TSTP Solution File: SWC293+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWC293+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Tue Jul 19 20:17:19 EDT 2022
% Result : Theorem 18.92s 6.29s
% Output : Proof 22.59s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : SWC293+1 : TPTP v8.1.0. Released v2.4.0.
% 0.05/0.10 % Command : ePrincess-casc -timeout=%d %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Sun Jun 12 22:50:41 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.14/0.49 ____ _
% 0.14/0.49 ___ / __ \_____(_)___ ________ __________
% 0.14/0.49 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.14/0.49 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.14/0.49 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.14/0.49
% 0.14/0.49 A Theorem Prover for First-Order Logic
% 0.14/0.49 (ePrincess v.1.0)
% 0.14/0.49
% 0.14/0.49 (c) Philipp Rümmer, 2009-2015
% 0.14/0.49 (c) Peter Backeman, 2014-2015
% 0.14/0.49 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.14/0.49 Free software under GNU Lesser General Public License (LGPL).
% 0.14/0.49 Bug reports to peter@backeman.se
% 0.14/0.49
% 0.14/0.49 For more information, visit http://user.uu.se/~petba168/breu/
% 0.14/0.49
% 0.14/0.49 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.54/0.54 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 1.99/0.96 Prover 0: Preprocessing ...
% 4.24/1.54 Prover 0: Constructing countermodel ...
% 16.91/5.84 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 17.48/5.96 Prover 1: Preprocessing ...
% 18.50/6.22 Prover 1: Constructing countermodel ...
% 18.92/6.28 Prover 1: proved (447ms)
% 18.92/6.29 Prover 0: stopped
% 18.92/6.29
% 18.92/6.29 No countermodel exists, formula is valid
% 18.92/6.29 % SZS status Theorem for theBenchmark
% 18.92/6.29
% 18.92/6.29 Generating proof ... found it (size 77)
% 21.59/6.97
% 21.59/6.97 % SZS output start Proof for theBenchmark
% 21.59/6.97 Assumed formulas after preprocessing and simplification:
% 21.59/6.97 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ( ~ (v9 = v8) & ~ (v2 = 0) & ~ (v0 = 0) & equalelemsP(nil) = 0 & duplicatefreeP(nil) = 0 & strictorderedP(v1) = v2 & strictorderedP(nil) = 0 & totalorderedP(nil) = 0 & strictorderP(nil) = 0 & totalorderP(nil) = 0 & cyclefreeP(nil) = 0 & singletonP(nil) = v0 & ssList(v3) = 0 & ssList(v1) = 0 & ssList(nil) = 0 & ssItem(v9) = 0 & ssItem(v8) = 0 & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v13 = 0 | ~ (strictorderedP(v10) = 0) | ~ (lt(v11, v12) = v13) | ~ (ssList(v14) = 0) | ~ (cons(v12, v18) = v19) | ~ (cons(v11, v15) = v16) | ~ (app(v17, v19) = v10) | ~ (app(v14, v16) = v17) | ~ (ssItem(v11) = 0) | ? [v20] : (( ~ (v20 = 0) & ssList(v18) = v20) | ( ~ (v20 = 0) & ssList(v15) = v20) | ( ~ (v20 = 0) & ssList(v10) = v20) | ( ~ (v20 = 0) & ssItem(v12) = v20))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v13 = 0 | ~ (totalorderedP(v10) = 0) | ~ (leq(v11, v12) = v13) | ~ (ssList(v14) = 0) | ~ (cons(v12, v18) = v19) | ~ (cons(v11, v15) = v16) | ~ (app(v17, v19) = v10) | ~ (app(v14, v16) = v17) | ~ (ssItem(v11) = 0) | ? [v20] : (( ~ (v20 = 0) & ssList(v18) = v20) | ( ~ (v20 = 0) & ssList(v15) = v20) | ( ~ (v20 = 0) & ssList(v10) = v20) | ( ~ (v20 = 0) & ssItem(v12) = v20))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (duplicatefreeP(v10) = 0) | ~ (ssList(v12) = 0) | ~ (cons(v11, v16) = v17) | ~ (cons(v11, v13) = v14) | ~ (app(v15, v17) = v10) | ~ (app(v12, v14) = v15) | ~ (ssItem(v11) = 0) | ? [v18] : (( ~ (v18 = 0) & ssList(v16) = v18) | ( ~ (v18 = 0) & ssList(v13) = v18) | ( ~ (v18 = 0) & ssList(v10) = v18))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v16 = 0 | ~ (segmentP(v15, v11) = v16) | ~ (segmentP(v10, v11) = 0) | ~ (ssList(v10) = 0) | ~ (app(v13, v14) = v15) | ~ (app(v12, v10) = v13) | ? [v17] : (( ~ (v17 = 0) & ssList(v14) = v17) | ( ~ (v17 = 0) & ssList(v12) = v17) | ( ~ (v17 = 0) & ssList(v11) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v12 = v11 | ~ (equalelemsP(v10) = 0) | ~ (ssList(v13) = 0) | ~ (cons(v12, v14) = v15) | ~ (cons(v11, v15) = v16) | ~ (app(v13, v16) = v10) | ~ (ssItem(v12) = 0) | ~ (ssItem(v11) = 0) | ? [v17] : (( ~ (v17 = 0) & ssList(v14) = v17) | ( ~ (v17 = 0) & ssList(v10) = v17))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (frontsegP(v13, v15) = v16) | ~ (cons(v11, v14) = v15) | ~ (cons(v10, v12) = v13) | ~ (ssItem(v11) = 0) | ~ (ssItem(v10) = 0) | ? [v17] : ? [v18] : (( ~ (v17 = 0) & ssList(v12) = v17) | (frontsegP(v12, v14) = v18 & ssList(v14) = v17 & ( ~ (v17 = 0) | (( ~ (v18 = 0) | ~ (v11 = v10) | v16 = 0) & ( ~ (v16 = 0) | (v18 = 0 & v11 = v10))))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = 0 | ~ (segmentP(v10, v11) = v12) | ~ (ssList(v10) = 0) | ~ (app(v14, v15) = v10) | ~ (app(v13, v11) = v14) | ? [v16] : (( ~ (v16 = 0) & ssList(v15) = v16) | ( ~ (v16 = 0) & ssList(v13) = v16) | ( ~ (v16 = 0) & ssList(v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = 0 | ~ (memberP(v10, v11) = v12) | ~ (ssList(v13) = 0) | ~ (ssList(v10) = 0) | ~ (cons(v11, v14) = v15) | ~ (app(v13, v15) = v10) | ? [v16] : (( ~ (v16 = 0) & ssList(v14) = v16) | ( ~ (v16 = 0) & ssItem(v11) = v16))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (memberP(v14, v10) = v15) | ~ (memberP(v11, v10) = v12) | ~ (app(v11, v13) = v14) | ~ (ssItem(v10) = 0) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & ssList(v11) = v16) | (memberP(v13, v10) = v17 & ssList(v13) = v16 & ( ~ (v16 = 0) | (( ~ (v15 = 0) | v17 = 0 | v12 = 0) & (v15 = 0 | ( ~ (v17 = 0) & ~ (v12 = 0)))))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (ssList(v10) = 0) | ~ (cons(v13, v11) = v14) | ~ (app(v14, v10) = v15) | ~ (app(v11, v10) = v12) | ? [v16] : ? [v17] : (( ~ (v16 = 0) & ssList(v11) = v16) | (cons(v13, v12) = v17 & ssItem(v13) = v16 & ( ~ (v16 = 0) | v17 = v15)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v12 | ~ (ssList(v11) = 0) | ~ (ssList(v10) = 0) | ~ (cons(v14, v11) = v13) | ~ (cons(v12, v10) = v13) | ? [v15] : (( ~ (v15 = 0) & ssItem(v14) = v15) | ( ~ (v15 = 0) & ssItem(v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (rearsegP(v13, v11) = v14) | ~ (rearsegP(v10, v11) = 0) | ~ (ssList(v10) = 0) | ~ (app(v12, v10) = v13) | ? [v15] : (( ~ (v15 = 0) & ssList(v12) = v15) | ( ~ (v15 = 0) & ssList(v11) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (frontsegP(v13, v11) = v14) | ~ (frontsegP(v10, v11) = 0) | ~ (ssList(v10) = 0) | ~ (app(v10, v12) = v13) | ? [v15] : (( ~ (v15 = 0) & ssList(v12) = v15) | ( ~ (v15 = 0) & ssList(v11) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = v10 | ~ (ssList(v11) = 0) | ~ (ssList(v10) = 0) | ~ (cons(v14, v11) = v13) | ~ (cons(v12, v10) = v13) | ? [v15] : (( ~ (v15 = 0) & ssItem(v14) = v15) | ( ~ (v15 = 0) & ssItem(v12) = v15))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (memberP(v13, v10) = v14) | ~ (cons(v11, v12) = v13) | ~ (ssItem(v11) = 0) | ~ (ssItem(v10) = 0) | ? [v15] : ? [v16] : (memberP(v12, v10) = v16 & ssList(v12) = v15 & ( ~ (v15 = 0) | (( ~ (v14 = 0) | v16 = 0 | v11 = v10) & (v14 = 0 | ( ~ (v16 = 0) & ~ (v11 = v10))))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (ssList(v10) = 0) | ~ (app(v12, v13) = v14) | ~ (app(v10, v11) = v12) | ? [v15] : ? [v16] : ? [v17] : (( ~ (v15 = 0) & ssList(v11) = v15) | (ssList(v13) = v15 & app(v11, v13) = v16 & app(v10, v16) = v17 & ( ~ (v15 = 0) | v17 = v14)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | v10 = nil | ~ (tl(v10) = v12) | ~ (hd(v10) = v11) | ~ (cons(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & ssList(v10) = v14)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (ssList(v10) = 0) | ~ (app(v13, v11) = v12) | ~ (app(v10, v11) = v12) | ? [v14] : (( ~ (v14 = 0) & ssList(v13) = v14) | ( ~ (v14 = 0) & ssList(v11) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = v10 | ~ (ssList(v10) = 0) | ~ (app(v11, v13) = v12) | ~ (app(v11, v10) = v12) | ? [v14] : (( ~ (v14 = 0) & ssList(v13) = v14) | ( ~ (v14 = 0) & ssList(v11) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (gt(v10, v12) = v13) | ~ (gt(v10, v11) = 0) | ~ (ssItem(v10) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssItem(v11) = v14) | (gt(v11, v12) = v15 & ssItem(v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (geq(v10, v12) = v13) | ~ (geq(v10, v11) = 0) | ~ (ssItem(v10) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssItem(v11) = v14) | (geq(v11, v12) = v15 & ssItem(v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (lt(v10, v12) = v13) | ~ (lt(v10, v11) = 0) | ~ (ssItem(v10) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssItem(v11) = v14) | (lt(v11, v12) = v15 & ssItem(v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (lt(v10, v12) = v13) | ~ (leq(v10, v11) = 0) | ~ (ssItem(v10) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssItem(v11) = v14) | (lt(v11, v12) = v15 & ssItem(v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (leq(v10, v12) = v13) | ~ (leq(v10, v11) = 0) | ~ (ssItem(v10) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssItem(v11) = v14) | (leq(v11, v12) = v15 & ssItem(v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (segmentP(v10, v12) = v13) | ~ (segmentP(v10, v11) = 0) | ~ (ssList(v10) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssList(v11) = v14) | (segmentP(v11, v12) = v15 & ssList(v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (rearsegP(v10, v12) = v13) | ~ (rearsegP(v10, v11) = 0) | ~ (ssList(v10) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssList(v11) = v14) | (rearsegP(v11, v12) = v15 & ssList(v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (frontsegP(v10, v12) = v13) | ~ (frontsegP(v10, v11) = 0) | ~ (ssList(v10) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssList(v11) = v14) | (frontsegP(v11, v12) = v15 & ssList(v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (rearsegP(v10, v11) = v12) | ~ (ssList(v10) = 0) | ~ (app(v13, v11) = v10) | ? [v14] : (( ~ (v14 = 0) & ssList(v13) = v14) | ( ~ (v14 = 0) & ssList(v11) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (frontsegP(v10, v11) = v12) | ~ (ssList(v10) = 0) | ~ (app(v11, v13) = v10) | ? [v14] : (( ~ (v14 = 0) & ssList(v13) = v14) | ( ~ (v14 = 0) & ssList(v11) = v14))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (gt(v13, v12) = v11) | ~ (gt(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (geq(v13, v12) = v11) | ~ (geq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (lt(v13, v12) = v11) | ~ (lt(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (leq(v13, v12) = v11) | ~ (leq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (segmentP(v13, v12) = v11) | ~ (segmentP(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (rearsegP(v13, v12) = v11) | ~ (rearsegP(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (frontsegP(v13, v12) = v11) | ~ (frontsegP(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (memberP(v13, v12) = v11) | ~ (memberP(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (cons(v13, v12) = v11) | ~ (cons(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (app(v13, v12) = v11) | ~ (app(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v11 = v10 | ~ (neq(v13, v12) = v11) | ~ (neq(v13, v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = nil | ~ (tl(v10) = v11) | ~ (app(v11, v12) = v13) | ? [v14] : ? [v15] : ? [v16] : (( ~ (v14 = 0) & ssList(v10) = v14) | (tl(v15) = v16 & ssList(v12) = v14 & app(v10, v12) = v15 & ( ~ (v14 = 0) | v16 = v13)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = nil | ~ (hd(v10) = v11) | ~ (app(v10, v12) = v13) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssList(v10) = v14) | (hd(v13) = v15 & ssList(v12) = v14 & ( ~ (v14 = 0) | v15 = v11)))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (hd(v11) = v12) | ~ (lt(v10, v12) = v13) | ~ (ssItem(v10) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (strictorderedP(v15) = v16 & strictorderedP(v11) = v17 & ssList(v11) = v14 & cons(v10, v11) = v15 & ( ~ (v14 = 0) | (( ~ (v16 = 0) | v11 = nil | (v17 = 0 & v13 = 0)) & (v16 = 0 | ( ~ (v11 = nil) & ( ~ (v17 = 0) | ~ (v13 = 0)))))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (hd(v11) = v12) | ~ (leq(v10, v12) = v13) | ~ (ssItem(v10) = 0) | ? [v14] : ? [v15] : ? [v16] : ? [v17] : (totalorderedP(v15) = v16 & totalorderedP(v11) = v17 & ssList(v11) = v14 & cons(v10, v11) = v15 & ( ~ (v14 = 0) | (( ~ (v16 = 0) | v11 = nil | (v17 = 0 & v13 = 0)) & (v16 = 0 | ( ~ (v11 = nil) & ( ~ (v17 = 0) | ~ (v13 = 0)))))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (strictorderP(v10) = 0) | ~ (lt(v11, v12) = v13) | ~ (ssItem(v11) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssList(v10) = v14) | (lt(v12, v11) = v15 & ssItem(v12) = v14 & ( ~ (v14 = 0) | ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v15 = 0 | v13 = 0 | ~ (ssList(v16) = 0) | ~ (cons(v12, v20) = v21) | ~ (cons(v11, v17) = v18) | ~ (app(v19, v21) = v10) | ~ (app(v16, v18) = v19) | ? [v22] : (( ~ (v22 = 0) & ssList(v20) = v22) | ( ~ (v22 = 0) & ssList(v17) = v22))))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (totalorderP(v10) = 0) | ~ (leq(v11, v12) = v13) | ~ (ssItem(v11) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssList(v10) = v14) | (leq(v12, v11) = v15 & ssItem(v12) = v14 & ( ~ (v14 = 0) | ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : (v15 = 0 | v13 = 0 | ~ (ssList(v16) = 0) | ~ (cons(v12, v20) = v21) | ~ (cons(v11, v17) = v18) | ~ (app(v19, v21) = v10) | ~ (app(v16, v18) = v19) | ? [v22] : (( ~ (v22 = 0) & ssList(v20) = v22) | ( ~ (v22 = 0) & ssList(v17) = v22))))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (cyclefreeP(v10) = 0) | ~ (leq(v11, v12) = v13) | ~ (ssItem(v11) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssList(v10) = v14) | (leq(v12, v11) = v15 & ssItem(v12) = v14 & ( ~ (v14 = 0) | ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ( ~ (v15 = 0) | ~ (v13 = 0) | ~ (ssList(v16) = 0) | ~ (cons(v12, v20) = v21) | ~ (cons(v11, v17) = v18) | ~ (app(v19, v21) = v10) | ~ (app(v16, v18) = v19) | ? [v22] : (( ~ (v22 = 0) & ssList(v20) = v22) | ( ~ (v22 = 0) & ssList(v17) = v22))))))) & ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (ssList(v10) = 0) | ~ (cons(v11, nil) = v12) | ~ (app(v12, v10) = v13) | ? [v14] : ? [v15] : (cons(v11, v10) = v15 & ssItem(v11) = v14 & ( ~ (v14 = 0) | v15 = v13))) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = v10 | ~ (lt(v10, v11) = v12) | ~ (ssItem(v10) = 0) | ? [v13] : ? [v14] : (leq(v10, v11) = v14 & ssItem(v11) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = v10 | ~ (ssList(v10) = 0) | ~ (neq(v10, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & ssList(v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | v11 = v10 | ~ (neq(v10, v11) = v12) | ~ (ssItem(v10) = 0) | ? [v13] : ( ~ (v13 = 0) & ssItem(v11) = v13)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (tl(v12) = v11) | ~ (tl(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (hd(v12) = v11) | ~ (hd(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (equalelemsP(v12) = v11) | ~ (equalelemsP(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (duplicatefreeP(v12) = v11) | ~ (duplicatefreeP(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (strictorderedP(v12) = v11) | ~ (strictorderedP(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (totalorderedP(v12) = v11) | ~ (totalorderedP(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (strictorderP(v12) = v11) | ~ (strictorderP(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (totalorderP(v12) = v11) | ~ (totalorderP(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (cyclefreeP(v12) = v11) | ~ (cyclefreeP(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (singletonP(v12) = v11) | ~ (singletonP(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (ssList(v12) = v11) | ~ (ssList(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = v10 | ~ (ssItem(v12) = v11) | ~ (ssItem(v12) = v10)) & ! [v10] : ! [v11] : ! [v12] : (v11 = 0 | ~ (singletonP(v10) = v11) | ~ (cons(v12, nil) = v10) | ? [v13] : (( ~ (v13 = 0) & ssList(v10) = v13) | ( ~ (v13 = 0) & ssItem(v12) = v13))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (gt(v10, v11) = v12) | ~ (ssItem(v10) = 0) | ? [v13] : ? [v14] : (lt(v11, v10) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | (( ~ (v14 = 0) | v12 = 0) & ( ~ (v12 = 0) | v14 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (geq(v10, v11) = v12) | ~ (ssItem(v10) = 0) | ? [v13] : ? [v14] : (leq(v11, v10) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | (( ~ (v14 = 0) | v12 = 0) & ( ~ (v12 = 0) | v14 = 0))))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (lt(v10, v11) = v12) | ~ (ssItem(v10) = 0) | ? [v13] : ? [v14] : (leq(v10, v11) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | (( ~ (v14 = 0) | v12 = 0 | v11 = v10) & ( ~ (v12 = 0) | (v14 = 0 & ~ (v11 = v10))))))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ssList(v10) = 0) | ~ (cons(v11, v10) = v12) | ? [v13] : ? [v14] : (tl(v12) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | v14 = v10))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ssList(v10) = 0) | ~ (cons(v11, v10) = v12) | ? [v13] : ? [v14] : (hd(v12) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | v14 = v11))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ssList(v10) = 0) | ~ (cons(v11, v10) = v12) | ? [v13] : ? [v14] : (ssList(v12) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v10] : ! [v11] : ! [v12] : ( ~ (ssList(v10) = 0) | ~ (app(v10, v11) = v12) | ? [v13] : ? [v14] : (ssList(v12) = v14 & ssList(v11) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v10] : ! [v11] : (v11 = v10 | ~ (geq(v10, v11) = 0) | ~ (ssItem(v10) = 0) | ? [v12] : ? [v13] : (geq(v11, v10) = v13 & ssItem(v11) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10] : ! [v11] : (v11 = v10 | ~ (leq(v10, v11) = 0) | ~ (ssItem(v10) = 0) | ? [v12] : ? [v13] : (leq(v11, v10) = v13 & ssItem(v11) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10] : ! [v11] : (v11 = v10 | ~ (segmentP(v10, v11) = 0) | ~ (ssList(v10) = 0) | ? [v12] : ? [v13] : (segmentP(v11, v10) = v13 & ssList(v11) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10] : ! [v11] : (v11 = v10 | ~ (rearsegP(v10, v11) = 0) | ~ (ssList(v10) = 0) | ? [v12] : ? [v13] : (rearsegP(v11, v10) = v13 & ssList(v11) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10] : ! [v11] : (v11 = v10 | ~ (frontsegP(v10, v11) = 0) | ~ (ssList(v10) = 0) | ? [v12] : ? [v13] : (frontsegP(v11, v10) = v13 & ssList(v11) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10] : ! [v11] : (v11 = v10 | ~ (app(v10, nil) = v11) | ? [v12] : ( ~ (v12 = 0) & ssList(v10) = v12)) & ! [v10] : ! [v11] : (v11 = v10 | ~ (app(nil, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & ssList(v10) = v12)) & ! [v10] : ! [v11] : (v11 = nil | ~ (ssList(v10) = 0) | ~ (app(v10, v11) = nil) | ? [v12] : ( ~ (v12 = 0) & ssList(v11) = v12)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (geq(v10, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & ssItem(v10) = v12)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (equalelemsP(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ((v22 = v10 & v19 = 0 & v17 = 0 & v15 = 0 & v13 = 0 & ~ (v14 = v12) & ssList(v18) = 0 & ssList(v16) = 0 & cons(v14, v18) = v20 & cons(v12, v20) = v21 & app(v16, v21) = v10 & ssItem(v14) = 0 & ssItem(v12) = 0) | ( ~ (v12 = 0) & ssList(v10) = v12))) & ! [v10] : ! [v11] : (v11 = 0 | ~ (duplicatefreeP(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = v10 & v23 = 0 & v19 = 0 & v17 = 0 & v15 = 0 & v14 = v12 & v13 = 0 & ssList(v22) = 0 & ssList(v18) = 0 & ssList(v16) = 0 & cons(v12, v22) = v24 & cons(v12, v18) = v20 & app(v21, v24) = v10 & app(v16, v20) = v21 & ssItem(v12) = 0) | ( ~ (v12 = 0) & ssList(v10) = v12))) & ! [v10] : ! [v11] : (v11 = 0 | ~ (strictorderedP(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ((v26 = v10 & v24 = 0 & v20 = 0 & v18 = 0 & v15 = 0 & v13 = 0 & ~ (v16 = 0) & lt(v12, v14) = v16 & ssList(v23) = 0 & ssList(v19) = 0 & ssList(v17) = 0 & cons(v14, v23) = v25 & cons(v12, v19) = v21 & app(v22, v25) = v10 & app(v17, v21) = v22 & ssItem(v14) = 0 & ssItem(v12) = 0) | ( ~ (v12 = 0) & ssList(v10) = v12))) & ! [v10] : ! [v11] : (v11 = 0 | ~ (totalorderedP(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ((v26 = v10 & v24 = 0 & v20 = 0 & v18 = 0 & v15 = 0 & v13 = 0 & ~ (v16 = 0) & leq(v12, v14) = v16 & ssList(v23) = 0 & ssList(v19) = 0 & ssList(v17) = 0 & cons(v14, v23) = v25 & cons(v12, v19) = v21 & app(v22, v25) = v10 & app(v17, v21) = v22 & ssItem(v14) = 0 & ssItem(v12) = 0) | ( ~ (v12 = 0) & ssList(v10) = v12))) & ! [v10] : ! [v11] : (v11 = 0 | ~ (strictorderP(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ((v27 = v10 & v25 = 0 & v21 = 0 & v19 = 0 & v15 = 0 & v13 = 0 & ~ (v17 = 0) & ~ (v16 = 0) & lt(v14, v12) = v17 & lt(v12, v14) = v16 & ssList(v24) = 0 & ssList(v20) = 0 & ssList(v18) = 0 & cons(v14, v24) = v26 & cons(v12, v20) = v22 & app(v23, v26) = v10 & app(v18, v22) = v23 & ssItem(v14) = 0 & ssItem(v12) = 0) | ( ~ (v12 = 0) & ssList(v10) = v12))) & ! [v10] : ! [v11] : (v11 = 0 | ~ (totalorderP(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ((v27 = v10 & v25 = 0 & v21 = 0 & v19 = 0 & v15 = 0 & v13 = 0 & ~ (v17 = 0) & ~ (v16 = 0) & leq(v14, v12) = v17 & leq(v12, v14) = v16 & ssList(v24) = 0 & ssList(v20) = 0 & ssList(v18) = 0 & cons(v14, v24) = v26 & cons(v12, v20) = v22 & app(v23, v26) = v10 & app(v18, v22) = v23 & ssItem(v14) = 0 & ssItem(v12) = 0) | ( ~ (v12 = 0) & ssList(v10) = v12))) & ! [v10] : ! [v11] : (v11 = 0 | ~ (cyclefreeP(v10) = v11) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ((v27 = v10 & v25 = 0 & v21 = 0 & v19 = 0 & v17 = 0 & v16 = 0 & v15 = 0 & v13 = 0 & leq(v14, v12) = 0 & leq(v12, v14) = 0 & ssList(v24) = 0 & ssList(v20) = 0 & ssList(v18) = 0 & cons(v14, v24) = v26 & cons(v12, v20) = v22 & app(v23, v26) = v10 & app(v18, v22) = v23 & ssItem(v14) = 0 & ssItem(v12) = 0) | ( ~ (v12 = 0) & ssList(v10) = v12))) & ! [v10] : ! [v11] : (v11 = 0 | ~ (leq(v10, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & ssItem(v10) = v12)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (segmentP(v10, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & ssList(v10) = v12)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (segmentP(v10, nil) = v11) | ? [v12] : ( ~ (v12 = 0) & ssList(v10) = v12)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (rearsegP(v10, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & ssList(v10) = v12)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (rearsegP(v10, nil) = v11) | ? [v12] : ( ~ (v12 = 0) & ssList(v10) = v12)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (frontsegP(v10, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & ssList(v10) = v12)) & ! [v10] : ! [v11] : (v11 = 0 | ~ (frontsegP(v10, nil) = v11) | ? [v12] : ( ~ (v12 = 0) & ssList(v10) = v12)) & ! [v10] : ! [v11] : (v10 = nil | ~ (tl(v10) = v11) | ? [v12] : ? [v13] : (ssList(v11) = v13 & ssList(v10) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v10] : ! [v11] : (v10 = nil | ~ (tl(v10) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = v11 & ssList(v11) = 0) | ( ~ (v12 = 0) & ssList(v10) = v12))) & ! [v10] : ! [v11] : (v10 = nil | ~ (hd(v10) = v11) | ? [v12] : ? [v13] : (ssList(v10) = v12 & ssItem(v11) = v13 & ( ~ (v12 = 0) | v13 = 0))) & ! [v10] : ! [v11] : (v10 = nil | ~ (hd(v10) = v11) | ? [v12] : ? [v13] : ((v13 = 0 & v12 = v11 & ssItem(v11) = 0) | ( ~ (v12 = 0) & ssList(v10) = v12))) & ! [v10] : ! [v11] : (v10 = nil | ~ (ssList(v10) = 0) | ~ (app(v10, v11) = nil) | ? [v12] : ( ~ (v12 = 0) & ssList(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (gt(v10, v11) = 0) | ~ (ssItem(v10) = 0) | ? [v12] : ? [v13] : (gt(v11, v10) = v13 & ssItem(v11) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10] : ! [v11] : ( ~ (tl(v10) = v11) | ? [v12] : ? [v13] : (hd(v10) = v13 & ssList(v10) = v12 & ( ~ (v12 = 0) | ! [v14] : (v14 = v10 | v14 = nil | v10 = nil | ~ (tl(v14) = v11) | ? [v15] : ? [v16] : (hd(v14) = v16 & ssList(v14) = v15 & ( ~ (v16 = v13) | ~ (v15 = 0))))))) & ! [v10] : ! [v11] : ( ~ (lt(v10, v11) = 0) | ~ (ssItem(v10) = 0) | ? [v12] : ? [v13] : (lt(v11, v10) = v13 & ssItem(v11) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0)))) & ! [v10] : ! [v11] : ( ~ (segmentP(v10, v11) = 0) | ~ (ssList(v10) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v10 & v16 = 0 & v13 = 0 & ssList(v15) = 0 & ssList(v12) = 0 & app(v14, v15) = v10 & app(v12, v11) = v14) | ( ~ (v12 = 0) & ssList(v11) = v12))) & ! [v10] : ! [v11] : ( ~ (rearsegP(v10, v11) = 0) | ~ (ssList(v10) = 0) | ? [v12] : ? [v13] : ? [v14] : ((v14 = v10 & v13 = 0 & ssList(v12) = 0 & app(v12, v11) = v10) | ( ~ (v12 = 0) & ssList(v11) = v12))) & ! [v10] : ! [v11] : ( ~ (frontsegP(v10, v11) = 0) | ~ (ssList(v10) = 0) | ? [v12] : ? [v13] : ? [v14] : ((v14 = v10 & v13 = 0 & ssList(v12) = 0 & app(v11, v12) = v10) | ( ~ (v12 = 0) & ssList(v11) = v12))) & ! [v10] : ! [v11] : ( ~ (memberP(v10, v11) = 0) | ~ (ssList(v10) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v10 & v15 = 0 & v13 = 0 & ssList(v14) = 0 & ssList(v12) = 0 & cons(v11, v14) = v16 & app(v12, v16) = v10) | ( ~ (v12 = 0) & ssItem(v11) = v12))) & ! [v10] : ! [v11] : ( ~ (ssList(v10) = 0) | ~ (cons(v11, v10) = v10) | ? [v12] : ( ~ (v12 = 0) & ssItem(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (ssList(v10) = 0) | ~ (cons(v11, v10) = nil) | ? [v12] : ( ~ (v12 = 0) & ssItem(v11) = v12)) & ! [v10] : ! [v11] : ( ~ (cons(v10, nil) = v11) | ? [v12] : ? [v13] : (equalelemsP(v11) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ( ~ (cons(v10, nil) = v11) | ? [v12] : ? [v13] : (duplicatefreeP(v11) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ( ~ (cons(v10, nil) = v11) | ? [v12] : ? [v13] : (strictorderedP(v11) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ( ~ (cons(v10, nil) = v11) | ? [v12] : ? [v13] : (totalorderedP(v11) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ( ~ (cons(v10, nil) = v11) | ? [v12] : ? [v13] : (strictorderP(v11) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ( ~ (cons(v10, nil) = v11) | ? [v12] : ? [v13] : (totalorderP(v11) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v10] : ! [v11] : ( ~ (cons(v10, nil) = v11) | ? [v12] : ? [v13] : (cyclefreeP(v11) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | v13 = 0))) & ! [v10] : (v10 = nil | ~ (segmentP(nil, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & ssList(v10) = v11)) & ! [v10] : (v10 = nil | ~ (rearsegP(nil, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & ssList(v10) = v11)) & ! [v10] : (v10 = nil | ~ (frontsegP(nil, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & ssList(v10) = v11)) & ! [v10] : (v10 = nil | ~ (ssList(v10) = 0) | ? [v11] : ? [v12] : (ssList(v11) = 0 & cons(v12, v11) = v10 & ssItem(v12) = 0)) & ! [v10] : (v10 = nil | ~ (app(nil, nil) = v10)) & ! [v10] : (v10 = 0 | ~ (segmentP(nil, nil) = v10)) & ! [v10] : (v10 = 0 | ~ (rearsegP(nil, nil) = v10)) & ! [v10] : (v10 = 0 | ~ (frontsegP(nil, nil) = v10)) & ! [v10] : ( ~ (lt(v10, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & ssItem(v10) = v11)) & ! [v10] : ( ~ (singletonP(v10) = 0) | ? [v11] : ? [v12] : ? [v13] : ((v13 = v10 & v12 = 0 & cons(v11, nil) = v10 & ssItem(v11) = 0) | ( ~ (v11 = 0) & ssList(v10) = v11))) & ! [v10] : ( ~ (memberP(nil, v10) = 0) | ? [v11] : ( ~ (v11 = 0) & ssItem(v10) = v11)) & ! [v10] : ( ~ (ssList(v10) = 0) | ~ (neq(v10, v10) = 0)) & ! [v10] : ( ~ (neq(v10, v10) = 0) | ~ (ssItem(v10) = 0)) & ((v7 = 0 & v6 = v1 & v5 = 0 & memberP(v3, v4) = 0 & cons(v4, nil) = v1 & ssItem(v4) = 0) | (v3 = nil & v1 = nil)))
% 22.20/7.05 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7, all_0_8_8, all_0_9_9 yields:
% 22.20/7.05 | (1) ~ (all_0_0_0 = all_0_1_1) & ~ (all_0_7_7 = 0) & ~ (all_0_9_9 = 0) & equalelemsP(nil) = 0 & duplicatefreeP(nil) = 0 & strictorderedP(all_0_8_8) = all_0_7_7 & strictorderedP(nil) = 0 & totalorderedP(nil) = 0 & strictorderP(nil) = 0 & totalorderP(nil) = 0 & cyclefreeP(nil) = 0 & singletonP(nil) = all_0_9_9 & ssList(all_0_6_6) = 0 & ssList(all_0_8_8) = 0 & ssList(nil) = 0 & 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 = all_0_8_8 & all_0_4_4 = 0 & memberP(all_0_6_6, all_0_5_5) = 0 & cons(all_0_5_5, nil) = all_0_8_8 & ssItem(all_0_5_5) = 0) | (all_0_6_6 = nil & all_0_8_8 = nil))
% 22.20/7.07 |
% 22.20/7.07 | Applying alpha-rule on (1) yields:
% 22.20/7.08 | (2) ! [v0] : ! [v1] : ( ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (gt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 22.20/7.08 | (3) ! [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)))))))
% 22.20/7.08 | (4) ! [v0] : (v0 = 0 | ~ (frontsegP(nil, nil) = v0))
% 22.20/7.08 | (5) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = v0))
% 22.20/7.08 | (6) ssList(all_0_6_6) = 0
% 22.20/7.08 | (7) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 22.20/7.08 | (8) ! [v0] : (v0 = 0 | ~ (segmentP(nil, nil) = v0))
% 22.20/7.08 | (9) ssList(all_0_8_8) = 0
% 22.20/7.08 | (10) ssItem(all_0_0_0) = 0
% 22.20/7.08 | (11) ! [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)))
% 22.20/7.08 | (12) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 22.20/7.08 | (13) ! [v0] : (v0 = nil | ~ (segmentP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 22.20/7.08 | (14) ! [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)))
% 22.20/7.08 | (15) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0))
% 22.20/7.08 | (16) ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 22.20/7.08 | (17) ssList(nil) = 0
% 22.20/7.08 | (18) equalelemsP(nil) = 0
% 22.20/7.08 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 22.20/7.08 | (20) ~ (all_0_0_0 = all_0_1_1)
% 22.20/7.08 | (21) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | ~ (equalelemsP(v2) = v0))
% 22.20/7.08 | (22) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 22.20/7.08 | (23) ssItem(all_0_1_1) = 0
% 22.20/7.08 | (24) ! [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)))))
% 22.20/7.08 | (25) ! [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)))))
% 22.20/7.08 | (26) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 22.20/7.08 | (27) strictorderP(nil) = 0
% 22.20/7.08 | (28) totalorderedP(nil) = 0
% 22.20/7.08 | (29) ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0))
% 22.20/7.08 | (30) ! [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)))))
% 22.20/7.08 | (31) ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (leq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 22.20/7.08 | (32) strictorderedP(nil) = 0
% 22.20/7.08 | (33) ! [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)))
% 22.20/7.08 | (34) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : (ssList(v0) = v2 & ssItem(v1) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 22.20/7.08 | (35) ! [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)))
% 22.20/7.08 | (36) ! [v0] : ( ~ (neq(v0, v0) = 0) | ~ (ssItem(v0) = 0))
% 22.20/7.08 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 22.20/7.08 | (38) ! [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)))))
% 22.20/7.08 | (39) ! [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)))
% 22.20/7.08 | (40) ~ (all_0_9_9 = 0)
% 22.20/7.08 | (41) ! [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)))
% 22.20/7.08 | (42) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0))
% 22.20/7.08 | (43) ! [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)))
% 22.20/7.08 | (44) (all_0_2_2 = 0 & all_0_3_3 = all_0_8_8 & all_0_4_4 = 0 & memberP(all_0_6_6, all_0_5_5) = 0 & cons(all_0_5_5, nil) = all_0_8_8 & ssItem(all_0_5_5) = 0) | (all_0_6_6 = nil & all_0_8_8 = nil)
% 22.20/7.08 | (45) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 22.20/7.08 | (46) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 22.20/7.08 | (47) ! [v0] : ! [v1] : (v1 = v0 | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 22.20/7.08 | (48) ! [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))))
% 22.20/7.09 | (49) ! [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)))
% 22.20/7.09 | (50) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 22.20/7.09 | (51) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 22.20/7.09 | (52) ! [v0] : (v0 = 0 | ~ (rearsegP(nil, nil) = v0))
% 22.20/7.09 | (53) ! [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)))))))
% 22.20/7.09 | (54) ! [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)))
% 22.20/7.09 | (55) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v0) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 22.20/7.09 | (56) ! [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)))))
% 22.20/7.09 | (57) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 22.20/7.09 | (58) ! [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)))
% 22.20/7.09 | (59) ! [v0] : ( ~ (lt(v0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 22.20/7.09 | (60) ! [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))))
% 22.20/7.09 | (61) ! [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)))))
% 22.20/7.09 | (62) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (ssList(v0) = 0) | ~ (neq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & ssList(v1) = v3))
% 22.20/7.09 | (63) ! [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))))
% 22.20/7.09 | (64) ! [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)))
% 22.20/7.09 | (65) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0))
% 22.20/7.09 | (66) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | ~ (duplicatefreeP(v2) = v0))
% 22.20/7.09 | (67) ! [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)))))
% 22.20/7.09 | (68) ! [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))))
% 22.20/7.09 | (69) ! [v0] : ! [v1] : (v1 = v0 | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 22.20/7.09 | (70) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0))
% 22.20/7.09 | (71) ! [v0] : ! [v1] : (v1 = v0 | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (frontsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 22.20/7.09 | (72) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0))
% 22.20/7.09 | (73) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0))
% 22.20/7.09 | (74) ! [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)))
% 22.20/7.09 | (75) ! [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)))))
% 22.20/7.09 | (76) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = nil) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 22.20/7.09 | (77) ! [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)))
% 22.20/7.09 | (78) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 22.20/7.09 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 22.20/7.09 | (80) ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (geq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 22.20/7.09 | (81) ! [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)))
% 22.20/7.09 | (82) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 22.20/7.09 | (83) ! [v0] : (v0 = nil | ~ (ssList(v0) = 0) | ? [v1] : ? [v2] : (ssList(v1) = 0 & cons(v2, v1) = v0 & ssItem(v2) = 0))
% 22.20/7.09 | (84) ! [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)))
% 22.20/7.10 | (85) ! [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)))
% 22.20/7.10 | (86) ! [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)))))))
% 22.20/7.10 | (87) ! [v0] : ( ~ (memberP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 22.20/7.10 | (88) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (tl(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v0)))
% 22.20/7.10 | (89) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v1)))
% 22.20/7.10 | (90) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssItem(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 22.20/7.10 | (91) strictorderedP(all_0_8_8) = all_0_7_7
% 22.20/7.10 | (92) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (neq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & ssItem(v1) = v3))
% 22.20/7.10 | (93) ! [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)))
% 22.20/7.10 | (94) totalorderP(nil) = 0
% 22.20/7.10 | (95) ! [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)))
% 22.20/7.10 | (96) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 22.20/7.10 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0))
% 22.20/7.10 | (98) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 22.20/7.10 | (99) ! [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)))))
% 22.20/7.10 | (100) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 22.20/7.10 | (101) ! [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)))
% 22.20/7.10 | (102) ! [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)))))))
% 22.20/7.10 | (103) duplicatefreeP(nil) = 0
% 22.20/7.10 | (104) ! [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)))))
% 22.20/7.10 | (105) ! [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)))))))
% 22.20/7.10 | (106) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssList(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 22.20/7.10 | (107) ! [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)))
% 22.20/7.10 | (108) ! [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)))
% 22.20/7.10 | (109) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 22.20/7.10 | (110) ! [v0] : ( ~ (ssList(v0) = 0) | ~ (neq(v0, v0) = 0))
% 22.20/7.10 | (111) ! [v0] : ! [v1] : (v1 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 22.20/7.10 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & ssList(v0) = v4))
% 22.20/7.10 | (113) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 22.20/7.10 | (114) ! [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))))))))
% 22.20/7.10 | (115) ! [v0] : (v0 = nil | ~ (rearsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 22.20/7.10 | (116) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (singletonP(v0) = v1) | ~ (cons(v2, nil) = v0) | ? [v3] : (( ~ (v3 = 0) & ssList(v0) = v3) | ( ~ (v3 = 0) & ssItem(v2) = v3)))
% 22.20/7.10 | (117) ! [v0] : ( ~ (singletonP(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v0 & v2 = 0 & cons(v1, nil) = v0 & ssItem(v1) = 0) | ( ~ (v1 = 0) & ssList(v0) = v1)))
% 22.20/7.11 | (118) ! [v0] : ! [v1] : (v0 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 22.20/7.11 | (119) ! [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)))
% 22.20/7.11 | (120) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 22.20/7.11 | (121) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) = v0))
% 22.20/7.11 | (122) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 22.20/7.11 | (123) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ (cyclefreeP(v2) = v0))
% 22.20/7.11 | (124) ! [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)))))))
% 22.20/7.11 | (125) cyclefreeP(nil) = 0
% 22.20/7.11 | (126) ! [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)))
% 22.20/7.11 | (127) singletonP(nil) = all_0_9_9
% 22.20/7.11 | (128) ! [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))))
% 22.20/7.11 | (129) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderP(v2) = v1) | ~ (strictorderP(v2) = v0))
% 22.20/7.11 | (130) ! [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))))))))
% 22.20/7.11 | (131) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0))
% 22.20/7.11 | (132) ! [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)))
% 22.20/7.11 | (133) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ (totalorderP(v2) = v0))
% 22.20/7.11 | (134) ~ (all_0_7_7 = 0)
% 22.20/7.11 | (135) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (app(v0, v1) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 22.59/7.11 | (136) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 22.59/7.11 | (137) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (ssList(v1) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 22.59/7.11 | (138) ! [v0] : (v0 = nil | ~ (frontsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 22.59/7.11 | (139) ! [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)))
% 22.59/7.11 | (140) ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (lt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 22.59/7.11 | (141) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0))
% 22.59/7.11 | (142) ! [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)))
% 22.59/7.11 | (143) ! [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))))))))
% 22.59/7.11 | (144) ! [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)))))))
% 22.59/7.11 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0))
% 22.59/7.11 | (146) ! [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)))
% 22.59/7.11 | (147) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 22.59/7.11 |
% 22.59/7.11 | Instantiating formula (5) with nil, 0, all_0_7_7 and discharging atoms strictorderedP(nil) = 0, yields:
% 22.59/7.11 | (148) all_0_7_7 = 0 | ~ (strictorderedP(nil) = all_0_7_7)
% 22.59/7.11 |
% 22.59/7.11 | Instantiating formula (119) with all_0_7_7, all_0_8_8 and discharging atoms strictorderedP(all_0_8_8) = all_0_7_7, yields:
% 22.59/7.11 | (149) all_0_7_7 = 0 | ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = all_0_8_8 & 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_8_8 & app(v5, v9) = v10 & ssItem(v2) = 0 & ssItem(v0) = 0) | ( ~ (v0 = 0) & ssList(all_0_8_8) = v0))
% 22.59/7.11 |
% 22.59/7.11 +-Applying beta-rule and splitting (44), into two cases.
% 22.59/7.11 |-Branch one:
% 22.59/7.11 | (150) all_0_2_2 = 0 & all_0_3_3 = all_0_8_8 & all_0_4_4 = 0 & memberP(all_0_6_6, all_0_5_5) = 0 & cons(all_0_5_5, nil) = all_0_8_8 & ssItem(all_0_5_5) = 0
% 22.59/7.11 |
% 22.59/7.11 | Applying alpha-rule on (150) yields:
% 22.59/7.11 | (151) all_0_3_3 = all_0_8_8
% 22.59/7.11 | (152) ssItem(all_0_5_5) = 0
% 22.59/7.11 | (153) all_0_2_2 = 0
% 22.59/7.11 | (154) memberP(all_0_6_6, all_0_5_5) = 0
% 22.59/7.11 | (155) cons(all_0_5_5, nil) = all_0_8_8
% 22.59/7.11 | (156) all_0_4_4 = 0
% 22.59/7.11 |
% 22.59/7.12 +-Applying beta-rule and splitting (149), into two cases.
% 22.59/7.12 |-Branch one:
% 22.59/7.12 | (157) all_0_7_7 = 0
% 22.59/7.12 |
% 22.59/7.12 | Equations (157) can reduce 134 to:
% 22.59/7.12 | (158) $false
% 22.59/7.12 |
% 22.59/7.12 |-The branch is then unsatisfiable
% 22.59/7.12 |-Branch two:
% 22.59/7.12 | (134) ~ (all_0_7_7 = 0)
% 22.59/7.12 | (160) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = all_0_8_8 & 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_8_8 & app(v5, v9) = v10 & ssItem(v2) = 0 & ssItem(v0) = 0) | ( ~ (v0 = 0) & ssList(all_0_8_8) = v0))
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (88) with all_0_8_8, all_0_5_5, nil and discharging atoms ssList(nil) = 0, cons(all_0_5_5, nil) = all_0_8_8, yields:
% 22.59/7.12 | (161) ? [v0] : ? [v1] : (tl(all_0_8_8) = v1 & ssItem(all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = nil))
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (89) with all_0_8_8, all_0_5_5, nil and discharging atoms ssList(nil) = 0, cons(all_0_5_5, nil) = all_0_8_8, yields:
% 22.59/7.12 | (162) ? [v0] : ? [v1] : (hd(all_0_8_8) = v1 & ssItem(all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = all_0_5_5))
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (46) with all_0_8_8, all_0_5_5 and discharging atoms cons(all_0_5_5, nil) = all_0_8_8, yields:
% 22.59/7.12 | (163) ? [v0] : ? [v1] : (equalelemsP(all_0_8_8) = v1 & ssItem(all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (50) with all_0_8_8, all_0_5_5 and discharging atoms cons(all_0_5_5, nil) = all_0_8_8, yields:
% 22.59/7.12 | (164) ? [v0] : ? [v1] : (duplicatefreeP(all_0_8_8) = v1 & ssItem(all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (7) with all_0_8_8, all_0_5_5 and discharging atoms cons(all_0_5_5, nil) = all_0_8_8, yields:
% 22.59/7.12 | (165) ? [v0] : ? [v1] : (strictorderedP(all_0_8_8) = v1 & ssItem(all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (57) with all_0_8_8, all_0_5_5 and discharging atoms cons(all_0_5_5, nil) = all_0_8_8, yields:
% 22.59/7.12 | (166) ? [v0] : ? [v1] : (totalorderedP(all_0_8_8) = v1 & ssItem(all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (26) with all_0_8_8, all_0_5_5 and discharging atoms cons(all_0_5_5, nil) = all_0_8_8, yields:
% 22.59/7.12 | (167) ? [v0] : ? [v1] : (strictorderP(all_0_8_8) = v1 & ssItem(all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (82) with all_0_8_8, all_0_5_5 and discharging atoms cons(all_0_5_5, nil) = all_0_8_8, yields:
% 22.59/7.12 | (168) ? [v0] : ? [v1] : (totalorderP(all_0_8_8) = v1 & ssItem(all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (122) with all_0_8_8, all_0_5_5 and discharging atoms cons(all_0_5_5, nil) = all_0_8_8, yields:
% 22.59/7.12 | (169) ? [v0] : ? [v1] : (cyclefreeP(all_0_8_8) = v1 & ssItem(all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 22.59/7.12 |
% 22.59/7.12 | Instantiating (169) with all_34_0_38, all_34_1_39 yields:
% 22.59/7.12 | (170) cyclefreeP(all_0_8_8) = all_34_0_38 & ssItem(all_0_5_5) = all_34_1_39 & ( ~ (all_34_1_39 = 0) | all_34_0_38 = 0)
% 22.59/7.12 |
% 22.59/7.12 | Applying alpha-rule on (170) yields:
% 22.59/7.12 | (171) cyclefreeP(all_0_8_8) = all_34_0_38
% 22.59/7.12 | (172) ssItem(all_0_5_5) = all_34_1_39
% 22.59/7.12 | (173) ~ (all_34_1_39 = 0) | all_34_0_38 = 0
% 22.59/7.12 |
% 22.59/7.12 | Instantiating (168) with all_36_0_40, all_36_1_41 yields:
% 22.59/7.12 | (174) totalorderP(all_0_8_8) = all_36_0_40 & ssItem(all_0_5_5) = all_36_1_41 & ( ~ (all_36_1_41 = 0) | all_36_0_40 = 0)
% 22.59/7.12 |
% 22.59/7.12 | Applying alpha-rule on (174) yields:
% 22.59/7.12 | (175) totalorderP(all_0_8_8) = all_36_0_40
% 22.59/7.12 | (176) ssItem(all_0_5_5) = all_36_1_41
% 22.59/7.12 | (177) ~ (all_36_1_41 = 0) | all_36_0_40 = 0
% 22.59/7.12 |
% 22.59/7.12 | Instantiating (165) with all_38_0_42, all_38_1_43 yields:
% 22.59/7.12 | (178) strictorderedP(all_0_8_8) = all_38_0_42 & ssItem(all_0_5_5) = all_38_1_43 & ( ~ (all_38_1_43 = 0) | all_38_0_42 = 0)
% 22.59/7.12 |
% 22.59/7.12 | Applying alpha-rule on (178) yields:
% 22.59/7.12 | (179) strictorderedP(all_0_8_8) = all_38_0_42
% 22.59/7.12 | (180) ssItem(all_0_5_5) = all_38_1_43
% 22.59/7.12 | (181) ~ (all_38_1_43 = 0) | all_38_0_42 = 0
% 22.59/7.12 |
% 22.59/7.12 | Instantiating (163) with all_40_0_44, all_40_1_45 yields:
% 22.59/7.12 | (182) equalelemsP(all_0_8_8) = all_40_0_44 & ssItem(all_0_5_5) = all_40_1_45 & ( ~ (all_40_1_45 = 0) | all_40_0_44 = 0)
% 22.59/7.12 |
% 22.59/7.12 | Applying alpha-rule on (182) yields:
% 22.59/7.12 | (183) equalelemsP(all_0_8_8) = all_40_0_44
% 22.59/7.12 | (184) ssItem(all_0_5_5) = all_40_1_45
% 22.59/7.12 | (185) ~ (all_40_1_45 = 0) | all_40_0_44 = 0
% 22.59/7.12 |
% 22.59/7.12 | Instantiating (162) with all_42_0_46, all_42_1_47 yields:
% 22.59/7.12 | (186) hd(all_0_8_8) = all_42_0_46 & ssItem(all_0_5_5) = all_42_1_47 & ( ~ (all_42_1_47 = 0) | all_42_0_46 = all_0_5_5)
% 22.59/7.12 |
% 22.59/7.12 | Applying alpha-rule on (186) yields:
% 22.59/7.12 | (187) hd(all_0_8_8) = all_42_0_46
% 22.59/7.12 | (188) ssItem(all_0_5_5) = all_42_1_47
% 22.59/7.12 | (189) ~ (all_42_1_47 = 0) | all_42_0_46 = all_0_5_5
% 22.59/7.12 |
% 22.59/7.12 | Instantiating (164) with all_44_0_48, all_44_1_49 yields:
% 22.59/7.12 | (190) duplicatefreeP(all_0_8_8) = all_44_0_48 & ssItem(all_0_5_5) = all_44_1_49 & ( ~ (all_44_1_49 = 0) | all_44_0_48 = 0)
% 22.59/7.12 |
% 22.59/7.12 | Applying alpha-rule on (190) yields:
% 22.59/7.12 | (191) duplicatefreeP(all_0_8_8) = all_44_0_48
% 22.59/7.12 | (192) ssItem(all_0_5_5) = all_44_1_49
% 22.59/7.12 | (193) ~ (all_44_1_49 = 0) | all_44_0_48 = 0
% 22.59/7.12 |
% 22.59/7.12 | Instantiating (167) with all_46_0_50, all_46_1_51 yields:
% 22.59/7.12 | (194) strictorderP(all_0_8_8) = all_46_0_50 & ssItem(all_0_5_5) = all_46_1_51 & ( ~ (all_46_1_51 = 0) | all_46_0_50 = 0)
% 22.59/7.12 |
% 22.59/7.12 | Applying alpha-rule on (194) yields:
% 22.59/7.12 | (195) strictorderP(all_0_8_8) = all_46_0_50
% 22.59/7.12 | (196) ssItem(all_0_5_5) = all_46_1_51
% 22.59/7.12 | (197) ~ (all_46_1_51 = 0) | all_46_0_50 = 0
% 22.59/7.12 |
% 22.59/7.12 | Instantiating (166) with all_56_0_60, all_56_1_61 yields:
% 22.59/7.12 | (198) totalorderedP(all_0_8_8) = all_56_0_60 & ssItem(all_0_5_5) = all_56_1_61 & ( ~ (all_56_1_61 = 0) | all_56_0_60 = 0)
% 22.59/7.12 |
% 22.59/7.12 | Applying alpha-rule on (198) yields:
% 22.59/7.12 | (199) totalorderedP(all_0_8_8) = all_56_0_60
% 22.59/7.12 | (200) ssItem(all_0_5_5) = all_56_1_61
% 22.59/7.12 | (201) ~ (all_56_1_61 = 0) | all_56_0_60 = 0
% 22.59/7.12 |
% 22.59/7.12 | Instantiating (161) with all_59_0_68, all_59_1_69 yields:
% 22.59/7.12 | (202) tl(all_0_8_8) = all_59_0_68 & ssItem(all_0_5_5) = all_59_1_69 & ( ~ (all_59_1_69 = 0) | all_59_0_68 = nil)
% 22.59/7.12 |
% 22.59/7.12 | Applying alpha-rule on (202) yields:
% 22.59/7.12 | (203) tl(all_0_8_8) = all_59_0_68
% 22.59/7.12 | (204) ssItem(all_0_5_5) = all_59_1_69
% 22.59/7.12 | (205) ~ (all_59_1_69 = 0) | all_59_0_68 = nil
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (5) with all_0_8_8, all_38_0_42, all_0_7_7 and discharging atoms strictorderedP(all_0_8_8) = all_38_0_42, strictorderedP(all_0_8_8) = all_0_7_7, yields:
% 22.59/7.12 | (206) all_38_0_42 = all_0_7_7
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (45) with all_0_5_5, all_56_1_61, all_59_1_69 and discharging atoms ssItem(all_0_5_5) = all_59_1_69, ssItem(all_0_5_5) = all_56_1_61, yields:
% 22.59/7.12 | (207) all_59_1_69 = all_56_1_61
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (45) with all_0_5_5, all_44_1_49, all_59_1_69 and discharging atoms ssItem(all_0_5_5) = all_59_1_69, ssItem(all_0_5_5) = all_44_1_49, yields:
% 22.59/7.12 | (208) all_59_1_69 = all_44_1_49
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (45) with all_0_5_5, all_42_1_47, all_46_1_51 and discharging atoms ssItem(all_0_5_5) = all_46_1_51, ssItem(all_0_5_5) = all_42_1_47, yields:
% 22.59/7.12 | (209) all_46_1_51 = all_42_1_47
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (45) with all_0_5_5, all_40_1_45, all_46_1_51 and discharging atoms ssItem(all_0_5_5) = all_46_1_51, ssItem(all_0_5_5) = all_40_1_45, yields:
% 22.59/7.12 | (210) all_46_1_51 = all_40_1_45
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (45) with all_0_5_5, all_40_1_45, all_44_1_49 and discharging atoms ssItem(all_0_5_5) = all_44_1_49, ssItem(all_0_5_5) = all_40_1_45, yields:
% 22.59/7.12 | (211) all_44_1_49 = all_40_1_45
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (45) with all_0_5_5, all_38_1_43, all_46_1_51 and discharging atoms ssItem(all_0_5_5) = all_46_1_51, ssItem(all_0_5_5) = all_38_1_43, yields:
% 22.59/7.12 | (212) all_46_1_51 = all_38_1_43
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (45) with all_0_5_5, all_36_1_41, 0 and discharging atoms ssItem(all_0_5_5) = all_36_1_41, ssItem(all_0_5_5) = 0, yields:
% 22.59/7.12 | (213) all_36_1_41 = 0
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (45) with all_0_5_5, all_36_1_41, all_40_1_45 and discharging atoms ssItem(all_0_5_5) = all_40_1_45, ssItem(all_0_5_5) = all_36_1_41, yields:
% 22.59/7.12 | (214) all_40_1_45 = all_36_1_41
% 22.59/7.12 |
% 22.59/7.12 | Instantiating formula (45) with all_0_5_5, all_34_1_39, all_59_1_69 and discharging atoms ssItem(all_0_5_5) = all_59_1_69, ssItem(all_0_5_5) = all_34_1_39, yields:
% 22.59/7.12 | (215) all_59_1_69 = all_34_1_39
% 22.59/7.12 |
% 22.59/7.12 | Combining equations (215,207) yields a new equation:
% 22.59/7.12 | (216) all_56_1_61 = all_34_1_39
% 22.59/7.12 |
% 22.59/7.12 | Combining equations (208,207) yields a new equation:
% 22.59/7.12 | (217) all_56_1_61 = all_44_1_49
% 22.59/7.12 |
% 22.59/7.12 | Combining equations (217,216) yields a new equation:
% 22.59/7.12 | (218) all_44_1_49 = all_34_1_39
% 22.59/7.12 |
% 22.59/7.12 | Simplifying 218 yields:
% 22.59/7.12 | (219) all_44_1_49 = all_34_1_39
% 22.59/7.12 |
% 22.59/7.12 | Combining equations (212,209) yields a new equation:
% 22.59/7.12 | (220) all_42_1_47 = all_38_1_43
% 22.59/7.12 |
% 22.59/7.12 | Combining equations (210,209) yields a new equation:
% 22.59/7.12 | (221) all_42_1_47 = all_40_1_45
% 22.59/7.12 |
% 22.59/7.13 | Combining equations (211,219) yields a new equation:
% 22.59/7.13 | (222) all_40_1_45 = all_34_1_39
% 22.59/7.13 |
% 22.59/7.13 | Simplifying 222 yields:
% 22.59/7.13 | (223) all_40_1_45 = all_34_1_39
% 22.59/7.13 |
% 22.59/7.13 | Combining equations (221,220) yields a new equation:
% 22.59/7.13 | (224) all_40_1_45 = all_38_1_43
% 22.59/7.13 |
% 22.59/7.13 | Simplifying 224 yields:
% 22.59/7.13 | (225) all_40_1_45 = all_38_1_43
% 22.59/7.13 |
% 22.59/7.13 | Combining equations (214,225) yields a new equation:
% 22.59/7.13 | (226) all_38_1_43 = all_36_1_41
% 22.59/7.13 |
% 22.59/7.13 | Combining equations (223,225) yields a new equation:
% 22.59/7.13 | (227) all_38_1_43 = all_34_1_39
% 22.59/7.13 |
% 22.59/7.13 | Combining equations (226,227) yields a new equation:
% 22.59/7.13 | (228) all_36_1_41 = all_34_1_39
% 22.59/7.13 |
% 22.59/7.13 | Simplifying 228 yields:
% 22.59/7.13 | (229) all_36_1_41 = all_34_1_39
% 22.59/7.13 |
% 22.59/7.13 | Combining equations (229,213) yields a new equation:
% 22.59/7.13 | (230) all_34_1_39 = 0
% 22.59/7.13 |
% 22.59/7.13 | Simplifying 230 yields:
% 22.59/7.13 | (231) all_34_1_39 = 0
% 22.59/7.13 |
% 22.59/7.13 | Combining equations (231,227) yields a new equation:
% 22.59/7.13 | (232) all_38_1_43 = 0
% 22.59/7.13 |
% 22.59/7.13 +-Applying beta-rule and splitting (181), into two cases.
% 22.59/7.13 |-Branch one:
% 22.59/7.13 | (233) ~ (all_38_1_43 = 0)
% 22.59/7.13 |
% 22.59/7.13 | Equations (232) can reduce 233 to:
% 22.59/7.13 | (158) $false
% 22.59/7.13 |
% 22.59/7.13 |-The branch is then unsatisfiable
% 22.59/7.13 |-Branch two:
% 22.59/7.13 | (232) all_38_1_43 = 0
% 22.59/7.13 | (236) all_38_0_42 = 0
% 22.59/7.13 |
% 22.59/7.13 | Combining equations (206,236) yields a new equation:
% 22.59/7.13 | (237) all_0_7_7 = 0
% 22.59/7.13 |
% 22.59/7.13 | Simplifying 237 yields:
% 22.59/7.13 | (157) all_0_7_7 = 0
% 22.59/7.13 |
% 22.59/7.13 | Equations (157) can reduce 134 to:
% 22.59/7.13 | (158) $false
% 22.59/7.13 |
% 22.59/7.13 |-The branch is then unsatisfiable
% 22.59/7.13 |-Branch two:
% 22.59/7.13 | (240) all_0_6_6 = nil & all_0_8_8 = nil
% 22.59/7.13 |
% 22.59/7.13 | Applying alpha-rule on (240) yields:
% 22.59/7.13 | (241) all_0_6_6 = nil
% 22.59/7.13 | (242) all_0_8_8 = nil
% 22.59/7.13 |
% 22.59/7.13 | From (242) and (91) follows:
% 22.59/7.13 | (243) strictorderedP(nil) = all_0_7_7
% 22.59/7.13 |
% 22.59/7.13 +-Applying beta-rule and splitting (148), into two cases.
% 22.59/7.13 |-Branch one:
% 22.59/7.13 | (244) ~ (strictorderedP(nil) = all_0_7_7)
% 22.59/7.13 |
% 22.59/7.13 | Using (243) and (244) yields:
% 22.59/7.13 | (245) $false
% 22.59/7.13 |
% 22.59/7.13 |-The branch is then unsatisfiable
% 22.59/7.13 |-Branch two:
% 22.59/7.13 | (243) strictorderedP(nil) = all_0_7_7
% 22.59/7.13 | (157) all_0_7_7 = 0
% 22.59/7.13 |
% 22.59/7.13 | Equations (157) can reduce 134 to:
% 22.59/7.13 | (158) $false
% 22.59/7.13 |
% 22.59/7.13 |-The branch is then unsatisfiable
% 22.59/7.13 % SZS output end Proof for theBenchmark
% 22.59/7.13
% 22.59/7.13 6632ms
%------------------------------------------------------------------------------