TSTP Solution File: SWC348+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWC348+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n012.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 20:17:37 EDT 2022
% Result : Theorem 23.05s 6.87s
% Output : Proof 31.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC348+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 11 20:40:26 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/0.59 ____ _
% 0.46/0.59 ___ / __ \_____(_)___ ________ __________
% 0.46/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.46/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.46/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.46/0.59
% 0.46/0.59 A Theorem Prover for First-Order Logic
% 0.46/0.59 (ePrincess v.1.0)
% 0.46/0.59
% 0.46/0.59 (c) Philipp Rümmer, 2009-2015
% 0.46/0.59 (c) Peter Backeman, 2014-2015
% 0.46/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.46/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.46/0.59 Bug reports to peter@backeman.se
% 0.46/0.59
% 0.46/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.46/0.59
% 0.46/0.59 Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.71/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.35/1.09 Prover 0: Preprocessing ...
% 4.73/1.68 Prover 0: Constructing countermodel ...
% 19.03/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.50/6.09 Prover 1: Preprocessing ...
% 20.63/6.29 Prover 1: Constructing countermodel ...
% 23.05/6.86 Prover 1: proved (933ms)
% 23.05/6.87 Prover 0: stopped
% 23.05/6.87
% 23.05/6.87 No countermodel exists, formula is valid
% 23.05/6.87 % SZS status Theorem for theBenchmark
% 23.05/6.87
% 23.05/6.87 Generating proof ... found it (size 133)
% 30.51/8.60
% 30.51/8.60 % SZS output start Proof for theBenchmark
% 30.51/8.60 Assumed formulas after preprocessing and simplification:
% 30.51/8.60 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ( ~ (v8 = v7) & ~ (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) = v4 & segmentP(v3, v1) = 0 & singletonP(v1) = v5 & singletonP(nil) = v0 & ssList(v3) = 0 & ssList(v1) = 0 & ssList(nil) = 0 & neq(v3, nil) = v6 & ssItem(v8) = 0 & ssItem(v7) = 0 & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v12 = 0 | ~ (strictorderedP(v9) = 0) | ~ (lt(v10, v11) = v12) | ~ (ssList(v13) = 0) | ~ (cons(v11, v17) = v18) | ~ (cons(v10, v14) = v15) | ~ (app(v16, v18) = v9) | ~ (app(v13, v15) = v16) | ~ (ssItem(v10) = 0) | ? [v19] : (( ~ (v19 = 0) & ssList(v17) = v19) | ( ~ (v19 = 0) & ssList(v14) = v19) | ( ~ (v19 = 0) & ssList(v9) = v19) | ( ~ (v19 = 0) & ssItem(v11) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v12 = 0 | ~ (totalorderedP(v9) = 0) | ~ (leq(v10, v11) = v12) | ~ (ssList(v13) = 0) | ~ (cons(v11, v17) = v18) | ~ (cons(v10, v14) = v15) | ~ (app(v16, v18) = v9) | ~ (app(v13, v15) = v16) | ~ (ssItem(v10) = 0) | ? [v19] : (( ~ (v19 = 0) & ssList(v17) = v19) | ( ~ (v19 = 0) & ssList(v14) = v19) | ( ~ (v19 = 0) & ssList(v9) = v19) | ( ~ (v19 = 0) & ssItem(v11) = v19))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (duplicatefreeP(v9) = 0) | ~ (ssList(v11) = 0) | ~ (cons(v10, v15) = v16) | ~ (cons(v10, v12) = v13) | ~ (app(v14, v16) = v9) | ~ (app(v11, v13) = v14) | ~ (ssItem(v10) = 0) | ? [v17] : (( ~ (v17 = 0) & ssList(v15) = v17) | ( ~ (v17 = 0) & ssList(v12) = v17) | ( ~ (v17 = 0) & ssList(v9) = v17))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (segmentP(v14, v10) = v15) | ~ (segmentP(v9, v10) = 0) | ~ (ssList(v9) = 0) | ~ (app(v12, v13) = v14) | ~ (app(v11, v9) = v12) | ? [v16] : (( ~ (v16 = 0) & ssList(v13) = v16) | ( ~ (v16 = 0) & ssList(v11) = v16) | ( ~ (v16 = 0) & ssList(v10) = v16))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v11 = v10 | ~ (equalelemsP(v9) = 0) | ~ (ssList(v12) = 0) | ~ (cons(v11, v13) = v14) | ~ (cons(v10, v14) = v15) | ~ (app(v12, v15) = v9) | ~ (ssItem(v11) = 0) | ~ (ssItem(v10) = 0) | ? [v16] : (( ~ (v16 = 0) & ssList(v13) = v16) | ( ~ (v16 = 0) & ssList(v9) = v16))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (frontsegP(v12, v14) = v15) | ~ (cons(v10, v13) = v14) | ~ (cons(v9, v11) = v12) | ~ (ssItem(v10) = 0) | ~ (ssItem(v9) = 0) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & ssList(v11) = v16) | (frontsegP(v11, v13) = v17 & ssList(v13) = v16 & ( ~ (v16 = 0) | (( ~ (v17 = 0) | ~ (v10 = v9) | v15 = 0) & ( ~ (v15 = 0) | (v17 = 0 & v10 = v9))))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = 0 | ~ (segmentP(v9, v10) = v11) | ~ (ssList(v9) = 0) | ~ (app(v13, v14) = v9) | ~ (app(v12, v10) = v13) | ? [v15] : (( ~ (v15 = 0) & ssList(v14) = v15) | ( ~ (v15 = 0) & ssList(v12) = v15) | ( ~ (v15 = 0) & ssList(v10) = v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = 0 | ~ (memberP(v9, v10) = v11) | ~ (ssList(v12) = 0) | ~ (ssList(v9) = 0) | ~ (cons(v10, v13) = v14) | ~ (app(v12, v14) = v9) | ? [v15] : (( ~ (v15 = 0) & ssList(v13) = v15) | ( ~ (v15 = 0) & ssItem(v10) = v15))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (memberP(v13, v9) = v14) | ~ (memberP(v10, v9) = v11) | ~ (app(v10, v12) = v13) | ~ (ssItem(v9) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssList(v10) = v15) | (memberP(v12, v9) = v16 & ssList(v12) = v15 & ( ~ (v15 = 0) | (( ~ (v14 = 0) | v16 = 0 | v11 = 0) & (v14 = 0 | ( ~ (v16 = 0) & ~ (v11 = 0)))))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (ssList(v9) = 0) | ~ (cons(v12, v10) = v13) | ~ (app(v13, v9) = v14) | ~ (app(v10, v9) = v11) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssList(v10) = v15) | (cons(v12, v11) = v16 & ssItem(v12) = v15 & ( ~ (v15 = 0) | v16 = v14)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v11 | ~ (ssList(v10) = 0) | ~ (ssList(v9) = 0) | ~ (cons(v13, v10) = v12) | ~ (cons(v11, v9) = v12) | ? [v14] : (( ~ (v14 = 0) & ssItem(v13) = v14) | ( ~ (v14 = 0) & ssItem(v11) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (rearsegP(v12, v10) = v13) | ~ (rearsegP(v9, v10) = 0) | ~ (ssList(v9) = 0) | ~ (app(v11, v9) = v12) | ? [v14] : (( ~ (v14 = 0) & ssList(v11) = v14) | ( ~ (v14 = 0) & ssList(v10) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (frontsegP(v12, v10) = v13) | ~ (frontsegP(v9, v10) = 0) | ~ (ssList(v9) = 0) | ~ (app(v9, v11) = v12) | ? [v14] : (( ~ (v14 = 0) & ssList(v11) = v14) | ( ~ (v14 = 0) & ssList(v10) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = v9 | ~ (ssList(v10) = 0) | ~ (ssList(v9) = 0) | ~ (cons(v13, v10) = v12) | ~ (cons(v11, v9) = v12) | ? [v14] : (( ~ (v14 = 0) & ssItem(v13) = v14) | ( ~ (v14 = 0) & ssItem(v11) = v14))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (memberP(v12, v9) = v13) | ~ (cons(v10, v11) = v12) | ~ (ssItem(v10) = 0) | ~ (ssItem(v9) = 0) | ? [v14] : ? [v15] : (memberP(v11, v9) = v15 & ssList(v11) = v14 & ( ~ (v14 = 0) | (( ~ (v13 = 0) | v15 = 0 | v10 = v9) & (v13 = 0 | ( ~ (v15 = 0) & ~ (v10 = v9))))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (ssList(v9) = 0) | ~ (app(v11, v12) = v13) | ~ (app(v9, v10) = v11) | ? [v14] : ? [v15] : ? [v16] : (( ~ (v14 = 0) & ssList(v10) = v14) | (ssList(v12) = v14 & app(v10, v12) = v15 & app(v9, v15) = v16 & ( ~ (v14 = 0) | v16 = v13)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | v9 = nil | ~ (tl(v9) = v11) | ~ (hd(v9) = v10) | ~ (cons(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & ssList(v9) = v13)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (ssList(v9) = 0) | ~ (app(v12, v10) = v11) | ~ (app(v9, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & ssList(v12) = v13) | ( ~ (v13 = 0) & ssList(v10) = v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v9 | ~ (ssList(v9) = 0) | ~ (app(v10, v12) = v11) | ~ (app(v10, v9) = v11) | ? [v13] : (( ~ (v13 = 0) & ssList(v12) = v13) | ( ~ (v13 = 0) & ssList(v10) = v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (gt(v9, v11) = v12) | ~ (gt(v9, v10) = 0) | ~ (ssItem(v9) = 0) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssItem(v10) = v13) | (gt(v10, v11) = v14 & ssItem(v11) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (geq(v9, v11) = v12) | ~ (geq(v9, v10) = 0) | ~ (ssItem(v9) = 0) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssItem(v10) = v13) | (geq(v10, v11) = v14 & ssItem(v11) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (lt(v9, v11) = v12) | ~ (lt(v9, v10) = 0) | ~ (ssItem(v9) = 0) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssItem(v10) = v13) | (lt(v10, v11) = v14 & ssItem(v11) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (lt(v9, v11) = v12) | ~ (leq(v9, v10) = 0) | ~ (ssItem(v9) = 0) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssItem(v10) = v13) | (lt(v10, v11) = v14 & ssItem(v11) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (leq(v9, v11) = v12) | ~ (leq(v9, v10) = 0) | ~ (ssItem(v9) = 0) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssItem(v10) = v13) | (leq(v10, v11) = v14 & ssItem(v11) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (segmentP(v9, v11) = v12) | ~ (segmentP(v9, v10) = 0) | ~ (ssList(v9) = 0) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssList(v10) = v13) | (segmentP(v10, v11) = v14 & ssList(v11) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (rearsegP(v9, v11) = v12) | ~ (rearsegP(v9, v10) = 0) | ~ (ssList(v9) = 0) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssList(v10) = v13) | (rearsegP(v10, v11) = v14 & ssList(v11) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (frontsegP(v9, v11) = v12) | ~ (frontsegP(v9, v10) = 0) | ~ (ssList(v9) = 0) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssList(v10) = v13) | (frontsegP(v10, v11) = v14 & ssList(v11) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (rearsegP(v9, v10) = v11) | ~ (ssList(v9) = 0) | ~ (app(v12, v10) = v9) | ? [v13] : (( ~ (v13 = 0) & ssList(v12) = v13) | ( ~ (v13 = 0) & ssList(v10) = v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (frontsegP(v9, v10) = v11) | ~ (ssList(v9) = 0) | ~ (app(v10, v12) = v9) | ? [v13] : (( ~ (v13 = 0) & ssList(v12) = v13) | ( ~ (v13 = 0) & ssList(v10) = v13))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (gt(v12, v11) = v10) | ~ (gt(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (geq(v12, v11) = v10) | ~ (geq(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (lt(v12, v11) = v10) | ~ (lt(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (leq(v12, v11) = v10) | ~ (leq(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (segmentP(v12, v11) = v10) | ~ (segmentP(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (rearsegP(v12, v11) = v10) | ~ (rearsegP(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (frontsegP(v12, v11) = v10) | ~ (frontsegP(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (memberP(v12, v11) = v10) | ~ (memberP(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (cons(v12, v11) = v10) | ~ (cons(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (app(v12, v11) = v10) | ~ (app(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v10 = v9 | ~ (neq(v12, v11) = v10) | ~ (neq(v12, v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = nil | ~ (tl(v9) = v10) | ~ (app(v10, v11) = v12) | ? [v13] : ? [v14] : ? [v15] : (( ~ (v13 = 0) & ssList(v9) = v13) | (tl(v14) = v15 & ssList(v11) = v13 & app(v9, v11) = v14 & ( ~ (v13 = 0) | v15 = v12)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = nil | ~ (hd(v9) = v10) | ~ (app(v9, v11) = v12) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssList(v9) = v13) | (hd(v12) = v14 & ssList(v11) = v13 & ( ~ (v13 = 0) | v14 = v10)))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (hd(v10) = v11) | ~ (lt(v9, v11) = v12) | ~ (ssItem(v9) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (strictorderedP(v14) = v15 & strictorderedP(v10) = v16 & ssList(v10) = v13 & cons(v9, v10) = v14 & ( ~ (v13 = 0) | (( ~ (v15 = 0) | v10 = nil | (v16 = 0 & v12 = 0)) & (v15 = 0 | ( ~ (v10 = nil) & ( ~ (v16 = 0) | ~ (v12 = 0)))))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (hd(v10) = v11) | ~ (leq(v9, v11) = v12) | ~ (ssItem(v9) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : (totalorderedP(v14) = v15 & totalorderedP(v10) = v16 & ssList(v10) = v13 & cons(v9, v10) = v14 & ( ~ (v13 = 0) | (( ~ (v15 = 0) | v10 = nil | (v16 = 0 & v12 = 0)) & (v15 = 0 | ( ~ (v10 = nil) & ( ~ (v16 = 0) | ~ (v12 = 0)))))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (strictorderP(v9) = 0) | ~ (lt(v10, v11) = v12) | ~ (ssItem(v10) = 0) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssList(v9) = v13) | (lt(v11, v10) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v14 = 0 | v12 = 0 | ~ (ssList(v15) = 0) | ~ (cons(v11, v19) = v20) | ~ (cons(v10, v16) = v17) | ~ (app(v18, v20) = v9) | ~ (app(v15, v17) = v18) | ? [v21] : (( ~ (v21 = 0) & ssList(v19) = v21) | ( ~ (v21 = 0) & ssList(v16) = v21))))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (totalorderP(v9) = 0) | ~ (leq(v10, v11) = v12) | ~ (ssItem(v10) = 0) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssList(v9) = v13) | (leq(v11, v10) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v14 = 0 | v12 = 0 | ~ (ssList(v15) = 0) | ~ (cons(v11, v19) = v20) | ~ (cons(v10, v16) = v17) | ~ (app(v18, v20) = v9) | ~ (app(v15, v17) = v18) | ? [v21] : (( ~ (v21 = 0) & ssList(v19) = v21) | ( ~ (v21 = 0) & ssList(v16) = v21))))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (cyclefreeP(v9) = 0) | ~ (leq(v10, v11) = v12) | ~ (ssItem(v10) = 0) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssList(v9) = v13) | (leq(v11, v10) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ( ~ (v14 = 0) | ~ (v12 = 0) | ~ (ssList(v15) = 0) | ~ (cons(v11, v19) = v20) | ~ (cons(v10, v16) = v17) | ~ (app(v18, v20) = v9) | ~ (app(v15, v17) = v18) | ? [v21] : (( ~ (v21 = 0) & ssList(v19) = v21) | ( ~ (v21 = 0) & ssList(v16) = v21))))))) & ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (ssList(v9) = 0) | ~ (cons(v10, nil) = v11) | ~ (app(v11, v9) = v12) | ? [v13] : ? [v14] : (cons(v10, v9) = v14 & ssItem(v10) = v13 & ( ~ (v13 = 0) | v14 = v12))) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = v9 | ~ (lt(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ? [v12] : ? [v13] : (leq(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = v9 | ~ (ssList(v9) = 0) | ~ (neq(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & ssList(v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | v10 = v9 | ~ (neq(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ? [v12] : ( ~ (v12 = 0) & ssItem(v10) = v12)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (tl(v11) = v10) | ~ (tl(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (hd(v11) = v10) | ~ (hd(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (equalelemsP(v11) = v10) | ~ (equalelemsP(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (duplicatefreeP(v11) = v10) | ~ (duplicatefreeP(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (strictorderedP(v11) = v10) | ~ (strictorderedP(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (totalorderedP(v11) = v10) | ~ (totalorderedP(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (strictorderP(v11) = v10) | ~ (strictorderP(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (totalorderP(v11) = v10) | ~ (totalorderP(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (cyclefreeP(v11) = v10) | ~ (cyclefreeP(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (singletonP(v11) = v10) | ~ (singletonP(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (ssList(v11) = v10) | ~ (ssList(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = v9 | ~ (ssItem(v11) = v10) | ~ (ssItem(v11) = v9)) & ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (singletonP(v9) = v10) | ~ (cons(v11, nil) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v9) = v12) | ( ~ (v12 = 0) & ssItem(v11) = v12))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (gt(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ? [v12] : ? [v13] : (lt(v10, v9) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | (( ~ (v13 = 0) | v11 = 0) & ( ~ (v11 = 0) | v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (geq(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ? [v12] : ? [v13] : (leq(v10, v9) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | (( ~ (v13 = 0) | v11 = 0) & ( ~ (v11 = 0) | v13 = 0))))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (lt(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ? [v12] : ? [v13] : (leq(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | (( ~ (v13 = 0) | v11 = 0 | v10 = v9) & ( ~ (v11 = 0) | (v13 = 0 & ~ (v10 = v9))))))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ssList(v9) = 0) | ~ (cons(v10, v9) = v11) | ? [v12] : ? [v13] : (tl(v11) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | v13 = v9))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ssList(v9) = 0) | ~ (cons(v10, v9) = v11) | ? [v12] : ? [v13] : (hd(v11) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | v13 = v10))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ssList(v9) = 0) | ~ (cons(v10, v9) = v11) | ? [v12] : ? [v13] : (ssList(v11) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v9] : ! [v10] : ! [v11] : ( ~ (ssList(v9) = 0) | ~ (app(v9, v10) = v11) | ? [v12] : ? [v13] : (ssList(v11) = v13 & ssList(v10) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v9] : ! [v10] : (v10 = v9 | ~ (geq(v9, v10) = 0) | ~ (ssItem(v9) = 0) | ? [v11] : ? [v12] : (geq(v10, v9) = v12 & ssItem(v10) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : (v10 = v9 | ~ (leq(v9, v10) = 0) | ~ (ssItem(v9) = 0) | ? [v11] : ? [v12] : (leq(v10, v9) = v12 & ssItem(v10) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : (v10 = v9 | ~ (segmentP(v9, v10) = 0) | ~ (ssList(v9) = 0) | ? [v11] : ? [v12] : (segmentP(v10, v9) = v12 & ssList(v10) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : (v10 = v9 | ~ (rearsegP(v9, v10) = 0) | ~ (ssList(v9) = 0) | ? [v11] : ? [v12] : (rearsegP(v10, v9) = v12 & ssList(v10) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : (v10 = v9 | ~ (frontsegP(v9, v10) = 0) | ~ (ssList(v9) = 0) | ? [v11] : ? [v12] : (frontsegP(v10, v9) = v12 & ssList(v10) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : (v10 = v9 | ~ (app(v9, nil) = v10) | ? [v11] : ( ~ (v11 = 0) & ssList(v9) = v11)) & ! [v9] : ! [v10] : (v10 = v9 | ~ (app(nil, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & ssList(v9) = v11)) & ! [v9] : ! [v10] : (v10 = nil | ~ (ssList(v9) = 0) | ~ (app(v9, v10) = nil) | ? [v11] : ( ~ (v11 = 0) & ssList(v10) = v11)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (geq(v9, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & ssItem(v9) = v11)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (equalelemsP(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ((v21 = v9 & v18 = 0 & v16 = 0 & v14 = 0 & v12 = 0 & ~ (v13 = v11) & ssList(v17) = 0 & ssList(v15) = 0 & cons(v13, v17) = v19 & cons(v11, v19) = v20 & app(v15, v20) = v9 & ssItem(v13) = 0 & ssItem(v11) = 0) | ( ~ (v11 = 0) & ssList(v9) = v11))) & ! [v9] : ! [v10] : (v10 = 0 | ~ (duplicatefreeP(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v24 = v9 & v22 = 0 & v18 = 0 & v16 = 0 & v14 = 0 & v13 = v11 & v12 = 0 & ssList(v21) = 0 & ssList(v17) = 0 & ssList(v15) = 0 & cons(v11, v21) = v23 & cons(v11, v17) = v19 & app(v20, v23) = v9 & app(v15, v19) = v20 & ssItem(v11) = 0) | ( ~ (v11 = 0) & ssList(v9) = v11))) & ! [v9] : ! [v10] : (v10 = 0 | ~ (strictorderedP(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = v9 & v23 = 0 & v19 = 0 & v17 = 0 & v14 = 0 & v12 = 0 & ~ (v15 = 0) & lt(v11, v13) = v15 & ssList(v22) = 0 & ssList(v18) = 0 & ssList(v16) = 0 & cons(v13, v22) = v24 & cons(v11, v18) = v20 & app(v21, v24) = v9 & app(v16, v20) = v21 & ssItem(v13) = 0 & ssItem(v11) = 0) | ( ~ (v11 = 0) & ssList(v9) = v11))) & ! [v9] : ! [v10] : (v10 = 0 | ~ (totalorderedP(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = v9 & v23 = 0 & v19 = 0 & v17 = 0 & v14 = 0 & v12 = 0 & ~ (v15 = 0) & leq(v11, v13) = v15 & ssList(v22) = 0 & ssList(v18) = 0 & ssList(v16) = 0 & cons(v13, v22) = v24 & cons(v11, v18) = v20 & app(v21, v24) = v9 & app(v16, v20) = v21 & ssItem(v13) = 0 & ssItem(v11) = 0) | ( ~ (v11 = 0) & ssList(v9) = v11))) & ! [v9] : ! [v10] : (v10 = 0 | ~ (strictorderP(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ((v26 = v9 & v24 = 0 & v20 = 0 & v18 = 0 & v14 = 0 & v12 = 0 & ~ (v16 = 0) & ~ (v15 = 0) & lt(v13, v11) = v16 & lt(v11, v13) = v15 & ssList(v23) = 0 & ssList(v19) = 0 & ssList(v17) = 0 & cons(v13, v23) = v25 & cons(v11, v19) = v21 & app(v22, v25) = v9 & app(v17, v21) = v22 & ssItem(v13) = 0 & ssItem(v11) = 0) | ( ~ (v11 = 0) & ssList(v9) = v11))) & ! [v9] : ! [v10] : (v10 = 0 | ~ (totalorderP(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ((v26 = v9 & v24 = 0 & v20 = 0 & v18 = 0 & v14 = 0 & v12 = 0 & ~ (v16 = 0) & ~ (v15 = 0) & leq(v13, v11) = v16 & leq(v11, v13) = v15 & ssList(v23) = 0 & ssList(v19) = 0 & ssList(v17) = 0 & cons(v13, v23) = v25 & cons(v11, v19) = v21 & app(v22, v25) = v9 & app(v17, v21) = v22 & ssItem(v13) = 0 & ssItem(v11) = 0) | ( ~ (v11 = 0) & ssList(v9) = v11))) & ! [v9] : ! [v10] : (v10 = 0 | ~ (cyclefreeP(v9) = v10) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ((v26 = v9 & v24 = 0 & v20 = 0 & v18 = 0 & v16 = 0 & v15 = 0 & v14 = 0 & v12 = 0 & leq(v13, v11) = 0 & leq(v11, v13) = 0 & ssList(v23) = 0 & ssList(v19) = 0 & ssList(v17) = 0 & cons(v13, v23) = v25 & cons(v11, v19) = v21 & app(v22, v25) = v9 & app(v17, v21) = v22 & ssItem(v13) = 0 & ssItem(v11) = 0) | ( ~ (v11 = 0) & ssList(v9) = v11))) & ! [v9] : ! [v10] : (v10 = 0 | ~ (leq(v9, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & ssItem(v9) = v11)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (segmentP(v9, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & ssList(v9) = v11)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (segmentP(v9, nil) = v10) | ? [v11] : ( ~ (v11 = 0) & ssList(v9) = v11)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (rearsegP(v9, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & ssList(v9) = v11)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (rearsegP(v9, nil) = v10) | ? [v11] : ( ~ (v11 = 0) & ssList(v9) = v11)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (frontsegP(v9, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & ssList(v9) = v11)) & ! [v9] : ! [v10] : (v10 = 0 | ~ (frontsegP(v9, nil) = v10) | ? [v11] : ( ~ (v11 = 0) & ssList(v9) = v11)) & ! [v9] : ! [v10] : (v9 = nil | ~ (tl(v9) = v10) | ? [v11] : ? [v12] : (ssList(v10) = v12 & ssList(v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v9] : ! [v10] : (v9 = nil | ~ (tl(v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = v10 & ssList(v10) = 0) | ( ~ (v11 = 0) & ssList(v9) = v11))) & ! [v9] : ! [v10] : (v9 = nil | ~ (hd(v9) = v10) | ? [v11] : ? [v12] : (ssList(v9) = v11 & ssItem(v10) = v12 & ( ~ (v11 = 0) | v12 = 0))) & ! [v9] : ! [v10] : (v9 = nil | ~ (hd(v9) = v10) | ? [v11] : ? [v12] : ((v12 = 0 & v11 = v10 & ssItem(v10) = 0) | ( ~ (v11 = 0) & ssList(v9) = v11))) & ! [v9] : ! [v10] : (v9 = nil | ~ (ssList(v9) = 0) | ~ (app(v9, v10) = nil) | ? [v11] : ( ~ (v11 = 0) & ssList(v10) = v11)) & ! [v9] : ! [v10] : ( ~ (gt(v9, v10) = 0) | ~ (ssItem(v9) = 0) | ? [v11] : ? [v12] : (gt(v10, v9) = v12 & ssItem(v10) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : ( ~ (tl(v9) = v10) | ? [v11] : ? [v12] : (hd(v9) = v12 & ssList(v9) = v11 & ( ~ (v11 = 0) | ! [v13] : (v13 = v9 | v13 = nil | v9 = nil | ~ (tl(v13) = v10) | ? [v14] : ? [v15] : (hd(v13) = v15 & ssList(v13) = v14 & ( ~ (v15 = v12) | ~ (v14 = 0))))))) & ! [v9] : ! [v10] : ( ~ (lt(v9, v10) = 0) | ~ (ssItem(v9) = 0) | ? [v11] : ? [v12] : (lt(v10, v9) = v12 & ssItem(v10) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v9] : ! [v10] : ( ~ (segmentP(v9, v10) = 0) | ~ (ssList(v9) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v9 & v15 = 0 & v12 = 0 & ssList(v14) = 0 & ssList(v11) = 0 & app(v13, v14) = v9 & app(v11, v10) = v13) | ( ~ (v11 = 0) & ssList(v10) = v11))) & ! [v9] : ! [v10] : ( ~ (rearsegP(v9, v10) = 0) | ~ (ssList(v9) = 0) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v9 & v12 = 0 & ssList(v11) = 0 & app(v11, v10) = v9) | ( ~ (v11 = 0) & ssList(v10) = v11))) & ! [v9] : ! [v10] : ( ~ (frontsegP(v9, v10) = 0) | ~ (ssList(v9) = 0) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v9 & v12 = 0 & ssList(v11) = 0 & app(v10, v11) = v9) | ( ~ (v11 = 0) & ssList(v10) = v11))) & ! [v9] : ! [v10] : ( ~ (memberP(v9, v10) = 0) | ~ (ssList(v9) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v9 & v14 = 0 & v12 = 0 & ssList(v13) = 0 & ssList(v11) = 0 & cons(v10, v13) = v15 & app(v11, v15) = v9) | ( ~ (v11 = 0) & ssItem(v10) = v11))) & ! [v9] : ! [v10] : ( ~ (ssList(v9) = 0) | ~ (cons(v10, v9) = v9) | ? [v11] : ( ~ (v11 = 0) & ssItem(v10) = v11)) & ! [v9] : ! [v10] : ( ~ (ssList(v9) = 0) | ~ (cons(v10, v9) = nil) | ? [v11] : ( ~ (v11 = 0) & ssItem(v10) = v11)) & ! [v9] : ! [v10] : ( ~ (cons(v9, nil) = v10) | ? [v11] : ? [v12] : (equalelemsP(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v9] : ! [v10] : ( ~ (cons(v9, nil) = v10) | ? [v11] : ? [v12] : (duplicatefreeP(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v9] : ! [v10] : ( ~ (cons(v9, nil) = v10) | ? [v11] : ? [v12] : (strictorderedP(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v9] : ! [v10] : ( ~ (cons(v9, nil) = v10) | ? [v11] : ? [v12] : (totalorderedP(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v9] : ! [v10] : ( ~ (cons(v9, nil) = v10) | ? [v11] : ? [v12] : (strictorderP(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v9] : ! [v10] : ( ~ (cons(v9, nil) = v10) | ? [v11] : ? [v12] : (totalorderP(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v9] : ! [v10] : ( ~ (cons(v9, nil) = v10) | ? [v11] : ? [v12] : (cyclefreeP(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v9] : (v9 = nil | ~ (segmentP(nil, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & ssList(v9) = v10)) & ! [v9] : (v9 = nil | ~ (rearsegP(nil, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & ssList(v9) = v10)) & ! [v9] : (v9 = nil | ~ (frontsegP(nil, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & ssList(v9) = v10)) & ! [v9] : (v9 = nil | ~ (ssList(v9) = 0) | ? [v10] : ? [v11] : (ssList(v10) = 0 & cons(v11, v10) = v9 & ssItem(v11) = 0)) & ! [v9] : (v9 = nil | ~ (app(nil, nil) = v9)) & ! [v9] : (v9 = 0 | ~ (segmentP(nil, nil) = v9)) & ! [v9] : (v9 = 0 | ~ (rearsegP(nil, nil) = v9)) & ! [v9] : (v9 = 0 | ~ (frontsegP(nil, nil) = v9)) & ! [v9] : ( ~ (lt(v9, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & ssItem(v9) = v10)) & ! [v9] : ( ~ (singletonP(v9) = 0) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v9 & v11 = 0 & cons(v10, nil) = v9 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v9) = v10))) & ! [v9] : ( ~ (memberP(nil, v9) = 0) | ? [v10] : ( ~ (v10 = 0) & ssItem(v9) = v10)) & ! [v9] : ( ~ (ssList(v9) = 0) | ~ (neq(v9, v9) = 0)) & ! [v9] : ( ~ (neq(v9, v9) = 0) | ~ (ssItem(v9) = 0)) & ( ~ (v6 = 0) | v5 = 0) & ( ~ (v4 = 0) | ~ (v2 = 0)))
% 30.88/8.68 | 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, all_0_8_8 yields:
% 30.88/8.68 | (1) ~ (all_0_0_0 = all_0_1_1) & ~ (all_0_8_8 = 0) & equalelemsP(nil) = 0 & duplicatefreeP(nil) = 0 & strictorderedP(all_0_7_7) = all_0_6_6 & strictorderedP(nil) = 0 & totalorderedP(nil) = 0 & strictorderP(nil) = 0 & totalorderP(nil) = 0 & cyclefreeP(nil) = 0 & segmentP(all_0_5_5, all_0_7_7) = all_0_4_4 & segmentP(all_0_5_5, all_0_7_7) = 0 & singletonP(all_0_7_7) = all_0_3_3 & singletonP(nil) = all_0_8_8 & ssList(all_0_5_5) = 0 & ssList(all_0_7_7) = 0 & ssList(nil) = 0 & neq(all_0_5_5, 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) & ( ~ (all_0_4_4 = 0) | ~ (all_0_6_6 = 0))
% 30.88/8.71 |
% 30.88/8.71 | Applying alpha-rule on (1) yields:
% 30.88/8.71 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0))
% 30.88/8.71 | (3) ! [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)))))))
% 30.88/8.71 | (4) ! [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)))
% 31.17/8.71 | (5) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (ssList(v0) = 0) | ~ (neq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & ssList(v1) = v3))
% 31.17/8.71 | (6) ! [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)))
% 31.17/8.71 | (7) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & ssList(v0) = v4))
% 31.17/8.71 | (8) ! [v0] : ( ~ (ssList(v0) = 0) | ~ (neq(v0, v0) = 0))
% 31.17/8.71 | (9) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 31.17/8.71 | (10) duplicatefreeP(nil) = 0
% 31.17/8.71 | (11) ! [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)))
% 31.17/8.72 | (12) ! [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)))
% 31.17/8.72 | (13) cyclefreeP(nil) = 0
% 31.17/8.72 | (14) totalorderP(nil) = 0
% 31.17/8.72 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 31.17/8.72 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 31.17/8.72 | (17) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v0) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 31.17/8.72 | (18) singletonP(nil) = all_0_8_8
% 31.17/8.72 | (19) ! [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)))))))
% 31.17/8.72 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0))
% 31.17/8.72 | (21) ! [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)))
% 31.17/8.72 | (22) ! [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)))))
% 31.17/8.72 | (23) segmentP(all_0_5_5, all_0_7_7) = 0
% 31.17/8.72 | (24) ssItem(all_0_0_0) = 0
% 31.17/8.72 | (25) ! [v0] : (v0 = nil | ~ (segmentP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 31.17/8.72 | (26) ! [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)))
% 31.17/8.72 | (27) ! [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)))
% 31.17/8.72 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | ~ (equalelemsP(v2) = v0))
% 31.17/8.72 | (29) ! [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)))
% 31.17/8.72 | (30) ! [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)))))))
% 31.17/8.72 | (31) ssItem(all_0_1_1) = 0
% 31.17/8.72 | (32) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 31.17/8.72 | (33) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 31.17/8.72 | (34) ! [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)))))
% 31.17/8.72 | (35) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 31.17/8.72 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0))
% 31.17/8.72 | (37) ! [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)))
% 31.17/8.72 | (38) ~ (all_0_4_4 = 0) | ~ (all_0_6_6 = 0)
% 31.17/8.72 | (39) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 31.17/8.72 | (40) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (ssList(v1) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 31.17/8.72 | (41) ! [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)))
% 31.17/8.72 | (42) ! [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))))))))
% 31.17/8.72 | (43) ! [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)))))))
% 31.17/8.73 | (44) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (tl(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v0)))
% 31.17/8.73 | (45) ! [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)))
% 31.17/8.73 | (46) ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (leq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 31.17/8.73 | (47) ! [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)))))
% 31.17/8.73 | (48) ~ (all_0_8_8 = 0)
% 31.17/8.73 | (49) singletonP(all_0_7_7) = all_0_3_3
% 31.17/8.73 | (50) ! [v0] : ( ~ (lt(v0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 31.17/8.73 | (51) ! [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)))))
% 31.17/8.73 | (52) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (singletonP(v0) = v1) | ~ (cons(v2, nil) = v0) | ? [v3] : (( ~ (v3 = 0) & ssList(v0) = v3) | ( ~ (v3 = 0) & ssItem(v2) = v3)))
% 31.17/8.73 | (53) ~ (all_0_0_0 = all_0_1_1)
% 31.17/8.73 | (54) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssItem(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 31.17/8.73 | (55) ssList(nil) = 0
% 31.17/8.73 | (56) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0))
% 31.17/8.73 | (57) ! [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)))
% 31.17/8.73 | (58) ! [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)))))
% 31.17/8.73 | (59) ! [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)))
% 31.17/8.73 | (60) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (neq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & ssItem(v1) = v3))
% 31.17/8.73 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v3 = 0 | ~ (strictorderedP(v0) = 0) | ~ (lt(v1, v2) = v3) | ~ (ssList(v4) = 0) | ~ (cons(v2, v8) = v9) | ~ (cons(v1, v5) = v6) | ~ (app(v7, v9) = v0) | ~ (app(v4, v6) = v7) | ~ (ssItem(v1) = 0) | ? [v10] : (( ~ (v10 = 0) & ssList(v8) = v10) | ( ~ (v10 = 0) & ssList(v5) = v10) | ( ~ (v10 = 0) & ssList(v0) = v10) | ( ~ (v10 = 0) & ssItem(v2) = v10)))
% 31.17/8.73 | (62) ! [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)))))))
% 31.17/8.73 | (63) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (app(v0, v1) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 31.17/8.73 | (64) ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (lt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 31.17/8.73 | (65) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 31.17/8.73 | (66) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 31.17/8.73 | (67) ! [v0] : ! [v1] : (v0 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 31.17/8.73 | (68) ! [v0] : ! [v1] : (v1 = v0 | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 31.17/8.73 | (69) ! [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)))
% 31.17/8.73 | (70) ! [v0] : (v0 = nil | ~ (frontsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 31.17/8.73 | (71) equalelemsP(nil) = 0
% 31.17/8.73 | (72) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 31.17/8.73 | (73) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 31.17/8.73 | (74) ! [v0] : (v0 = 0 | ~ (frontsegP(nil, nil) = v0))
% 31.17/8.73 | (75) ! [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)))
% 31.17/8.73 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ (cyclefreeP(v2) = v0))
% 31.17/8.73 | (77) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ (totalorderP(v2) = v0))
% 31.17/8.73 | (78) ssList(all_0_5_5) = 0
% 31.17/8.73 | (79) ! [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)))
% 31.17/8.73 | (80) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 31.17/8.74 | (81) segmentP(all_0_5_5, all_0_7_7) = all_0_4_4
% 31.17/8.74 | (82) ! [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)))
% 31.17/8.74 | (83) ! [v0] : (v0 = nil | ~ (ssList(v0) = 0) | ? [v1] : ? [v2] : (ssList(v1) = 0 & cons(v2, v1) = v0 & ssItem(v2) = 0))
% 31.17/8.74 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0))
% 31.17/8.74 | (85) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 31.17/8.74 | (86) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssList(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 31.17/8.74 | (87) ! [v0] : ( ~ (neq(v0, v0) = 0) | ~ (ssItem(v0) = 0))
% 31.17/8.74 | (88) ! [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)))))))
% 31.17/8.74 | (89) strictorderP(nil) = 0
% 31.17/8.74 | (90) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 31.17/8.74 | (91) strictorderedP(nil) = 0
% 31.17/8.74 | (92) ! [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)))
% 31.17/8.74 | (93) ! [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))))
% 31.17/8.74 | (94) ! [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)))
% 31.17/8.74 | (95) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = nil) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 31.17/8.74 | (96) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v1)))
% 31.17/8.74 | (97) strictorderedP(all_0_7_7) = all_0_6_6
% 31.17/8.74 | (98) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 31.17/8.74 | (99) ! [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)))))))
% 31.17/8.74 | (100) ! [v0] : (v0 = nil | ~ (rearsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 31.17/8.74 | (101) ~ (all_0_2_2 = 0) | all_0_3_3 = 0
% 31.17/8.74 | (102) ! [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)))))
% 31.17/8.74 | (103) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 31.17/8.74 | (104) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 31.17/8.74 | (105) ! [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)))
% 31.17/8.74 | (106) totalorderedP(nil) = 0
% 31.17/8.74 | (107) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 31.17/8.74 | (108) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0))
% 31.17/8.74 | (109) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0))
% 31.17/8.74 | (110) neq(all_0_5_5, nil) = all_0_2_2
% 31.17/8.74 | (111) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : (ssList(v0) = v2 & ssItem(v1) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 31.17/8.74 | (112) ! [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)))))
% 31.17/8.74 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (gt(v0, v2) = v3) | ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (gt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 31.17/8.74 | (114) ! [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)))
% 31.17/8.74 | (115) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0))
% 31.17/8.74 | (116) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = v0))
% 31.17/8.74 | (117) ! [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))))
% 31.17/8.74 | (118) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0))
% 31.17/8.74 | (119) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 31.17/8.74 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0))
% 31.17/8.74 | (121) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) = v0))
% 31.17/8.74 | (122) ! [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))))
% 31.17/8.74 | (123) ! [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))))))))
% 31.17/8.74 | (124) ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0))
% 31.17/8.74 | (125) ! [v0] : (v0 = 0 | ~ (segmentP(nil, nil) = v0))
% 31.17/8.74 | (126) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 31.17/8.75 | (127) ! [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)))))
% 31.17/8.75 | (128) ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (geq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 31.17/8.75 | (129) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | ~ (duplicatefreeP(v2) = v0))
% 31.17/8.75 | (130) ! [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))))))))
% 31.17/8.75 | (131) ! [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))))
% 31.17/8.75 | (132) ! [v0] : ! [v1] : ( ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (gt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 31.17/8.75 | (133) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 31.17/8.75 | (134) ! [v0] : ! [v1] : (v1 = v0 | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (frontsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 31.17/8.75 | (135) ! [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)))
% 31.17/8.75 | (136) ! [v0] : ( ~ (singletonP(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v0 & v2 = 0 & cons(v1, nil) = v0 & ssItem(v1) = 0) | ( ~ (v1 = 0) & ssList(v0) = v1)))
% 31.17/8.75 | (137) ! [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)))
% 31.17/8.75 | (138) ! [v0] : ! [v1] : (v1 = v0 | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 31.17/8.75 | (139) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderP(v2) = v1) | ~ (strictorderP(v2) = v0))
% 31.17/8.75 | (140) ! [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))))
% 31.17/8.75 | (141) ! [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)))
% 31.17/8.75 | (142) ! [v0] : ! [v1] : (v1 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 31.17/8.75 | (143) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 31.17/8.75 | (144) ! [v0] : (v0 = 0 | ~ (rearsegP(nil, nil) = v0))
% 31.17/8.75 | (145) ! [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)))))
% 31.17/8.75 | (146) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 31.17/8.75 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 31.17/8.75 | (148) ! [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)))
% 31.17/8.75 | (149) ssList(all_0_7_7) = 0
% 31.17/8.75 | (150) ! [v0] : ( ~ (memberP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 31.17/8.75 | (151) ! [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)))
% 31.17/8.75 |
% 31.17/8.75 | Instantiating formula (116) with nil, 0, all_0_6_6 and discharging atoms strictorderedP(nil) = 0, yields:
% 31.17/8.75 | (152) all_0_6_6 = 0 | ~ (strictorderedP(nil) = all_0_6_6)
% 31.17/8.75 |
% 31.17/8.75 | Instantiating formula (120) with all_0_5_5, all_0_7_7, 0, all_0_4_4 and discharging atoms segmentP(all_0_5_5, all_0_7_7) = all_0_4_4, segmentP(all_0_5_5, all_0_7_7) = 0, yields:
% 31.17/8.75 | (153) all_0_4_4 = 0
% 31.17/8.75 |
% 31.17/8.75 | From (153) and (81) follows:
% 31.17/8.75 | (23) segmentP(all_0_5_5, all_0_7_7) = 0
% 31.17/8.75 |
% 31.17/8.75 +-Applying beta-rule and splitting (38), into two cases.
% 31.17/8.75 |-Branch one:
% 31.17/8.75 | (155) ~ (all_0_4_4 = 0)
% 31.17/8.75 |
% 31.17/8.75 | Equations (153) can reduce 155 to:
% 31.17/8.75 | (156) $false
% 31.17/8.75 |
% 31.17/8.75 |-The branch is then unsatisfiable
% 31.17/8.75 |-Branch two:
% 31.17/8.75 | (153) all_0_4_4 = 0
% 31.17/8.75 | (158) ~ (all_0_6_6 = 0)
% 31.17/8.75 |
% 31.17/8.75 | Instantiating formula (57) with all_0_6_6, all_0_7_7 and discharging atoms strictorderedP(all_0_7_7) = all_0_6_6, yields:
% 31.17/8.75 | (159) all_0_6_6 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = all_0_7_7 & 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_7_7 & app(v5, v9) = v10 & ssItem(v2) = 0 & ssItem(v0) = 0) | ( ~ (v0 = 0) & ssList(all_0_7_7) = v0))
% 31.36/8.76 |
% 31.36/8.76 | Instantiating formula (25) with all_0_7_7 yields:
% 31.36/8.76 | (160) all_0_7_7 = nil | ~ (segmentP(nil, all_0_7_7) = 0) | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_7_7) = v0)
% 31.36/8.76 |
% 31.36/8.76 | Instantiating formula (136) with all_0_7_7 yields:
% 31.36/8.76 | (161) ~ (singletonP(all_0_7_7) = 0) | ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_7_7 & v1 = 0 & cons(v0, nil) = all_0_7_7 & ssItem(v0) = 0) | ( ~ (v0 = 0) & ssList(all_0_7_7) = v0))
% 31.36/8.76 |
% 31.36/8.76 | Instantiating formula (83) with all_0_7_7 and discharging atoms ssList(all_0_7_7) = 0, yields:
% 31.36/8.76 | (162) all_0_7_7 = nil | ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_7_7 & ssItem(v1) = 0)
% 31.36/8.76 |
% 31.36/8.76 | Instantiating formula (138) with all_0_7_7, nil and discharging atoms ssList(nil) = 0, yields:
% 31.36/8.76 | (163) all_0_7_7 = nil | ~ (segmentP(nil, all_0_7_7) = 0) | ? [v0] : ? [v1] : (segmentP(all_0_7_7, nil) = v1 & ssList(all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 31.36/8.76 |
% 31.36/8.76 | Instantiating formula (105) with all_0_7_7, nil and discharging atoms ssList(nil) = 0, yields:
% 31.36/8.76 | (164) ~ (segmentP(nil, all_0_7_7) = 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_7_7) = v2) | ( ~ (v0 = 0) & ssList(all_0_7_7) = v0))
% 31.36/8.76 |
% 31.36/8.76 | Instantiating formula (5) with all_0_2_2, nil, all_0_5_5 and discharging atoms ssList(all_0_5_5) = 0, neq(all_0_5_5, nil) = all_0_2_2, yields:
% 31.36/8.76 | (165) all_0_2_2 = 0 | all_0_5_5 = nil | ? [v0] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 31.36/8.76 |
% 31.36/8.76 +-Applying beta-rule and splitting (152), into two cases.
% 31.36/8.76 |-Branch one:
% 31.36/8.76 | (166) ~ (strictorderedP(nil) = all_0_6_6)
% 31.36/8.76 |
% 31.36/8.76 +-Applying beta-rule and splitting (159), into two cases.
% 31.36/8.76 |-Branch one:
% 31.36/8.76 | (167) all_0_6_6 = 0
% 31.36/8.76 |
% 31.36/8.76 | Equations (167) can reduce 158 to:
% 31.36/8.76 | (156) $false
% 31.36/8.76 |
% 31.36/8.76 |-The branch is then unsatisfiable
% 31.36/8.76 |-Branch two:
% 31.36/8.76 | (158) ~ (all_0_6_6 = 0)
% 31.36/8.76 | (170) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = all_0_7_7 & 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_7_7 & app(v5, v9) = v10 & ssItem(v2) = 0 & ssItem(v0) = 0) | ( ~ (v0 = 0) & ssList(all_0_7_7) = v0))
% 31.36/8.76 |
% 31.36/8.76 | Using (97) and (166) yields:
% 31.36/8.76 | (171) ~ (all_0_7_7 = nil)
% 31.36/8.76 |
% 31.36/8.76 +-Applying beta-rule and splitting (160), into two cases.
% 31.36/8.76 |-Branch one:
% 31.36/8.76 | (172) ~ (segmentP(nil, all_0_7_7) = 0)
% 31.36/8.76 |
% 31.36/8.76 | Using (23) and (172) yields:
% 31.36/8.76 | (173) ~ (all_0_5_5 = nil)
% 31.36/8.76 |
% 31.36/8.76 +-Applying beta-rule and splitting (165), into two cases.
% 31.36/8.76 |-Branch one:
% 31.36/8.76 | (174) all_0_5_5 = nil
% 31.36/8.76 |
% 31.36/8.76 | Equations (174) can reduce 173 to:
% 31.36/8.76 | (156) $false
% 31.36/8.76 |
% 31.36/8.76 |-The branch is then unsatisfiable
% 31.36/8.76 |-Branch two:
% 31.36/8.76 | (173) ~ (all_0_5_5 = nil)
% 31.36/8.76 | (177) all_0_2_2 = 0 | ? [v0] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 31.36/8.76 |
% 31.36/8.76 +-Applying beta-rule and splitting (177), into two cases.
% 31.36/8.76 |-Branch one:
% 31.36/8.76 | (178) all_0_2_2 = 0
% 31.36/8.76 |
% 31.36/8.76 +-Applying beta-rule and splitting (101), into two cases.
% 31.36/8.76 |-Branch one:
% 31.36/8.76 | (179) ~ (all_0_2_2 = 0)
% 31.36/8.76 |
% 31.36/8.76 | Equations (178) can reduce 179 to:
% 31.36/8.76 | (156) $false
% 31.36/8.76 |
% 31.36/8.76 |-The branch is then unsatisfiable
% 31.36/8.76 |-Branch two:
% 31.36/8.76 | (178) all_0_2_2 = 0
% 31.36/8.76 | (182) all_0_3_3 = 0
% 31.36/8.76 |
% 31.36/8.76 | From (182) and (49) follows:
% 31.36/8.76 | (183) singletonP(all_0_7_7) = 0
% 31.36/8.76 |
% 31.36/8.76 +-Applying beta-rule and splitting (161), into two cases.
% 31.36/8.76 |-Branch one:
% 31.36/8.76 | (184) ~ (singletonP(all_0_7_7) = 0)
% 31.36/8.76 |
% 31.36/8.76 | Using (183) and (184) yields:
% 31.36/8.76 | (185) $false
% 31.36/8.76 |
% 31.36/8.76 |-The branch is then unsatisfiable
% 31.36/8.76 |-Branch two:
% 31.36/8.76 | (183) singletonP(all_0_7_7) = 0
% 31.36/8.76 | (187) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_7_7 & v1 = 0 & cons(v0, nil) = all_0_7_7 & ssItem(v0) = 0) | ( ~ (v0 = 0) & ssList(all_0_7_7) = v0))
% 31.36/8.76 |
% 31.36/8.76 | Instantiating (187) with all_70_0_34, all_70_1_35, all_70_2_36 yields:
% 31.36/8.76 | (188) (all_70_0_34 = all_0_7_7 & all_70_1_35 = 0 & cons(all_70_2_36, nil) = all_0_7_7 & ssItem(all_70_2_36) = 0) | ( ~ (all_70_2_36 = 0) & ssList(all_0_7_7) = all_70_2_36)
% 31.36/8.76 |
% 31.36/8.76 +-Applying beta-rule and splitting (188), into two cases.
% 31.36/8.76 |-Branch one:
% 31.36/8.76 | (189) all_70_0_34 = all_0_7_7 & all_70_1_35 = 0 & cons(all_70_2_36, nil) = all_0_7_7 & ssItem(all_70_2_36) = 0
% 31.36/8.76 |
% 31.36/8.76 | Applying alpha-rule on (189) yields:
% 31.36/8.76 | (190) all_70_0_34 = all_0_7_7
% 31.36/8.76 | (191) all_70_1_35 = 0
% 31.36/8.76 | (192) cons(all_70_2_36, nil) = all_0_7_7
% 31.36/8.76 | (193) ssItem(all_70_2_36) = 0
% 31.36/8.76 |
% 31.36/8.76 | Instantiating formula (44) with all_0_7_7, all_70_2_36, nil and discharging atoms ssList(nil) = 0, cons(all_70_2_36, nil) = all_0_7_7, yields:
% 31.36/8.76 | (194) ? [v0] : ? [v1] : (tl(all_0_7_7) = v1 & ssItem(all_70_2_36) = v0 & ( ~ (v0 = 0) | v1 = nil))
% 31.36/8.76 |
% 31.36/8.76 | Instantiating formula (96) with all_0_7_7, all_70_2_36, nil and discharging atoms ssList(nil) = 0, cons(all_70_2_36, nil) = all_0_7_7, yields:
% 31.36/8.76 | (195) ? [v0] : ? [v1] : (hd(all_0_7_7) = v1 & ssItem(all_70_2_36) = v0 & ( ~ (v0 = 0) | v1 = all_70_2_36))
% 31.36/8.76 |
% 31.36/8.76 | Instantiating formula (146) with all_0_7_7, all_70_2_36 and discharging atoms cons(all_70_2_36, nil) = all_0_7_7, yields:
% 31.36/8.76 | (196) ? [v0] : ? [v1] : (equalelemsP(all_0_7_7) = v1 & ssItem(all_70_2_36) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 31.36/8.76 |
% 31.36/8.76 | Instantiating formula (98) with all_0_7_7, all_70_2_36 and discharging atoms cons(all_70_2_36, nil) = all_0_7_7, yields:
% 31.36/8.76 | (197) ? [v0] : ? [v1] : (duplicatefreeP(all_0_7_7) = v1 & ssItem(all_70_2_36) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 31.36/8.76 |
% 31.36/8.76 | Instantiating formula (33) with all_0_7_7, all_70_2_36 and discharging atoms cons(all_70_2_36, nil) = all_0_7_7, yields:
% 31.36/8.76 | (198) ? [v0] : ? [v1] : (strictorderedP(all_0_7_7) = v1 & ssItem(all_70_2_36) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 31.36/8.76 |
% 31.36/8.76 | Instantiating formula (119) with all_0_7_7, all_70_2_36 and discharging atoms cons(all_70_2_36, nil) = all_0_7_7, yields:
% 31.36/8.76 | (199) ? [v0] : ? [v1] : (totalorderedP(all_0_7_7) = v1 & ssItem(all_70_2_36) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 31.36/8.76 |
% 31.36/8.76 | Instantiating formula (65) with all_0_7_7, all_70_2_36 and discharging atoms cons(all_70_2_36, nil) = all_0_7_7, yields:
% 31.36/8.76 | (200) ? [v0] : ? [v1] : (strictorderP(all_0_7_7) = v1 & ssItem(all_70_2_36) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 31.36/8.76 |
% 31.36/8.76 | Instantiating formula (107) with all_0_7_7, all_70_2_36 and discharging atoms cons(all_70_2_36, nil) = all_0_7_7, yields:
% 31.36/8.76 | (201) ? [v0] : ? [v1] : (totalorderP(all_0_7_7) = v1 & ssItem(all_70_2_36) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 31.36/8.76 |
% 31.36/8.76 | Instantiating formula (85) with all_0_7_7, all_70_2_36 and discharging atoms cons(all_70_2_36, nil) = all_0_7_7, yields:
% 31.36/8.76 | (202) ? [v0] : ? [v1] : (cyclefreeP(all_0_7_7) = v1 & ssItem(all_70_2_36) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 31.36/8.76 |
% 31.36/8.76 | Instantiating (202) with all_89_0_47, all_89_1_48 yields:
% 31.36/8.76 | (203) cyclefreeP(all_0_7_7) = all_89_0_47 & ssItem(all_70_2_36) = all_89_1_48 & ( ~ (all_89_1_48 = 0) | all_89_0_47 = 0)
% 31.36/8.76 |
% 31.36/8.76 | Applying alpha-rule on (203) yields:
% 31.36/8.76 | (204) cyclefreeP(all_0_7_7) = all_89_0_47
% 31.36/8.76 | (205) ssItem(all_70_2_36) = all_89_1_48
% 31.36/8.76 | (206) ~ (all_89_1_48 = 0) | all_89_0_47 = 0
% 31.36/8.76 |
% 31.36/8.76 | Instantiating (200) with all_91_0_49, all_91_1_50 yields:
% 31.36/8.76 | (207) strictorderP(all_0_7_7) = all_91_0_49 & ssItem(all_70_2_36) = all_91_1_50 & ( ~ (all_91_1_50 = 0) | all_91_0_49 = 0)
% 31.36/8.76 |
% 31.36/8.76 | Applying alpha-rule on (207) yields:
% 31.36/8.76 | (208) strictorderP(all_0_7_7) = all_91_0_49
% 31.36/8.76 | (209) ssItem(all_70_2_36) = all_91_1_50
% 31.36/8.76 | (210) ~ (all_91_1_50 = 0) | all_91_0_49 = 0
% 31.36/8.76 |
% 31.36/8.76 | Instantiating (198) with all_93_0_51, all_93_1_52 yields:
% 31.36/8.76 | (211) strictorderedP(all_0_7_7) = all_93_0_51 & ssItem(all_70_2_36) = all_93_1_52 & ( ~ (all_93_1_52 = 0) | all_93_0_51 = 0)
% 31.36/8.76 |
% 31.36/8.76 | Applying alpha-rule on (211) yields:
% 31.36/8.76 | (212) strictorderedP(all_0_7_7) = all_93_0_51
% 31.36/8.76 | (213) ssItem(all_70_2_36) = all_93_1_52
% 31.36/8.76 | (214) ~ (all_93_1_52 = 0) | all_93_0_51 = 0
% 31.36/8.76 |
% 31.36/8.76 | Instantiating (197) with all_95_0_53, all_95_1_54 yields:
% 31.36/8.76 | (215) duplicatefreeP(all_0_7_7) = all_95_0_53 & ssItem(all_70_2_36) = all_95_1_54 & ( ~ (all_95_1_54 = 0) | all_95_0_53 = 0)
% 31.36/8.76 |
% 31.36/8.76 | Applying alpha-rule on (215) yields:
% 31.36/8.76 | (216) duplicatefreeP(all_0_7_7) = all_95_0_53
% 31.36/8.76 | (217) ssItem(all_70_2_36) = all_95_1_54
% 31.36/8.76 | (218) ~ (all_95_1_54 = 0) | all_95_0_53 = 0
% 31.36/8.76 |
% 31.36/8.76 | Instantiating (199) with all_97_0_55, all_97_1_56 yields:
% 31.36/8.76 | (219) totalorderedP(all_0_7_7) = all_97_0_55 & ssItem(all_70_2_36) = all_97_1_56 & ( ~ (all_97_1_56 = 0) | all_97_0_55 = 0)
% 31.36/8.76 |
% 31.36/8.76 | Applying alpha-rule on (219) yields:
% 31.36/8.76 | (220) totalorderedP(all_0_7_7) = all_97_0_55
% 31.36/8.76 | (221) ssItem(all_70_2_36) = all_97_1_56
% 31.36/8.76 | (222) ~ (all_97_1_56 = 0) | all_97_0_55 = 0
% 31.36/8.76 |
% 31.36/8.76 | Instantiating (196) with all_99_0_57, all_99_1_58 yields:
% 31.36/8.76 | (223) equalelemsP(all_0_7_7) = all_99_0_57 & ssItem(all_70_2_36) = all_99_1_58 & ( ~ (all_99_1_58 = 0) | all_99_0_57 = 0)
% 31.36/8.76 |
% 31.36/8.77 | Applying alpha-rule on (223) yields:
% 31.36/8.77 | (224) equalelemsP(all_0_7_7) = all_99_0_57
% 31.36/8.77 | (225) ssItem(all_70_2_36) = all_99_1_58
% 31.36/8.77 | (226) ~ (all_99_1_58 = 0) | all_99_0_57 = 0
% 31.36/8.77 |
% 31.36/8.77 | Instantiating (195) with all_101_0_59, all_101_1_60 yields:
% 31.36/8.77 | (227) hd(all_0_7_7) = all_101_0_59 & ssItem(all_70_2_36) = all_101_1_60 & ( ~ (all_101_1_60 = 0) | all_101_0_59 = all_70_2_36)
% 31.36/8.77 |
% 31.36/8.77 | Applying alpha-rule on (227) yields:
% 31.36/8.77 | (228) hd(all_0_7_7) = all_101_0_59
% 31.36/8.77 | (229) ssItem(all_70_2_36) = all_101_1_60
% 31.36/8.77 | (230) ~ (all_101_1_60 = 0) | all_101_0_59 = all_70_2_36
% 31.36/8.77 |
% 31.36/8.77 | Instantiating (201) with all_103_0_61, all_103_1_62 yields:
% 31.36/8.77 | (231) totalorderP(all_0_7_7) = all_103_0_61 & ssItem(all_70_2_36) = all_103_1_62 & ( ~ (all_103_1_62 = 0) | all_103_0_61 = 0)
% 31.36/8.77 |
% 31.36/8.77 | Applying alpha-rule on (231) yields:
% 31.36/8.77 | (232) totalorderP(all_0_7_7) = all_103_0_61
% 31.36/8.77 | (233) ssItem(all_70_2_36) = all_103_1_62
% 31.36/8.77 | (234) ~ (all_103_1_62 = 0) | all_103_0_61 = 0
% 31.36/8.77 |
% 31.36/8.77 | Instantiating (194) with all_114_0_74, all_114_1_75 yields:
% 31.36/8.77 | (235) tl(all_0_7_7) = all_114_0_74 & ssItem(all_70_2_36) = all_114_1_75 & ( ~ (all_114_1_75 = 0) | all_114_0_74 = nil)
% 31.36/8.77 |
% 31.36/8.77 | Applying alpha-rule on (235) yields:
% 31.36/8.77 | (236) tl(all_0_7_7) = all_114_0_74
% 31.36/8.77 | (237) ssItem(all_70_2_36) = all_114_1_75
% 31.36/8.77 | (238) ~ (all_114_1_75 = 0) | all_114_0_74 = nil
% 31.36/8.77 |
% 31.36/8.77 | Instantiating formula (116) with all_0_7_7, all_93_0_51, all_0_6_6 and discharging atoms strictorderedP(all_0_7_7) = all_93_0_51, strictorderedP(all_0_7_7) = all_0_6_6, yields:
% 31.36/8.77 | (239) all_93_0_51 = all_0_6_6
% 31.36/8.77 |
% 31.36/8.77 | Instantiating formula (103) with all_70_2_36, all_103_1_62, all_114_1_75 and discharging atoms ssItem(all_70_2_36) = all_114_1_75, ssItem(all_70_2_36) = all_103_1_62, yields:
% 31.36/8.77 | (240) all_114_1_75 = all_103_1_62
% 31.36/8.77 |
% 31.36/8.77 | Instantiating formula (103) with all_70_2_36, all_101_1_60, all_114_1_75 and discharging atoms ssItem(all_70_2_36) = all_114_1_75, ssItem(all_70_2_36) = all_101_1_60, yields:
% 31.36/8.77 | (241) all_114_1_75 = all_101_1_60
% 31.36/8.77 |
% 31.36/8.77 | Instantiating formula (103) with all_70_2_36, all_99_1_58, all_103_1_62 and discharging atoms ssItem(all_70_2_36) = all_103_1_62, ssItem(all_70_2_36) = all_99_1_58, yields:
% 31.36/8.77 | (242) all_103_1_62 = all_99_1_58
% 31.36/8.77 |
% 31.36/8.77 | Instantiating formula (103) with all_70_2_36, all_97_1_56, 0 and discharging atoms ssItem(all_70_2_36) = all_97_1_56, ssItem(all_70_2_36) = 0, yields:
% 31.36/8.77 | (243) all_97_1_56 = 0
% 31.36/8.77 |
% 31.36/8.77 | Instantiating formula (103) with all_70_2_36, all_95_1_54, all_97_1_56 and discharging atoms ssItem(all_70_2_36) = all_97_1_56, ssItem(all_70_2_36) = all_95_1_54, yields:
% 31.36/8.77 | (244) all_97_1_56 = all_95_1_54
% 31.36/8.77 |
% 31.36/8.77 | Instantiating formula (103) with all_70_2_36, all_93_1_52, all_99_1_58 and discharging atoms ssItem(all_70_2_36) = all_99_1_58, ssItem(all_70_2_36) = all_93_1_52, yields:
% 31.36/8.77 | (245) all_99_1_58 = all_93_1_52
% 31.36/8.77 |
% 31.36/8.77 | Instantiating formula (103) with all_70_2_36, all_93_1_52, all_95_1_54 and discharging atoms ssItem(all_70_2_36) = all_95_1_54, ssItem(all_70_2_36) = all_93_1_52, yields:
% 31.36/8.77 | (246) all_95_1_54 = all_93_1_52
% 31.36/8.77 |
% 31.36/8.77 | Instantiating formula (103) with all_70_2_36, all_91_1_50, all_95_1_54 and discharging atoms ssItem(all_70_2_36) = all_95_1_54, ssItem(all_70_2_36) = all_91_1_50, yields:
% 31.36/8.77 | (247) all_95_1_54 = all_91_1_50
% 31.36/8.77 |
% 31.36/8.77 | Instantiating formula (103) with all_70_2_36, all_89_1_48, all_103_1_62 and discharging atoms ssItem(all_70_2_36) = all_103_1_62, ssItem(all_70_2_36) = all_89_1_48, yields:
% 31.36/8.77 | (248) all_103_1_62 = all_89_1_48
% 31.36/8.77 |
% 31.36/8.77 | Combining equations (240,241) yields a new equation:
% 31.36/8.77 | (249) all_103_1_62 = all_101_1_60
% 31.36/8.77 |
% 31.36/8.77 | Simplifying 249 yields:
% 31.36/8.77 | (250) all_103_1_62 = all_101_1_60
% 31.36/8.77 |
% 31.36/8.77 | Combining equations (242,250) yields a new equation:
% 31.36/8.77 | (251) all_101_1_60 = all_99_1_58
% 31.36/8.77 |
% 31.36/8.77 | Combining equations (248,250) yields a new equation:
% 31.36/8.77 | (252) all_101_1_60 = all_89_1_48
% 31.36/8.77 |
% 31.36/8.77 | Combining equations (251,252) yields a new equation:
% 31.36/8.77 | (253) all_99_1_58 = all_89_1_48
% 31.36/8.77 |
% 31.36/8.77 | Simplifying 253 yields:
% 31.36/8.77 | (254) all_99_1_58 = all_89_1_48
% 31.36/8.77 |
% 31.36/8.77 | Combining equations (245,254) yields a new equation:
% 31.36/8.77 | (255) all_93_1_52 = all_89_1_48
% 31.36/8.77 |
% 31.36/8.77 | Simplifying 255 yields:
% 31.36/8.77 | (256) all_93_1_52 = all_89_1_48
% 31.36/8.77 |
% 31.36/8.77 | Combining equations (244,243) yields a new equation:
% 31.36/8.77 | (257) all_95_1_54 = 0
% 31.36/8.77 |
% 31.36/8.77 | Simplifying 257 yields:
% 31.36/8.77 | (258) all_95_1_54 = 0
% 31.36/8.77 |
% 31.36/8.77 | Combining equations (246,247) yields a new equation:
% 31.36/8.77 | (259) all_93_1_52 = all_91_1_50
% 31.36/8.77 |
% 31.36/8.77 | Simplifying 259 yields:
% 31.36/8.77 | (260) all_93_1_52 = all_91_1_50
% 31.36/8.77 |
% 31.36/8.77 | Combining equations (258,247) yields a new equation:
% 31.36/8.77 | (261) all_91_1_50 = 0
% 31.36/8.77 |
% 31.36/8.77 | Combining equations (260,256) yields a new equation:
% 31.36/8.77 | (262) all_91_1_50 = all_89_1_48
% 31.36/8.77 |
% 31.36/8.77 | Simplifying 262 yields:
% 31.36/8.77 | (263) all_91_1_50 = all_89_1_48
% 31.36/8.77 |
% 31.36/8.77 | Combining equations (263,261) yields a new equation:
% 31.36/8.77 | (264) all_89_1_48 = 0
% 31.36/8.77 |
% 31.36/8.77 | Simplifying 264 yields:
% 31.36/8.77 | (265) all_89_1_48 = 0
% 31.36/8.77 |
% 31.36/8.77 | Combining equations (265,256) yields a new equation:
% 31.36/8.77 | (266) all_93_1_52 = 0
% 31.36/8.77 |
% 31.36/8.77 +-Applying beta-rule and splitting (214), into two cases.
% 31.36/8.77 |-Branch one:
% 31.36/8.77 | (267) ~ (all_93_1_52 = 0)
% 31.36/8.77 |
% 31.36/8.77 | Equations (266) can reduce 267 to:
% 31.36/8.77 | (156) $false
% 31.36/8.77 |
% 31.36/8.77 |-The branch is then unsatisfiable
% 31.36/8.77 |-Branch two:
% 31.36/8.77 | (266) all_93_1_52 = 0
% 31.36/8.77 | (270) all_93_0_51 = 0
% 31.36/8.77 |
% 31.36/8.77 | Combining equations (239,270) yields a new equation:
% 31.36/8.77 | (271) all_0_6_6 = 0
% 31.36/8.77 |
% 31.36/8.77 | Simplifying 271 yields:
% 31.36/8.77 | (167) all_0_6_6 = 0
% 31.36/8.77 |
% 31.36/8.77 | Equations (167) can reduce 158 to:
% 31.36/8.77 | (156) $false
% 31.36/8.77 |
% 31.36/8.77 |-The branch is then unsatisfiable
% 31.36/8.77 |-Branch two:
% 31.36/8.77 | (274) ~ (all_70_2_36 = 0) & ssList(all_0_7_7) = all_70_2_36
% 31.36/8.77 |
% 31.36/8.77 | Applying alpha-rule on (274) yields:
% 31.36/8.77 | (275) ~ (all_70_2_36 = 0)
% 31.36/8.77 | (276) ssList(all_0_7_7) = all_70_2_36
% 31.36/8.77 |
% 31.36/8.77 | Instantiating formula (143) with all_0_7_7, all_70_2_36, 0 and discharging atoms ssList(all_0_7_7) = all_70_2_36, ssList(all_0_7_7) = 0, yields:
% 31.36/8.77 | (277) all_70_2_36 = 0
% 31.36/8.77 |
% 31.36/8.77 | Equations (277) can reduce 275 to:
% 31.36/8.77 | (156) $false
% 31.36/8.77 |
% 31.36/8.77 |-The branch is then unsatisfiable
% 31.36/8.77 |-Branch two:
% 31.36/8.77 | (179) ~ (all_0_2_2 = 0)
% 31.36/8.77 | (280) ? [v0] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 31.36/8.77 |
% 31.36/8.77 | Instantiating (280) with all_62_0_91 yields:
% 31.36/8.77 | (281) ~ (all_62_0_91 = 0) & ssList(nil) = all_62_0_91
% 31.36/8.77 |
% 31.36/8.77 | Applying alpha-rule on (281) yields:
% 31.36/8.77 | (282) ~ (all_62_0_91 = 0)
% 31.36/8.77 | (283) ssList(nil) = all_62_0_91
% 31.36/8.77 |
% 31.36/8.77 | Instantiating formula (143) with nil, all_62_0_91, 0 and discharging atoms ssList(nil) = all_62_0_91, ssList(nil) = 0, yields:
% 31.36/8.77 | (284) all_62_0_91 = 0
% 31.36/8.77 |
% 31.36/8.77 | Equations (284) can reduce 282 to:
% 31.36/8.77 | (156) $false
% 31.36/8.77 |
% 31.36/8.77 |-The branch is then unsatisfiable
% 31.36/8.77 |-Branch two:
% 31.36/8.77 | (286) segmentP(nil, all_0_7_7) = 0
% 31.36/8.77 | (287) all_0_7_7 = nil | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_7_7) = v0)
% 31.36/8.77 |
% 31.36/8.77 +-Applying beta-rule and splitting (162), into two cases.
% 31.36/8.77 |-Branch one:
% 31.36/8.77 | (288) all_0_7_7 = nil
% 31.36/8.77 |
% 31.36/8.77 | Equations (288) can reduce 171 to:
% 31.36/8.77 | (156) $false
% 31.36/8.77 |
% 31.36/8.77 |-The branch is then unsatisfiable
% 31.36/8.77 |-Branch two:
% 31.36/8.77 | (171) ~ (all_0_7_7 = nil)
% 31.36/8.77 | (291) ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_7_7 & ssItem(v1) = 0)
% 31.36/8.77 |
% 31.36/8.77 +-Applying beta-rule and splitting (287), into two cases.
% 31.36/8.77 |-Branch one:
% 31.36/8.77 | (288) all_0_7_7 = nil
% 31.36/8.77 |
% 31.36/8.77 | Equations (288) can reduce 171 to:
% 31.36/8.77 | (156) $false
% 31.36/8.77 |
% 31.36/8.77 |-The branch is then unsatisfiable
% 31.36/8.77 |-Branch two:
% 31.36/8.77 | (171) ~ (all_0_7_7 = nil)
% 31.36/8.77 | (295) ? [v0] : ( ~ (v0 = 0) & ssList(all_0_7_7) = v0)
% 31.36/8.77 |
% 31.36/8.77 | Instantiating (295) with all_49_0_94 yields:
% 31.36/8.77 | (296) ~ (all_49_0_94 = 0) & ssList(all_0_7_7) = all_49_0_94
% 31.36/8.77 |
% 31.36/8.77 | Applying alpha-rule on (296) yields:
% 31.36/8.77 | (297) ~ (all_49_0_94 = 0)
% 31.36/8.77 | (298) ssList(all_0_7_7) = all_49_0_94
% 31.36/8.77 |
% 31.36/8.77 +-Applying beta-rule and splitting (164), into two cases.
% 31.36/8.77 |-Branch one:
% 31.36/8.77 | (172) ~ (segmentP(nil, all_0_7_7) = 0)
% 31.36/8.77 |
% 31.36/8.77 | Using (286) and (172) yields:
% 31.36/8.77 | (185) $false
% 31.36/8.77 |
% 31.36/8.77 |-The branch is then unsatisfiable
% 31.36/8.77 |-Branch two:
% 31.36/8.77 | (286) segmentP(nil, all_0_7_7) = 0
% 31.36/8.77 | (302) ? [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_7_7) = v2) | ( ~ (v0 = 0) & ssList(all_0_7_7) = v0))
% 31.36/8.77 |
% 31.36/8.77 +-Applying beta-rule and splitting (163), into two cases.
% 31.36/8.77 |-Branch one:
% 31.36/8.77 | (172) ~ (segmentP(nil, all_0_7_7) = 0)
% 31.36/8.77 |
% 31.36/8.77 | Using (286) and (172) yields:
% 31.36/8.77 | (185) $false
% 31.36/8.77 |
% 31.36/8.77 |-The branch is then unsatisfiable
% 31.36/8.77 |-Branch two:
% 31.36/8.77 | (286) segmentP(nil, all_0_7_7) = 0
% 31.36/8.77 | (306) all_0_7_7 = nil | ? [v0] : ? [v1] : (segmentP(all_0_7_7, nil) = v1 & ssList(all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 31.36/8.78 |
% 31.36/8.78 +-Applying beta-rule and splitting (306), into two cases.
% 31.36/8.78 |-Branch one:
% 31.36/8.78 | (288) all_0_7_7 = nil
% 31.36/8.78 |
% 31.36/8.78 | Equations (288) can reduce 171 to:
% 31.36/8.78 | (156) $false
% 31.36/8.78 |
% 31.36/8.78 |-The branch is then unsatisfiable
% 31.36/8.78 |-Branch two:
% 31.36/8.78 | (171) ~ (all_0_7_7 = nil)
% 31.36/8.78 | (310) ? [v0] : ? [v1] : (segmentP(all_0_7_7, nil) = v1 & ssList(all_0_7_7) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 31.36/8.78 |
% 31.36/8.78 | Instantiating (310) with all_62_0_101, all_62_1_102 yields:
% 31.36/8.78 | (311) segmentP(all_0_7_7, nil) = all_62_0_101 & ssList(all_0_7_7) = all_62_1_102 & ( ~ (all_62_0_101 = 0) | ~ (all_62_1_102 = 0))
% 31.36/8.78 |
% 31.36/8.78 | Applying alpha-rule on (311) yields:
% 31.36/8.78 | (312) segmentP(all_0_7_7, nil) = all_62_0_101
% 31.36/8.78 | (313) ssList(all_0_7_7) = all_62_1_102
% 31.36/8.78 | (314) ~ (all_62_0_101 = 0) | ~ (all_62_1_102 = 0)
% 31.36/8.78 |
% 31.36/8.78 | Instantiating formula (143) with all_0_7_7, all_62_1_102, 0 and discharging atoms ssList(all_0_7_7) = all_62_1_102, ssList(all_0_7_7) = 0, yields:
% 31.36/8.78 | (315) all_62_1_102 = 0
% 31.36/8.78 |
% 31.36/8.78 | Instantiating formula (143) with all_0_7_7, all_49_0_94, all_62_1_102 and discharging atoms ssList(all_0_7_7) = all_62_1_102, ssList(all_0_7_7) = all_49_0_94, yields:
% 31.36/8.78 | (316) all_62_1_102 = all_49_0_94
% 31.36/8.78 |
% 31.36/8.78 | Combining equations (315,316) yields a new equation:
% 31.36/8.78 | (317) all_49_0_94 = 0
% 31.36/8.78 |
% 31.36/8.78 | Equations (317) can reduce 297 to:
% 31.36/8.78 | (156) $false
% 31.36/8.78 |
% 31.36/8.78 |-The branch is then unsatisfiable
% 31.36/8.78 |-Branch two:
% 31.36/8.78 | (319) strictorderedP(nil) = all_0_6_6
% 31.36/8.78 | (167) all_0_6_6 = 0
% 31.36/8.78 |
% 31.36/8.78 | Equations (167) can reduce 158 to:
% 31.36/8.78 | (156) $false
% 31.36/8.78 |
% 31.36/8.78 |-The branch is then unsatisfiable
% 31.36/8.78 % SZS output end Proof for theBenchmark
% 31.36/8.78
% 31.36/8.78 8179ms
%------------------------------------------------------------------------------