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 30.82/8.73 | (62) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 30.82/8.73 | (63) ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 30.82/8.73 | (64) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 30.82/8.73 | (65) ! [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))))
% 30.82/8.73 | (66) ! [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)))
% 30.82/8.73 | (67) duplicatefreeP(nil) = 0
% 30.82/8.73 | (68) strictorderedP(all_0_6_6) = all_0_5_5
% 30.82/8.73 | (69) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 30.82/8.73 | (70) ! [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)))
% 30.82/8.73 | (71) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ (cyclefreeP(v2) = v0))
% 30.82/8.73 | (72) ! [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)))
% 30.82/8.73 | (73) ! [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)))
% 30.82/8.73 | (74) ! [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)))
% 30.82/8.73 | (75) ! [v0] : ! [v1] : (v1 = v0 | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (frontsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 30.82/8.73 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 30.82/8.73 | (77) ! [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)))))
% 30.82/8.73 | (78) ! [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)))))))
% 30.82/8.73 | (79) ! [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)))))
% 30.82/8.73 | (80) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0))
% 30.82/8.73 | (81) ! [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)))
% 30.82/8.73 | (82) ! [v0] : ( ~ (singletonP(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v0 & v2 = 0 & cons(v1, nil) = v0 & ssItem(v1) = 0) | ( ~ (v1 = 0) & ssList(v0) = v1)))
% 30.82/8.73 | (83) ! [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)))
% 30.82/8.73 | (84) ! [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)))
% 30.82/8.73 | (85) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssList(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 30.82/8.73 | (86) singletonP(all_0_6_6) = all_0_3_3
% 30.82/8.73 | (87) ! [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)))
% 30.82/8.73 | (88) ssList(all_0_6_6) = 0
% 30.82/8.73 | (89) ~ (all_0_2_2 = 0) | all_0_3_3 = 0
% 30.82/8.73 | (90) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (ssList(v1) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 30.82/8.73 | (91) ! [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)))
% 30.82/8.73 | (92) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & ssList(v0) = v4))
% 30.82/8.73 | (93) ! [v0] : ! [v1] : (v0 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 30.82/8.74 | (94) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (tl(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v0)))
% 30.82/8.74 | (95) ! [v0] : (v0 = 0 | ~ (rearsegP(nil, nil) = v0))
% 30.82/8.74 | (96) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 30.82/8.74 | (97) ! [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)))
% 30.82/8.74 | (98) ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (lt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 30.82/8.74 | (99) ssItem(all_0_0_0) = 0
% 30.82/8.74 | (100) ! [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)))
% 30.82/8.74 | (101) ! [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)))))))
% 30.82/8.74 | (102) equalelemsP(nil) = 0
% 30.82/8.74 | (103) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v1)))
% 30.82/8.74 | (104) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : (ssList(v0) = v2 & ssItem(v1) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 30.82/8.74 | (105) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 30.82/8.74 | (106) ! [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)))))
% 30.82/8.74 | (107) ! [v0] : (v0 = nil | ~ (frontsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 30.82/8.74 | (108) ! [v0] : (v0 = nil | ~ (segmentP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 30.82/8.74 | (109) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 30.82/8.74 | (110) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 30.82/8.74 | (111) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 30.82/8.74 | (112) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (singletonP(v0) = v1) | ~ (cons(v2, nil) = v0) | ? [v3] : (( ~ (v3 = 0) & ssList(v0) = v3) | ( ~ (v3 = 0) & ssItem(v2) = v3)))
% 30.82/8.74 | (113) ! [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)))
% 30.82/8.74 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0))
% 30.82/8.74 | (115) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 30.82/8.74 | (116) ! [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)))
% 30.82/8.74 | (117) ! [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))))))))
% 30.82/8.74 | (118) ! [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)))))))
% 30.82/8.74 | (119) ! [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)))))
% 30.82/8.74 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 30.82/8.74 | (121) ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (geq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 30.82/8.74 | (122) ! [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)))
% 30.82/8.74 | (123) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0))
% 30.82/8.74 | (124) ! [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)))
% 30.82/8.74 | (125) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (neq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & ssItem(v1) = v3))
% 30.82/8.74 | (126) neq(all_0_4_4, nil) = all_0_2_2
% 30.82/8.74 | (127) ! [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))))
% 30.82/8.74 | (128) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 30.82/8.74 | (129) totalorderedP(nil) = 0
% 30.82/8.74 | (130) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | ~ (duplicatefreeP(v2) = v0))
% 30.82/8.74 | (131) ! [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)))
% 30.82/8.74 | (132) ! [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))))))))
% 30.82/8.74 | (133) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderP(v2) = v1) | ~ (strictorderP(v2) = v0))
% 30.82/8.74 | (134) ssItem(all_0_1_1) = 0
% 30.82/8.74 | (135) ! [v0] : ( ~ (lt(v0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 30.82/8.74 | (136) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0))
% 30.82/8.74 | (137) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 30.82/8.74 | (138) ~ (all_0_7_7 = 0)
% 30.82/8.74 | (139) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | ~ (equalelemsP(v2) = v0))
% 30.82/8.74 | (140) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 30.82/8.74 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 30.82/8.74 | (142) ! [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)))
% 30.82/8.74 | (143) ! [v0] : (v0 = 0 | ~ (frontsegP(nil, nil) = v0))
% 30.82/8.74 | (144) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (app(v0, v1) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 30.82/8.74 | (145) totalorderP(nil) = 0
% 30.82/8.74 | (146) ! [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)))
% 30.82/8.74 | (147) ! [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)))))))
% 30.82/8.74 | (148) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ (totalorderP(v2) = v0))
% 30.82/8.74 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0))
% 30.82/8.74 | (150) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 30.82/8.74 |
% 30.82/8.75 | Instantiating formula (31) with nil, 0, all_0_5_5 and discharging atoms strictorderedP(nil) = 0, yields:
% 30.82/8.75 | (151) all_0_5_5 = 0 | ~ (strictorderedP(nil) = all_0_5_5)
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (123) with nil, all_0_7_7, all_0_3_3 and discharging atoms singletonP(nil) = all_0_7_7, yields:
% 30.82/8.75 | (152) all_0_3_3 = all_0_7_7 | ~ (singletonP(nil) = all_0_3_3)
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (113) with all_0_5_5, all_0_6_6 and discharging atoms strictorderedP(all_0_6_6) = all_0_5_5, yields:
% 30.82/8.75 | (153) all_0_5_5 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = all_0_6_6 & v12 = 0 & v8 = 0 & v6 = 0 & v3 = 0 & v1 = 0 & ~ (v4 = 0) & lt(v0, v2) = v4 & ssList(v11) = 0 & ssList(v7) = 0 & ssList(v5) = 0 & cons(v2, v11) = v13 & cons(v0, v7) = v9 & app(v10, v13) = all_0_6_6 & app(v5, v9) = v10 & ssItem(v2) = 0 & ssItem(v0) = 0) | ( ~ (v0 = 0) & ssList(all_0_6_6) = v0))
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (108) with all_0_6_6 yields:
% 30.82/8.75 | (154) all_0_6_6 = nil | ~ (segmentP(nil, all_0_6_6) = 0) | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (82) with all_0_6_6 yields:
% 30.82/8.75 | (155) ~ (singletonP(all_0_6_6) = 0) | ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_6_6 & v1 = 0 & cons(v0, nil) = all_0_6_6 & ssItem(v0) = 0) | ( ~ (v0 = 0) & ssList(all_0_6_6) = v0))
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (57) with all_0_6_6, all_0_4_4 and discharging atoms segmentP(all_0_4_4, all_0_6_6) = 0, ssList(all_0_4_4) = 0, yields:
% 30.82/8.75 | (156) all_0_4_4 = all_0_6_6 | ? [v0] : ? [v1] : (segmentP(all_0_6_6, all_0_4_4) = v1 & ssList(all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (39) with all_0_6_6 and discharging atoms ssList(all_0_6_6) = 0, yields:
% 30.82/8.75 | (157) all_0_6_6 = nil | ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_6_6 & ssItem(v1) = 0)
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (57) with all_0_6_6, nil and discharging atoms ssList(nil) = 0, yields:
% 30.82/8.75 | (158) all_0_6_6 = nil | ~ (segmentP(nil, all_0_6_6) = 0) | ? [v0] : ? [v1] : (segmentP(all_0_6_6, nil) = v1 & ssList(all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (73) with all_0_6_6, nil and discharging atoms ssList(nil) = 0, yields:
% 30.82/8.75 | (159) ~ (segmentP(nil, all_0_6_6) = 0) | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = nil & v4 = 0 & v1 = 0 & ssList(v3) = 0 & ssList(v0) = 0 & app(v2, v3) = nil & app(v0, all_0_6_6) = v2) | ( ~ (v0 = 0) & ssList(all_0_6_6) = v0))
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (17) with all_0_2_2, nil, all_0_4_4 and discharging atoms ssList(all_0_4_4) = 0, neq(all_0_4_4, nil) = all_0_2_2, yields:
% 30.82/8.75 | (160) all_0_2_2 = 0 | all_0_4_4 = nil | ? [v0] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 30.82/8.75 |
% 30.82/8.75 +-Applying beta-rule and splitting (152), into two cases.
% 30.82/8.75 |-Branch one:
% 30.82/8.75 | (161) ~ (singletonP(nil) = all_0_3_3)
% 30.82/8.75 |
% 30.82/8.75 +-Applying beta-rule and splitting (153), into two cases.
% 30.82/8.75 |-Branch one:
% 30.82/8.75 | (162) all_0_5_5 = 0
% 30.82/8.75 |
% 30.82/8.75 | Equations (162) can reduce 30 to:
% 30.82/8.75 | (163) $false
% 30.82/8.75 |
% 30.82/8.75 |-The branch is then unsatisfiable
% 30.82/8.75 |-Branch two:
% 30.82/8.75 | (30) ~ (all_0_5_5 = 0)
% 30.82/8.75 | (165) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = all_0_6_6 & v12 = 0 & v8 = 0 & v6 = 0 & v3 = 0 & v1 = 0 & ~ (v4 = 0) & lt(v0, v2) = v4 & ssList(v11) = 0 & ssList(v7) = 0 & ssList(v5) = 0 & cons(v2, v11) = v13 & cons(v0, v7) = v9 & app(v10, v13) = all_0_6_6 & app(v5, v9) = v10 & ssItem(v2) = 0 & ssItem(v0) = 0) | ( ~ (v0 = 0) & ssList(all_0_6_6) = v0))
% 30.82/8.75 |
% 30.82/8.75 | Using (86) and (161) yields:
% 30.82/8.75 | (166) ~ (all_0_6_6 = nil)
% 30.82/8.75 |
% 30.82/8.75 +-Applying beta-rule and splitting (154), into two cases.
% 30.82/8.75 |-Branch one:
% 30.82/8.75 | (167) ~ (segmentP(nil, all_0_6_6) = 0)
% 30.82/8.75 |
% 30.82/8.75 | Using (41) and (167) yields:
% 30.82/8.75 | (168) ~ (all_0_4_4 = nil)
% 30.82/8.75 |
% 30.82/8.75 +-Applying beta-rule and splitting (160), into two cases.
% 30.82/8.75 |-Branch one:
% 30.82/8.75 | (169) all_0_4_4 = nil
% 30.82/8.75 |
% 30.82/8.75 | Equations (169) can reduce 168 to:
% 30.82/8.75 | (163) $false
% 30.82/8.75 |
% 30.82/8.75 |-The branch is then unsatisfiable
% 30.82/8.75 |-Branch two:
% 30.82/8.75 | (168) ~ (all_0_4_4 = nil)
% 30.82/8.75 | (172) all_0_2_2 = 0 | ? [v0] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 30.82/8.75 |
% 30.82/8.75 +-Applying beta-rule and splitting (172), into two cases.
% 30.82/8.75 |-Branch one:
% 30.82/8.75 | (173) all_0_2_2 = 0
% 30.82/8.75 |
% 30.82/8.75 +-Applying beta-rule and splitting (89), into two cases.
% 30.82/8.75 |-Branch one:
% 30.82/8.75 | (174) ~ (all_0_2_2 = 0)
% 30.82/8.75 |
% 30.82/8.75 | Equations (173) can reduce 174 to:
% 30.82/8.75 | (163) $false
% 30.82/8.75 |
% 30.82/8.75 |-The branch is then unsatisfiable
% 30.82/8.75 |-Branch two:
% 30.82/8.75 | (173) all_0_2_2 = 0
% 30.82/8.75 | (177) all_0_3_3 = 0
% 30.82/8.75 |
% 30.82/8.75 | From (177) and (86) follows:
% 30.82/8.75 | (178) singletonP(all_0_6_6) = 0
% 30.82/8.75 |
% 30.82/8.75 +-Applying beta-rule and splitting (155), into two cases.
% 30.82/8.75 |-Branch one:
% 30.82/8.75 | (179) ~ (singletonP(all_0_6_6) = 0)
% 30.82/8.75 |
% 30.82/8.75 | Using (178) and (179) yields:
% 30.82/8.75 | (180) $false
% 30.82/8.75 |
% 30.82/8.75 |-The branch is then unsatisfiable
% 30.82/8.75 |-Branch two:
% 30.82/8.75 | (178) singletonP(all_0_6_6) = 0
% 30.82/8.75 | (182) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_6_6 & v1 = 0 & cons(v0, nil) = all_0_6_6 & ssItem(v0) = 0) | ( ~ (v0 = 0) & ssList(all_0_6_6) = v0))
% 30.82/8.75 |
% 30.82/8.75 | Instantiating (182) with all_61_0_33, all_61_1_34, all_61_2_35 yields:
% 30.82/8.75 | (183) (all_61_0_33 = all_0_6_6 & all_61_1_34 = 0 & cons(all_61_2_35, nil) = all_0_6_6 & ssItem(all_61_2_35) = 0) | ( ~ (all_61_2_35 = 0) & ssList(all_0_6_6) = all_61_2_35)
% 30.82/8.75 |
% 30.82/8.75 +-Applying beta-rule and splitting (183), into two cases.
% 30.82/8.75 |-Branch one:
% 30.82/8.75 | (184) all_61_0_33 = all_0_6_6 & all_61_1_34 = 0 & cons(all_61_2_35, nil) = all_0_6_6 & ssItem(all_61_2_35) = 0
% 30.82/8.75 |
% 30.82/8.75 | Applying alpha-rule on (184) yields:
% 30.82/8.75 | (185) all_61_0_33 = all_0_6_6
% 30.82/8.75 | (186) all_61_1_34 = 0
% 30.82/8.75 | (187) cons(all_61_2_35, nil) = all_0_6_6
% 30.82/8.75 | (188) ssItem(all_61_2_35) = 0
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (94) with all_0_6_6, all_61_2_35, nil and discharging atoms ssList(nil) = 0, cons(all_61_2_35, nil) = all_0_6_6, yields:
% 30.82/8.75 | (189) ? [v0] : ? [v1] : (tl(all_0_6_6) = v1 & ssItem(all_61_2_35) = v0 & ( ~ (v0 = 0) | v1 = nil))
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (103) with all_0_6_6, all_61_2_35, nil and discharging atoms ssList(nil) = 0, cons(all_61_2_35, nil) = all_0_6_6, yields:
% 30.82/8.75 | (190) ? [v0] : ? [v1] : (hd(all_0_6_6) = v1 & ssItem(all_61_2_35) = v0 & ( ~ (v0 = 0) | v1 = all_61_2_35))
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (61) with all_0_6_6, all_61_2_35 and discharging atoms cons(all_61_2_35, nil) = all_0_6_6, yields:
% 30.82/8.75 | (191) ? [v0] : ? [v1] : (equalelemsP(all_0_6_6) = v1 & ssItem(all_61_2_35) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (62) with all_0_6_6, all_61_2_35 and discharging atoms cons(all_61_2_35, nil) = all_0_6_6, yields:
% 30.82/8.75 | (192) ? [v0] : ? [v1] : (duplicatefreeP(all_0_6_6) = v1 & ssItem(all_61_2_35) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (96) with all_0_6_6, all_61_2_35 and discharging atoms cons(all_61_2_35, nil) = all_0_6_6, yields:
% 30.82/8.75 | (193) ? [v0] : ? [v1] : (strictorderedP(all_0_6_6) = v1 & ssItem(all_61_2_35) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (110) with all_0_6_6, all_61_2_35 and discharging atoms cons(all_61_2_35, nil) = all_0_6_6, yields:
% 30.82/8.75 | (194) ? [v0] : ? [v1] : (totalorderedP(all_0_6_6) = v1 & ssItem(all_61_2_35) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (59) with all_0_6_6, all_61_2_35 and discharging atoms cons(all_61_2_35, nil) = all_0_6_6, yields:
% 30.82/8.75 | (195) ? [v0] : ? [v1] : (strictorderP(all_0_6_6) = v1 & ssItem(all_61_2_35) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (140) with all_0_6_6, all_61_2_35 and discharging atoms cons(all_61_2_35, nil) = all_0_6_6, yields:
% 30.82/8.75 | (196) ? [v0] : ? [v1] : (totalorderP(all_0_6_6) = v1 & ssItem(all_61_2_35) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 30.82/8.75 |
% 30.82/8.75 | Instantiating formula (111) with all_0_6_6, all_61_2_35 and discharging atoms cons(all_61_2_35, nil) = all_0_6_6, yields:
% 30.82/8.75 | (197) ? [v0] : ? [v1] : (cyclefreeP(all_0_6_6) = v1 & ssItem(all_61_2_35) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 30.82/8.75 |
% 30.82/8.75 | Instantiating (197) with all_80_0_46, all_80_1_47 yields:
% 30.82/8.75 | (198) cyclefreeP(all_0_6_6) = all_80_0_46 & ssItem(all_61_2_35) = all_80_1_47 & ( ~ (all_80_1_47 = 0) | all_80_0_46 = 0)
% 30.82/8.75 |
% 30.82/8.75 | Applying alpha-rule on (198) yields:
% 30.82/8.75 | (199) cyclefreeP(all_0_6_6) = all_80_0_46
% 30.82/8.75 | (200) ssItem(all_61_2_35) = all_80_1_47
% 30.82/8.75 | (201) ~ (all_80_1_47 = 0) | all_80_0_46 = 0
% 30.82/8.75 |
% 30.82/8.75 | Instantiating (195) with all_82_0_48, all_82_1_49 yields:
% 30.82/8.75 | (202) strictorderP(all_0_6_6) = all_82_0_48 & ssItem(all_61_2_35) = all_82_1_49 & ( ~ (all_82_1_49 = 0) | all_82_0_48 = 0)
% 30.82/8.75 |
% 30.82/8.75 | Applying alpha-rule on (202) yields:
% 30.82/8.75 | (203) strictorderP(all_0_6_6) = all_82_0_48
% 30.82/8.75 | (204) ssItem(all_61_2_35) = all_82_1_49
% 30.82/8.75 | (205) ~ (all_82_1_49 = 0) | all_82_0_48 = 0
% 30.82/8.75 |
% 30.82/8.75 | Instantiating (193) with all_84_0_50, all_84_1_51 yields:
% 30.82/8.75 | (206) strictorderedP(all_0_6_6) = all_84_0_50 & ssItem(all_61_2_35) = all_84_1_51 & ( ~ (all_84_1_51 = 0) | all_84_0_50 = 0)
% 30.82/8.75 |
% 30.82/8.75 | Applying alpha-rule on (206) yields:
% 30.82/8.75 | (207) strictorderedP(all_0_6_6) = all_84_0_50
% 30.82/8.75 | (208) ssItem(all_61_2_35) = all_84_1_51
% 30.82/8.75 | (209) ~ (all_84_1_51 = 0) | all_84_0_50 = 0
% 30.82/8.75 |
% 30.82/8.75 | Instantiating (192) with all_86_0_52, all_86_1_53 yields:
% 30.82/8.75 | (210) duplicatefreeP(all_0_6_6) = all_86_0_52 & ssItem(all_61_2_35) = all_86_1_53 & ( ~ (all_86_1_53 = 0) | all_86_0_52 = 0)
% 30.82/8.75 |
% 30.82/8.75 | Applying alpha-rule on (210) yields:
% 30.82/8.75 | (211) duplicatefreeP(all_0_6_6) = all_86_0_52
% 30.82/8.75 | (212) ssItem(all_61_2_35) = all_86_1_53
% 30.82/8.75 | (213) ~ (all_86_1_53 = 0) | all_86_0_52 = 0
% 30.82/8.75 |
% 30.82/8.75 | Instantiating (194) with all_88_0_54, all_88_1_55 yields:
% 30.82/8.75 | (214) totalorderedP(all_0_6_6) = all_88_0_54 & ssItem(all_61_2_35) = all_88_1_55 & ( ~ (all_88_1_55 = 0) | all_88_0_54 = 0)
% 30.82/8.75 |
% 30.82/8.75 | Applying alpha-rule on (214) yields:
% 30.82/8.75 | (215) totalorderedP(all_0_6_6) = all_88_0_54
% 30.82/8.76 | (216) ssItem(all_61_2_35) = all_88_1_55
% 30.82/8.76 | (217) ~ (all_88_1_55 = 0) | all_88_0_54 = 0
% 30.82/8.76 |
% 30.82/8.76 | Instantiating (191) with all_90_0_56, all_90_1_57 yields:
% 30.82/8.76 | (218) equalelemsP(all_0_6_6) = all_90_0_56 & ssItem(all_61_2_35) = all_90_1_57 & ( ~ (all_90_1_57 = 0) | all_90_0_56 = 0)
% 30.82/8.76 |
% 30.82/8.76 | Applying alpha-rule on (218) yields:
% 30.82/8.76 | (219) equalelemsP(all_0_6_6) = all_90_0_56
% 30.82/8.76 | (220) ssItem(all_61_2_35) = all_90_1_57
% 30.82/8.76 | (221) ~ (all_90_1_57 = 0) | all_90_0_56 = 0
% 30.82/8.76 |
% 30.82/8.76 | Instantiating (190) with all_92_0_58, all_92_1_59 yields:
% 30.82/8.76 | (222) hd(all_0_6_6) = all_92_0_58 & ssItem(all_61_2_35) = all_92_1_59 & ( ~ (all_92_1_59 = 0) | all_92_0_58 = all_61_2_35)
% 30.82/8.76 |
% 30.82/8.76 | Applying alpha-rule on (222) yields:
% 30.82/8.76 | (223) hd(all_0_6_6) = all_92_0_58
% 30.82/8.76 | (224) ssItem(all_61_2_35) = all_92_1_59
% 30.82/8.76 | (225) ~ (all_92_1_59 = 0) | all_92_0_58 = all_61_2_35
% 30.82/8.76 |
% 30.82/8.76 | Instantiating (196) with all_94_0_60, all_94_1_61 yields:
% 30.82/8.76 | (226) totalorderP(all_0_6_6) = all_94_0_60 & ssItem(all_61_2_35) = all_94_1_61 & ( ~ (all_94_1_61 = 0) | all_94_0_60 = 0)
% 30.82/8.76 |
% 30.82/8.76 | Applying alpha-rule on (226) yields:
% 30.82/8.76 | (227) totalorderP(all_0_6_6) = all_94_0_60
% 30.82/8.76 | (228) ssItem(all_61_2_35) = all_94_1_61
% 30.82/8.76 | (229) ~ (all_94_1_61 = 0) | all_94_0_60 = 0
% 30.82/8.76 |
% 30.82/8.76 | Instantiating (189) with all_105_0_73, all_105_1_74 yields:
% 30.82/8.76 | (230) tl(all_0_6_6) = all_105_0_73 & ssItem(all_61_2_35) = all_105_1_74 & ( ~ (all_105_1_74 = 0) | all_105_0_73 = nil)
% 30.82/8.76 |
% 30.82/8.76 | Applying alpha-rule on (230) yields:
% 30.82/8.76 | (231) tl(all_0_6_6) = all_105_0_73
% 30.82/8.76 | (232) ssItem(all_61_2_35) = all_105_1_74
% 30.82/8.76 | (233) ~ (all_105_1_74 = 0) | all_105_0_73 = nil
% 30.82/8.76 |
% 30.82/8.76 | Instantiating formula (31) with all_0_6_6, all_84_0_50, all_0_5_5 and discharging atoms strictorderedP(all_0_6_6) = all_84_0_50, strictorderedP(all_0_6_6) = all_0_5_5, yields:
% 30.82/8.76 | (234) all_84_0_50 = all_0_5_5
% 30.82/8.76 |
% 30.82/8.76 | Instantiating formula (5) with all_61_2_35, all_94_1_61, all_105_1_74 and discharging atoms ssItem(all_61_2_35) = all_105_1_74, ssItem(all_61_2_35) = all_94_1_61, yields:
% 30.82/8.76 | (235) all_105_1_74 = all_94_1_61
% 30.82/8.76 |
% 30.82/8.76 | Instantiating formula (5) with all_61_2_35, all_92_1_59, all_94_1_61 and discharging atoms ssItem(all_61_2_35) = all_94_1_61, ssItem(all_61_2_35) = all_92_1_59, yields:
% 30.82/8.76 | (236) all_94_1_61 = all_92_1_59
% 30.82/8.76 |
% 30.82/8.76 | Instantiating formula (5) with all_61_2_35, all_90_1_57, all_94_1_61 and discharging atoms ssItem(all_61_2_35) = all_94_1_61, ssItem(all_61_2_35) = all_90_1_57, yields:
% 30.82/8.76 | (237) all_94_1_61 = all_90_1_57
% 30.82/8.76 |
% 30.82/8.76 | Instantiating formula (5) with all_61_2_35, all_88_1_55, all_92_1_59 and discharging atoms ssItem(all_61_2_35) = all_92_1_59, ssItem(all_61_2_35) = all_88_1_55, yields:
% 30.82/8.76 | (238) all_92_1_59 = all_88_1_55
% 30.82/8.76 |
% 30.82/8.76 | Instantiating formula (5) with all_61_2_35, all_86_1_53, all_105_1_74 and discharging atoms ssItem(all_61_2_35) = all_105_1_74, ssItem(all_61_2_35) = all_86_1_53, yields:
% 30.82/8.76 | (239) all_105_1_74 = all_86_1_53
% 30.82/8.76 |
% 30.82/8.76 | Instantiating formula (5) with all_61_2_35, all_84_1_51, 0 and discharging atoms ssItem(all_61_2_35) = all_84_1_51, ssItem(all_61_2_35) = 0, yields:
% 30.82/8.76 | (240) all_84_1_51 = 0
% 30.82/8.76 |
% 30.82/8.76 | Instantiating formula (5) with all_61_2_35, all_84_1_51, all_92_1_59 and discharging atoms ssItem(all_61_2_35) = all_92_1_59, ssItem(all_61_2_35) = all_84_1_51, yields:
% 30.82/8.76 | (241) all_92_1_59 = all_84_1_51
% 30.82/8.76 |
% 30.82/8.76 | Instantiating formula (5) with all_61_2_35, all_82_1_49, all_92_1_59 and discharging atoms ssItem(all_61_2_35) = all_92_1_59, ssItem(all_61_2_35) = all_82_1_49, yields:
% 30.82/8.76 | (242) all_92_1_59 = all_82_1_49
% 30.82/8.76 |
% 30.82/8.76 | Instantiating formula (5) with all_61_2_35, all_80_1_47, all_84_1_51 and discharging atoms ssItem(all_61_2_35) = all_84_1_51, ssItem(all_61_2_35) = all_80_1_47, yields:
% 30.82/8.76 | (243) all_84_1_51 = all_80_1_47
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (235,239) yields a new equation:
% 30.82/8.76 | (244) all_94_1_61 = all_86_1_53
% 30.82/8.76 |
% 30.82/8.76 | Simplifying 244 yields:
% 30.82/8.76 | (245) all_94_1_61 = all_86_1_53
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (236,237) yields a new equation:
% 30.82/8.76 | (246) all_92_1_59 = all_90_1_57
% 30.82/8.76 |
% 30.82/8.76 | Simplifying 246 yields:
% 30.82/8.76 | (247) all_92_1_59 = all_90_1_57
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (245,237) yields a new equation:
% 30.82/8.76 | (248) all_90_1_57 = all_86_1_53
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (241,238) yields a new equation:
% 30.82/8.76 | (249) all_88_1_55 = all_84_1_51
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (242,238) yields a new equation:
% 30.82/8.76 | (250) all_88_1_55 = all_82_1_49
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (247,238) yields a new equation:
% 30.82/8.76 | (251) all_90_1_57 = all_88_1_55
% 30.82/8.76 |
% 30.82/8.76 | Simplifying 251 yields:
% 30.82/8.76 | (252) all_90_1_57 = all_88_1_55
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (252,248) yields a new equation:
% 30.82/8.76 | (253) all_88_1_55 = all_86_1_53
% 30.82/8.76 |
% 30.82/8.76 | Simplifying 253 yields:
% 30.82/8.76 | (254) all_88_1_55 = all_86_1_53
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (250,254) yields a new equation:
% 30.82/8.76 | (255) all_86_1_53 = all_82_1_49
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (249,254) yields a new equation:
% 30.82/8.76 | (256) all_86_1_53 = all_84_1_51
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (256,255) yields a new equation:
% 30.82/8.76 | (257) all_84_1_51 = all_82_1_49
% 30.82/8.76 |
% 30.82/8.76 | Simplifying 257 yields:
% 30.82/8.76 | (258) all_84_1_51 = all_82_1_49
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (240,258) yields a new equation:
% 30.82/8.76 | (259) all_82_1_49 = 0
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (243,258) yields a new equation:
% 30.82/8.76 | (260) all_82_1_49 = all_80_1_47
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (259,260) yields a new equation:
% 30.82/8.76 | (261) all_80_1_47 = 0
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (261,260) yields a new equation:
% 30.82/8.76 | (259) all_82_1_49 = 0
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (259,258) yields a new equation:
% 30.82/8.76 | (240) all_84_1_51 = 0
% 30.82/8.76 |
% 30.82/8.76 +-Applying beta-rule and splitting (209), into two cases.
% 30.82/8.76 |-Branch one:
% 30.82/8.76 | (264) ~ (all_84_1_51 = 0)
% 30.82/8.76 |
% 30.82/8.76 | Equations (240) can reduce 264 to:
% 30.82/8.76 | (163) $false
% 30.82/8.76 |
% 30.82/8.76 |-The branch is then unsatisfiable
% 30.82/8.76 |-Branch two:
% 30.82/8.76 | (240) all_84_1_51 = 0
% 30.82/8.76 | (267) all_84_0_50 = 0
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (234,267) yields a new equation:
% 30.82/8.76 | (268) all_0_5_5 = 0
% 30.82/8.76 |
% 30.82/8.76 | Simplifying 268 yields:
% 30.82/8.76 | (162) all_0_5_5 = 0
% 30.82/8.76 |
% 30.82/8.76 | Equations (162) can reduce 30 to:
% 30.82/8.76 | (163) $false
% 30.82/8.76 |
% 30.82/8.76 |-The branch is then unsatisfiable
% 30.82/8.76 |-Branch two:
% 30.82/8.76 | (271) ~ (all_61_2_35 = 0) & ssList(all_0_6_6) = all_61_2_35
% 30.82/8.76 |
% 30.82/8.76 | Applying alpha-rule on (271) yields:
% 30.82/8.76 | (272) ~ (all_61_2_35 = 0)
% 30.82/8.76 | (273) ssList(all_0_6_6) = all_61_2_35
% 30.82/8.76 |
% 30.82/8.76 | Instantiating formula (2) with all_0_6_6, all_61_2_35, 0 and discharging atoms ssList(all_0_6_6) = all_61_2_35, ssList(all_0_6_6) = 0, yields:
% 30.82/8.76 | (274) all_61_2_35 = 0
% 30.82/8.76 |
% 30.82/8.76 | Equations (274) can reduce 272 to:
% 30.82/8.76 | (163) $false
% 30.82/8.76 |
% 30.82/8.76 |-The branch is then unsatisfiable
% 30.82/8.76 |-Branch two:
% 30.82/8.76 | (174) ~ (all_0_2_2 = 0)
% 30.82/8.76 | (277) ? [v0] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 30.82/8.76 |
% 30.82/8.76 | Instantiating (277) with all_48_0_90 yields:
% 30.82/8.76 | (278) ~ (all_48_0_90 = 0) & ssList(nil) = all_48_0_90
% 30.82/8.76 |
% 30.82/8.76 | Applying alpha-rule on (278) yields:
% 30.82/8.76 | (279) ~ (all_48_0_90 = 0)
% 30.82/8.76 | (280) ssList(nil) = all_48_0_90
% 30.82/8.76 |
% 30.82/8.76 | Instantiating formula (2) with nil, all_48_0_90, 0 and discharging atoms ssList(nil) = all_48_0_90, ssList(nil) = 0, yields:
% 30.82/8.76 | (281) all_48_0_90 = 0
% 30.82/8.76 |
% 30.82/8.76 | Equations (281) can reduce 279 to:
% 30.82/8.76 | (163) $false
% 30.82/8.76 |
% 30.82/8.76 |-The branch is then unsatisfiable
% 30.82/8.76 |-Branch two:
% 30.82/8.76 | (283) segmentP(nil, all_0_6_6) = 0
% 30.82/8.76 | (284) all_0_6_6 = nil | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 30.82/8.76 |
% 30.82/8.76 +-Applying beta-rule and splitting (157), into two cases.
% 30.82/8.76 |-Branch one:
% 30.82/8.76 | (285) all_0_6_6 = nil
% 30.82/8.76 |
% 30.82/8.76 | Equations (285) can reduce 166 to:
% 30.82/8.76 | (163) $false
% 30.82/8.76 |
% 30.82/8.76 |-The branch is then unsatisfiable
% 30.82/8.76 |-Branch two:
% 30.82/8.76 | (166) ~ (all_0_6_6 = nil)
% 30.82/8.76 | (288) ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_6_6 & ssItem(v1) = 0)
% 30.82/8.76 |
% 30.82/8.76 +-Applying beta-rule and splitting (284), into two cases.
% 30.82/8.76 |-Branch one:
% 30.82/8.76 | (285) all_0_6_6 = nil
% 30.82/8.76 |
% 30.82/8.76 | Equations (285) can reduce 166 to:
% 30.82/8.76 | (163) $false
% 30.82/8.76 |
% 30.82/8.76 |-The branch is then unsatisfiable
% 30.82/8.76 |-Branch two:
% 30.82/8.76 | (166) ~ (all_0_6_6 = nil)
% 30.82/8.76 | (292) ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 30.82/8.76 |
% 30.82/8.76 | Instantiating (292) with all_40_0_95 yields:
% 30.82/8.76 | (293) ~ (all_40_0_95 = 0) & ssList(all_0_6_6) = all_40_0_95
% 30.82/8.76 |
% 30.82/8.76 | Applying alpha-rule on (293) yields:
% 30.82/8.76 | (294) ~ (all_40_0_95 = 0)
% 30.82/8.76 | (295) ssList(all_0_6_6) = all_40_0_95
% 30.82/8.76 |
% 30.82/8.76 +-Applying beta-rule and splitting (159), into two cases.
% 30.82/8.76 |-Branch one:
% 30.82/8.76 | (167) ~ (segmentP(nil, all_0_6_6) = 0)
% 30.82/8.76 |
% 30.82/8.76 | Using (283) and (167) yields:
% 30.82/8.76 | (180) $false
% 30.82/8.76 |
% 30.82/8.76 |-The branch is then unsatisfiable
% 30.82/8.76 |-Branch two:
% 30.82/8.76 | (283) segmentP(nil, all_0_6_6) = 0
% 30.82/8.76 | (299) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = nil & v4 = 0 & v1 = 0 & ssList(v3) = 0 & ssList(v0) = 0 & app(v2, v3) = nil & app(v0, all_0_6_6) = v2) | ( ~ (v0 = 0) & ssList(all_0_6_6) = v0))
% 30.82/8.76 |
% 30.82/8.76 +-Applying beta-rule and splitting (158), into two cases.
% 30.82/8.76 |-Branch one:
% 30.82/8.76 | (167) ~ (segmentP(nil, all_0_6_6) = 0)
% 30.82/8.76 |
% 30.82/8.76 | Using (283) and (167) yields:
% 30.82/8.76 | (180) $false
% 30.82/8.76 |
% 30.82/8.76 |-The branch is then unsatisfiable
% 30.82/8.76 |-Branch two:
% 30.82/8.76 | (283) segmentP(nil, all_0_6_6) = 0
% 30.82/8.76 | (303) all_0_6_6 = nil | ? [v0] : ? [v1] : (segmentP(all_0_6_6, nil) = v1 & ssList(all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 30.82/8.76 |
% 30.82/8.76 +-Applying beta-rule and splitting (303), into two cases.
% 30.82/8.76 |-Branch one:
% 30.82/8.76 | (285) all_0_6_6 = nil
% 30.82/8.76 |
% 30.82/8.76 | Equations (285) can reduce 166 to:
% 30.82/8.76 | (163) $false
% 30.82/8.76 |
% 30.82/8.76 |-The branch is then unsatisfiable
% 30.82/8.76 |-Branch two:
% 30.82/8.76 | (166) ~ (all_0_6_6 = nil)
% 30.82/8.76 | (307) ? [v0] : ? [v1] : (segmentP(all_0_6_6, nil) = v1 & ssList(all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 30.82/8.76 |
% 30.82/8.76 | Instantiating (307) with all_54_0_102, all_54_1_103 yields:
% 30.82/8.76 | (308) segmentP(all_0_6_6, nil) = all_54_0_102 & ssList(all_0_6_6) = all_54_1_103 & ( ~ (all_54_0_102 = 0) | ~ (all_54_1_103 = 0))
% 30.82/8.76 |
% 30.82/8.76 | Applying alpha-rule on (308) yields:
% 30.82/8.76 | (309) segmentP(all_0_6_6, nil) = all_54_0_102
% 30.82/8.76 | (310) ssList(all_0_6_6) = all_54_1_103
% 30.82/8.76 | (311) ~ (all_54_0_102 = 0) | ~ (all_54_1_103 = 0)
% 30.82/8.76 |
% 30.82/8.76 | Instantiating formula (2) with all_0_6_6, all_54_1_103, 0 and discharging atoms ssList(all_0_6_6) = all_54_1_103, ssList(all_0_6_6) = 0, yields:
% 30.82/8.76 | (312) all_54_1_103 = 0
% 30.82/8.76 |
% 30.82/8.76 | Instantiating formula (2) with all_0_6_6, all_40_0_95, all_54_1_103 and discharging atoms ssList(all_0_6_6) = all_54_1_103, ssList(all_0_6_6) = all_40_0_95, yields:
% 30.82/8.76 | (313) all_54_1_103 = all_40_0_95
% 30.82/8.76 |
% 30.82/8.76 | Combining equations (312,313) yields a new equation:
% 30.82/8.76 | (314) all_40_0_95 = 0
% 30.82/8.76 |
% 30.82/8.76 | Equations (314) can reduce 294 to:
% 30.82/8.76 | (163) $false
% 30.82/8.76 |
% 30.82/8.76 |-The branch is then unsatisfiable
% 30.82/8.76 |-Branch two:
% 30.82/8.76 | (316) singletonP(nil) = all_0_3_3
% 30.82/8.77 | (317) all_0_3_3 = all_0_7_7
% 30.82/8.77 |
% 30.82/8.77 +-Applying beta-rule and splitting (153), into two cases.
% 30.82/8.77 |-Branch one:
% 30.82/8.77 | (162) all_0_5_5 = 0
% 30.82/8.77 |
% 30.82/8.77 | Equations (162) can reduce 30 to:
% 30.82/8.77 | (163) $false
% 30.82/8.77 |
% 30.82/8.77 |-The branch is then unsatisfiable
% 30.82/8.77 |-Branch two:
% 30.82/8.77 | (30) ~ (all_0_5_5 = 0)
% 30.82/8.77 | (165) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = all_0_6_6 & v12 = 0 & v8 = 0 & v6 = 0 & v3 = 0 & v1 = 0 & ~ (v4 = 0) & lt(v0, v2) = v4 & ssList(v11) = 0 & ssList(v7) = 0 & ssList(v5) = 0 & cons(v2, v11) = v13 & cons(v0, v7) = v9 & app(v10, v13) = all_0_6_6 & app(v5, v9) = v10 & ssItem(v2) = 0 & ssItem(v0) = 0) | ( ~ (v0 = 0) & ssList(all_0_6_6) = v0))
% 30.82/8.77 |
% 30.82/8.77 +-Applying beta-rule and splitting (89), into two cases.
% 30.82/8.77 |-Branch one:
% 30.82/8.77 | (174) ~ (all_0_2_2 = 0)
% 30.82/8.77 |
% 30.82/8.77 +-Applying beta-rule and splitting (160), into two cases.
% 30.82/8.77 |-Branch one:
% 30.82/8.77 | (169) all_0_4_4 = nil
% 30.82/8.77 |
% 30.82/8.77 | From (169) and (41) follows:
% 30.82/8.77 | (283) segmentP(nil, all_0_6_6) = 0
% 30.82/8.77 |
% 30.82/8.77 +-Applying beta-rule and splitting (154), into two cases.
% 30.82/8.77 |-Branch one:
% 30.82/8.77 | (167) ~ (segmentP(nil, all_0_6_6) = 0)
% 30.82/8.77 |
% 30.82/8.77 | Using (283) and (167) yields:
% 30.82/8.77 | (180) $false
% 30.82/8.77 |
% 30.82/8.77 |-The branch is then unsatisfiable
% 30.82/8.77 |-Branch two:
% 30.82/8.77 | (283) segmentP(nil, all_0_6_6) = 0
% 30.82/8.77 | (284) all_0_6_6 = nil | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 30.82/8.77 |
% 30.82/8.77 +-Applying beta-rule and splitting (284), into two cases.
% 30.82/8.77 |-Branch one:
% 30.82/8.77 | (285) all_0_6_6 = nil
% 30.82/8.77 |
% 30.82/8.77 | From (285) and (68) follows:
% 30.82/8.77 | (330) strictorderedP(nil) = all_0_5_5
% 30.82/8.77 |
% 30.82/8.77 +-Applying beta-rule and splitting (151), into two cases.
% 30.82/8.77 |-Branch one:
% 30.82/8.77 | (331) ~ (strictorderedP(nil) = all_0_5_5)
% 30.82/8.77 |
% 30.82/8.77 | Using (330) and (331) yields:
% 30.82/8.77 | (180) $false
% 30.82/8.77 |
% 30.82/8.77 |-The branch is then unsatisfiable
% 30.82/8.77 |-Branch two:
% 30.82/8.77 | (330) strictorderedP(nil) = all_0_5_5
% 30.82/8.77 | (162) all_0_5_5 = 0
% 30.82/8.77 |
% 30.82/8.77 | Equations (162) can reduce 30 to:
% 30.82/8.77 | (163) $false
% 30.82/8.77 |
% 30.82/8.77 |-The branch is then unsatisfiable
% 30.82/8.77 |-Branch two:
% 30.82/8.77 | (166) ~ (all_0_6_6 = nil)
% 30.82/8.77 | (292) ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 30.82/8.77 |
% 30.82/8.77 | Instantiating (292) with all_47_0_125 yields:
% 30.82/8.77 | (338) ~ (all_47_0_125 = 0) & ssList(all_0_6_6) = all_47_0_125
% 30.82/8.77 |
% 30.82/8.77 | Applying alpha-rule on (338) yields:
% 30.82/8.77 | (339) ~ (all_47_0_125 = 0)
% 30.82/8.77 | (340) ssList(all_0_6_6) = all_47_0_125
% 30.82/8.77 |
% 30.82/8.77 +-Applying beta-rule and splitting (156), into two cases.
% 30.82/8.77 |-Branch one:
% 30.82/8.77 | (341) all_0_4_4 = all_0_6_6
% 30.82/8.77 |
% 30.82/8.77 | Combining equations (169,341) yields a new equation:
% 30.82/8.77 | (285) all_0_6_6 = nil
% 30.82/8.77 |
% 30.82/8.77 | Equations (285) can reduce 166 to:
% 30.82/8.77 | (163) $false
% 30.82/8.77 |
% 30.82/8.77 |-The branch is then unsatisfiable
% 30.82/8.77 |-Branch two:
% 30.82/8.77 | (344) ~ (all_0_4_4 = all_0_6_6)
% 30.82/8.77 | (345) ? [v0] : ? [v1] : (segmentP(all_0_6_6, all_0_4_4) = v1 & ssList(all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 30.82/8.77 |
% 30.82/8.77 | Instantiating (345) with all_59_0_126, all_59_1_127 yields:
% 30.82/8.77 | (346) segmentP(all_0_6_6, all_0_4_4) = all_59_0_126 & ssList(all_0_6_6) = all_59_1_127 & ( ~ (all_59_0_126 = 0) | ~ (all_59_1_127 = 0))
% 30.82/8.77 |
% 30.82/8.77 | Applying alpha-rule on (346) yields:
% 30.82/8.77 | (347) segmentP(all_0_6_6, all_0_4_4) = all_59_0_126
% 30.82/8.77 | (348) ssList(all_0_6_6) = all_59_1_127
% 30.82/8.77 | (349) ~ (all_59_0_126 = 0) | ~ (all_59_1_127 = 0)
% 30.82/8.77 |
% 30.82/8.77 | Instantiating formula (2) with all_0_6_6, all_59_1_127, 0 and discharging atoms ssList(all_0_6_6) = all_59_1_127, ssList(all_0_6_6) = 0, yields:
% 30.82/8.77 | (350) all_59_1_127 = 0
% 30.82/8.77 |
% 30.82/8.77 | Instantiating formula (2) with all_0_6_6, all_47_0_125, all_59_1_127 and discharging atoms ssList(all_0_6_6) = all_59_1_127, ssList(all_0_6_6) = all_47_0_125, yields:
% 30.82/8.77 | (351) all_59_1_127 = all_47_0_125
% 30.82/8.77 |
% 30.82/8.77 | Combining equations (350,351) yields a new equation:
% 30.82/8.77 | (352) all_47_0_125 = 0
% 30.82/8.77 |
% 30.82/8.77 | Equations (352) can reduce 339 to:
% 30.82/8.77 | (163) $false
% 30.82/8.77 |
% 30.82/8.77 |-The branch is then unsatisfiable
% 30.82/8.77 |-Branch two:
% 30.82/8.77 | (168) ~ (all_0_4_4 = nil)
% 30.82/8.77 | (172) all_0_2_2 = 0 | ? [v0] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 30.82/8.77 |
% 30.82/8.77 +-Applying beta-rule and splitting (172), into two cases.
% 30.82/8.77 |-Branch one:
% 30.82/8.77 | (173) all_0_2_2 = 0
% 30.82/8.77 |
% 30.82/8.77 | Equations (173) can reduce 174 to:
% 30.82/8.77 | (163) $false
% 30.82/8.77 |
% 30.82/8.77 |-The branch is then unsatisfiable
% 30.82/8.77 |-Branch two:
% 30.82/8.77 | (174) ~ (all_0_2_2 = 0)
% 30.82/8.77 | (277) ? [v0] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 30.82/8.77 |
% 30.82/8.77 | Instantiating (277) with all_40_0_132 yields:
% 30.82/8.77 | (360) ~ (all_40_0_132 = 0) & ssList(nil) = all_40_0_132
% 30.82/8.77 |
% 30.82/8.77 | Applying alpha-rule on (360) yields:
% 30.82/8.77 | (361) ~ (all_40_0_132 = 0)
% 30.82/8.77 | (362) ssList(nil) = all_40_0_132
% 30.82/8.77 |
% 30.82/8.77 | Instantiating formula (2) with nil, all_40_0_132, 0 and discharging atoms ssList(nil) = all_40_0_132, ssList(nil) = 0, yields:
% 30.82/8.77 | (363) all_40_0_132 = 0
% 30.82/8.77 |
% 30.82/8.77 | Equations (363) can reduce 361 to:
% 30.82/8.77 | (163) $false
% 30.82/8.77 |
% 30.82/8.77 |-The branch is then unsatisfiable
% 30.82/8.77 |-Branch two:
% 30.82/8.77 | (173) all_0_2_2 = 0
% 30.82/8.77 | (177) all_0_3_3 = 0
% 30.82/8.77 |
% 30.82/8.77 | Combining equations (317,177) yields a new equation:
% 30.82/8.77 | (367) all_0_7_7 = 0
% 30.82/8.77 |
% 30.82/8.77 | Simplifying 367 yields:
% 30.82/8.77 | (368) all_0_7_7 = 0
% 30.82/8.77 |
% 30.82/8.77 | Equations (368) can reduce 138 to:
% 30.82/8.77 | (163) $false
% 30.82/8.77 |
% 30.82/8.77 |-The branch is then unsatisfiable
% 30.82/8.77 % SZS output end Proof for theBenchmark
% 30.82/8.77
% 30.82/8.77 8156ms
%------------------------------------------------------------------------------