TSTP Solution File: SWC069+1 by ePrincess---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWC069+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n029.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 20:16:02 EDT 2022
% Result : Theorem 21.08s 6.48s
% Output : Proof 23.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC069+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 12 19:29:39 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.57/0.58 ____ _
% 0.57/0.58 ___ / __ \_____(_)___ ________ __________
% 0.57/0.58 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.57/0.58 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.57/0.58 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.57/0.58
% 0.57/0.58 A Theorem Prover for First-Order Logic
% 0.57/0.58 (ePrincess v.1.0)
% 0.57/0.58
% 0.57/0.58 (c) Philipp Rümmer, 2009-2015
% 0.57/0.58 (c) Peter Backeman, 2014-2015
% 0.57/0.58 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.57/0.58 Free software under GNU Lesser General Public License (LGPL).
% 0.57/0.58 Bug reports to peter@backeman.se
% 0.57/0.58
% 0.57/0.58 For more information, visit http://user.uu.se/~petba168/breu/
% 0.57/0.58
% 0.57/0.58 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.57/0.63 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.18/1.08 Prover 0: Preprocessing ...
% 4.40/1.67 Prover 0: Constructing countermodel ...
% 18.61/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.09/6.09 Prover 1: Preprocessing ...
% 20.78/6.40 Prover 1: Constructing countermodel ...
% 21.08/6.48 Prover 1: proved (557ms)
% 21.08/6.48 Prover 0: stopped
% 21.08/6.48
% 21.08/6.48 No countermodel exists, formula is valid
% 21.08/6.48 % SZS status Theorem for theBenchmark
% 21.08/6.48
% 21.08/6.48 Generating proof ... found it (size 36)
% 22.90/6.86
% 22.90/6.86 % SZS output start Proof for theBenchmark
% 22.90/6.86 Assumed formulas after preprocessing and simplification:
% 22.90/6.86 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ( ~ (v10 = v9) & ~ (v0 = 0) & equalelemsP(nil) = 0 & duplicatefreeP(nil) = 0 & strictorderedP(nil) = 0 & totalorderedP(nil) = 0 & strictorderP(nil) = 0 & totalorderP(nil) = 0 & cyclefreeP(nil) = 0 & singletonP(nil) = v0 & ssList(v2) = 0 & ssList(v1) = 0 & ssList(nil) = 0 & neq(v2, nil) = v3 & ssItem(v10) = 0 & ssItem(v9) = 0 & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v14 = 0 | ~ (strictorderedP(v11) = 0) | ~ (lt(v12, v13) = v14) | ~ (ssList(v15) = 0) | ~ (cons(v13, v19) = v20) | ~ (cons(v12, v16) = v17) | ~ (app(v18, v20) = v11) | ~ (app(v15, v17) = v18) | ~ (ssItem(v12) = 0) | ? [v21] : (( ~ (v21 = 0) & ssList(v19) = v21) | ( ~ (v21 = 0) & ssList(v16) = v21) | ( ~ (v21 = 0) & ssList(v11) = v21) | ( ~ (v21 = 0) & ssItem(v13) = v21))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ! [v20] : (v14 = 0 | ~ (totalorderedP(v11) = 0) | ~ (leq(v12, v13) = v14) | ~ (ssList(v15) = 0) | ~ (cons(v13, v19) = v20) | ~ (cons(v12, v16) = v17) | ~ (app(v18, v20) = v11) | ~ (app(v15, v17) = v18) | ~ (ssItem(v12) = 0) | ? [v21] : (( ~ (v21 = 0) & ssList(v19) = v21) | ( ~ (v21 = 0) & ssList(v16) = v21) | ( ~ (v21 = 0) & ssList(v11) = v21) | ( ~ (v21 = 0) & ssItem(v13) = v21))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (duplicatefreeP(v11) = 0) | ~ (ssList(v13) = 0) | ~ (cons(v12, v17) = v18) | ~ (cons(v12, v14) = v15) | ~ (app(v16, v18) = v11) | ~ (app(v13, v15) = v16) | ~ (ssItem(v12) = 0) | ? [v19] : (( ~ (v19 = 0) & ssList(v17) = v19) | ( ~ (v19 = 0) & ssList(v14) = v19) | ( ~ (v19 = 0) & ssList(v11) = v19))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v17 = 0 | ~ (segmentP(v16, v12) = v17) | ~ (segmentP(v11, v12) = 0) | ~ (ssList(v11) = 0) | ~ (app(v14, v15) = v16) | ~ (app(v13, v11) = v14) | ? [v18] : (( ~ (v18 = 0) & ssList(v15) = v18) | ( ~ (v18 = 0) & ssList(v13) = v18) | ( ~ (v18 = 0) & ssList(v12) = v18))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v13 = v12 | ~ (equalelemsP(v11) = 0) | ~ (ssList(v14) = 0) | ~ (cons(v13, v15) = v16) | ~ (cons(v12, v16) = v17) | ~ (app(v14, v17) = v11) | ~ (ssItem(v13) = 0) | ~ (ssItem(v12) = 0) | ? [v18] : (( ~ (v18 = 0) & ssList(v15) = v18) | ( ~ (v18 = 0) & ssList(v11) = v18))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ( ~ (frontsegP(v14, v16) = v17) | ~ (cons(v12, v15) = v16) | ~ (cons(v11, v13) = v14) | ~ (ssItem(v12) = 0) | ~ (ssItem(v11) = 0) | ? [v18] : ? [v19] : (( ~ (v18 = 0) & ssList(v13) = v18) | (frontsegP(v13, v15) = v19 & ssList(v15) = v18 & ( ~ (v18 = 0) | (( ~ (v19 = 0) | ~ (v12 = v11) | v17 = 0) & ( ~ (v17 = 0) | (v19 = 0 & v12 = v11))))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = 0 | ~ (segmentP(v11, v12) = v13) | ~ (ssList(v11) = 0) | ~ (app(v15, v16) = v11) | ~ (app(v14, v12) = v15) | ? [v17] : (( ~ (v17 = 0) & ssList(v16) = v17) | ( ~ (v17 = 0) & ssList(v14) = v17) | ( ~ (v17 = 0) & ssList(v12) = v17))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v13 = 0 | ~ (memberP(v11, v12) = v13) | ~ (ssList(v14) = 0) | ~ (ssList(v11) = 0) | ~ (cons(v12, v15) = v16) | ~ (app(v14, v16) = v11) | ? [v17] : (( ~ (v17 = 0) & ssList(v15) = v17) | ( ~ (v17 = 0) & ssItem(v12) = v17))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (memberP(v15, v11) = v16) | ~ (memberP(v12, v11) = v13) | ~ (app(v12, v14) = v15) | ~ (ssItem(v11) = 0) | ? [v17] : ? [v18] : (( ~ (v17 = 0) & ssList(v12) = v17) | (memberP(v14, v11) = v18 & ssList(v14) = v17 & ( ~ (v17 = 0) | (( ~ (v16 = 0) | v18 = 0 | v13 = 0) & (v16 = 0 | ( ~ (v18 = 0) & ~ (v13 = 0)))))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ( ~ (ssList(v11) = 0) | ~ (cons(v14, v12) = v15) | ~ (app(v15, v11) = v16) | ~ (app(v12, v11) = v13) | ? [v17] : ? [v18] : (( ~ (v17 = 0) & ssList(v12) = v17) | (cons(v14, v13) = v18 & ssItem(v14) = v17 & ( ~ (v17 = 0) | v18 = v16)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = v13 | ~ (ssList(v12) = 0) | ~ (ssList(v11) = 0) | ~ (cons(v15, v12) = v14) | ~ (cons(v13, v11) = v14) | ? [v16] : (( ~ (v16 = 0) & ssItem(v15) = v16) | ( ~ (v16 = 0) & ssItem(v13) = v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (rearsegP(v14, v12) = v15) | ~ (rearsegP(v11, v12) = 0) | ~ (ssList(v11) = 0) | ~ (app(v13, v11) = v14) | ? [v16] : (( ~ (v16 = 0) & ssList(v13) = v16) | ( ~ (v16 = 0) & ssList(v12) = v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v15 = 0 | ~ (frontsegP(v14, v12) = v15) | ~ (frontsegP(v11, v12) = 0) | ~ (ssList(v11) = 0) | ~ (app(v11, v13) = v14) | ? [v16] : (( ~ (v16 = 0) & ssList(v13) = v16) | ( ~ (v16 = 0) & ssList(v12) = v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : (v12 = v11 | ~ (ssList(v12) = 0) | ~ (ssList(v11) = 0) | ~ (cons(v15, v12) = v14) | ~ (cons(v13, v11) = v14) | ? [v16] : (( ~ (v16 = 0) & ssItem(v15) = v16) | ( ~ (v16 = 0) & ssItem(v13) = v16))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (memberP(v14, v11) = v15) | ~ (cons(v12, v13) = v14) | ~ (ssItem(v12) = 0) | ~ (ssItem(v11) = 0) | ? [v16] : ? [v17] : (memberP(v13, v11) = v17 & ssList(v13) = v16 & ( ~ (v16 = 0) | (( ~ (v15 = 0) | v17 = 0 | v12 = v11) & (v15 = 0 | ( ~ (v17 = 0) & ~ (v12 = v11))))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (ssList(v11) = 0) | ~ (app(v13, v14) = v15) | ~ (app(v11, v12) = v13) | ? [v16] : ? [v17] : ? [v18] : (( ~ (v16 = 0) & ssList(v12) = v16) | (ssList(v14) = v16 & app(v12, v14) = v17 & app(v11, v17) = v18 & ( ~ (v16 = 0) | v18 = v15)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | v11 = nil | ~ (tl(v11) = v13) | ~ (hd(v11) = v12) | ~ (cons(v12, v13) = v14) | ? [v15] : ( ~ (v15 = 0) & ssList(v11) = v15)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (ssList(v11) = 0) | ~ (app(v14, v12) = v13) | ~ (app(v11, v12) = v13) | ? [v15] : (( ~ (v15 = 0) & ssList(v14) = v15) | ( ~ (v15 = 0) & ssList(v12) = v15))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = v11 | ~ (ssList(v11) = 0) | ~ (app(v12, v14) = v13) | ~ (app(v12, v11) = v13) | ? [v15] : (( ~ (v15 = 0) & ssList(v14) = v15) | ( ~ (v15 = 0) & ssList(v12) = v15))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (gt(v11, v13) = v14) | ~ (gt(v11, v12) = 0) | ~ (ssItem(v11) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssItem(v12) = v15) | (gt(v12, v13) = v16 & ssItem(v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (geq(v11, v13) = v14) | ~ (geq(v11, v12) = 0) | ~ (ssItem(v11) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssItem(v12) = v15) | (geq(v12, v13) = v16 & ssItem(v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (lt(v11, v13) = v14) | ~ (lt(v11, v12) = 0) | ~ (ssItem(v11) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssItem(v12) = v15) | (lt(v12, v13) = v16 & ssItem(v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (lt(v11, v13) = v14) | ~ (leq(v11, v12) = 0) | ~ (ssItem(v11) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssItem(v12) = v15) | (lt(v12, v13) = v16 & ssItem(v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (leq(v11, v13) = v14) | ~ (leq(v11, v12) = 0) | ~ (ssItem(v11) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssItem(v12) = v15) | (leq(v12, v13) = v16 & ssItem(v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (segmentP(v11, v13) = v14) | ~ (segmentP(v11, v12) = 0) | ~ (ssList(v11) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssList(v12) = v15) | (segmentP(v12, v13) = v16 & ssList(v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (rearsegP(v11, v13) = v14) | ~ (rearsegP(v11, v12) = 0) | ~ (ssList(v11) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssList(v12) = v15) | (rearsegP(v12, v13) = v16 & ssList(v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (frontsegP(v11, v13) = v14) | ~ (frontsegP(v11, v12) = 0) | ~ (ssList(v11) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssList(v12) = v15) | (frontsegP(v12, v13) = v16 & ssList(v13) = v15 & ( ~ (v16 = 0) | ~ (v15 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (rearsegP(v11, v12) = v13) | ~ (ssList(v11) = 0) | ~ (app(v14, v12) = v11) | ? [v15] : (( ~ (v15 = 0) & ssList(v14) = v15) | ( ~ (v15 = 0) & ssList(v12) = v15))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v13 = 0 | ~ (frontsegP(v11, v12) = v13) | ~ (ssList(v11) = 0) | ~ (app(v12, v14) = v11) | ? [v15] : (( ~ (v15 = 0) & ssList(v14) = v15) | ( ~ (v15 = 0) & ssList(v12) = v15))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (gt(v14, v13) = v12) | ~ (gt(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (geq(v14, v13) = v12) | ~ (geq(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (lt(v14, v13) = v12) | ~ (lt(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (leq(v14, v13) = v12) | ~ (leq(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (segmentP(v14, v13) = v12) | ~ (segmentP(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (rearsegP(v14, v13) = v12) | ~ (rearsegP(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (frontsegP(v14, v13) = v12) | ~ (frontsegP(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (memberP(v14, v13) = v12) | ~ (memberP(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (cons(v14, v13) = v12) | ~ (cons(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (app(v14, v13) = v12) | ~ (app(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v12 = v11 | ~ (neq(v14, v13) = v12) | ~ (neq(v14, v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = nil | ~ (tl(v11) = v12) | ~ (app(v12, v13) = v14) | ? [v15] : ? [v16] : ? [v17] : (( ~ (v15 = 0) & ssList(v11) = v15) | (tl(v16) = v17 & ssList(v13) = v15 & app(v11, v13) = v16 & ( ~ (v15 = 0) | v17 = v14)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v11 = nil | ~ (hd(v11) = v12) | ~ (app(v11, v13) = v14) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssList(v11) = v15) | (hd(v14) = v16 & ssList(v13) = v15 & ( ~ (v15 = 0) | v16 = v12)))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (hd(v12) = v13) | ~ (lt(v11, v13) = v14) | ~ (ssItem(v11) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (strictorderedP(v16) = v17 & strictorderedP(v12) = v18 & ssList(v12) = v15 & cons(v11, v12) = v16 & ( ~ (v15 = 0) | (( ~ (v17 = 0) | v12 = nil | (v18 = 0 & v14 = 0)) & (v17 = 0 | ( ~ (v12 = nil) & ( ~ (v18 = 0) | ~ (v14 = 0)))))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (hd(v12) = v13) | ~ (leq(v11, v13) = v14) | ~ (ssItem(v11) = 0) | ? [v15] : ? [v16] : ? [v17] : ? [v18] : (totalorderedP(v16) = v17 & totalorderedP(v12) = v18 & ssList(v12) = v15 & cons(v11, v12) = v16 & ( ~ (v15 = 0) | (( ~ (v17 = 0) | v12 = nil | (v18 = 0 & v14 = 0)) & (v17 = 0 | ( ~ (v12 = nil) & ( ~ (v18 = 0) | ~ (v14 = 0)))))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (strictorderP(v11) = 0) | ~ (lt(v12, v13) = v14) | ~ (ssItem(v12) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssList(v11) = v15) | (lt(v13, v12) = v16 & ssItem(v13) = v15 & ( ~ (v15 = 0) | ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v16 = 0 | v14 = 0 | ~ (ssList(v17) = 0) | ~ (cons(v13, v21) = v22) | ~ (cons(v12, v18) = v19) | ~ (app(v20, v22) = v11) | ~ (app(v17, v19) = v20) | ? [v23] : (( ~ (v23 = 0) & ssList(v21) = v23) | ( ~ (v23 = 0) & ssList(v18) = v23))))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (totalorderP(v11) = 0) | ~ (leq(v12, v13) = v14) | ~ (ssItem(v12) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssList(v11) = v15) | (leq(v13, v12) = v16 & ssItem(v13) = v15 & ( ~ (v15 = 0) | ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : (v16 = 0 | v14 = 0 | ~ (ssList(v17) = 0) | ~ (cons(v13, v21) = v22) | ~ (cons(v12, v18) = v19) | ~ (app(v20, v22) = v11) | ~ (app(v17, v19) = v20) | ? [v23] : (( ~ (v23 = 0) & ssList(v21) = v23) | ( ~ (v23 = 0) & ssList(v18) = v23))))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (cyclefreeP(v11) = 0) | ~ (leq(v12, v13) = v14) | ~ (ssItem(v12) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssList(v11) = v15) | (leq(v13, v12) = v16 & ssItem(v13) = v15 & ( ~ (v15 = 0) | ! [v17] : ! [v18] : ! [v19] : ! [v20] : ! [v21] : ! [v22] : ( ~ (v16 = 0) | ~ (v14 = 0) | ~ (ssList(v17) = 0) | ~ (cons(v13, v21) = v22) | ~ (cons(v12, v18) = v19) | ~ (app(v20, v22) = v11) | ~ (app(v17, v19) = v20) | ? [v23] : (( ~ (v23 = 0) & ssList(v21) = v23) | ( ~ (v23 = 0) & ssList(v18) = v23))))))) & ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (ssList(v11) = 0) | ~ (cons(v12, nil) = v13) | ~ (app(v13, v11) = v14) | ? [v15] : ? [v16] : (cons(v12, v11) = v16 & ssItem(v12) = v15 & ( ~ (v15 = 0) | v16 = v14))) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = v11 | ~ (lt(v11, v12) = v13) | ~ (ssItem(v11) = 0) | ? [v14] : ? [v15] : (leq(v11, v12) = v15 & ssItem(v12) = v14 & ( ~ (v15 = 0) | ~ (v14 = 0)))) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = v11 | ~ (ssList(v11) = 0) | ~ (neq(v11, v12) = v13) | ? [v14] : ( ~ (v14 = 0) & ssList(v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | v12 = v11 | ~ (neq(v11, v12) = v13) | ~ (ssItem(v11) = 0) | ? [v14] : ( ~ (v14 = 0) & ssItem(v12) = v14)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (tl(v13) = v12) | ~ (tl(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (hd(v13) = v12) | ~ (hd(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (equalelemsP(v13) = v12) | ~ (equalelemsP(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (duplicatefreeP(v13) = v12) | ~ (duplicatefreeP(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (strictorderedP(v13) = v12) | ~ (strictorderedP(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (totalorderedP(v13) = v12) | ~ (totalorderedP(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (strictorderP(v13) = v12) | ~ (strictorderP(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (totalorderP(v13) = v12) | ~ (totalorderP(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (cyclefreeP(v13) = v12) | ~ (cyclefreeP(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (singletonP(v13) = v12) | ~ (singletonP(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (ssList(v13) = v12) | ~ (ssList(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = v11 | ~ (ssItem(v13) = v12) | ~ (ssItem(v13) = v11)) & ! [v11] : ! [v12] : ! [v13] : (v12 = 0 | ~ (singletonP(v11) = v12) | ~ (cons(v13, nil) = v11) | ? [v14] : (( ~ (v14 = 0) & ssList(v11) = v14) | ( ~ (v14 = 0) & ssItem(v13) = v14))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (gt(v11, v12) = v13) | ~ (ssItem(v11) = 0) | ? [v14] : ? [v15] : (lt(v12, v11) = v15 & ssItem(v12) = v14 & ( ~ (v14 = 0) | (( ~ (v15 = 0) | v13 = 0) & ( ~ (v13 = 0) | v15 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (geq(v11, v12) = v13) | ~ (ssItem(v11) = 0) | ? [v14] : ? [v15] : (leq(v12, v11) = v15 & ssItem(v12) = v14 & ( ~ (v14 = 0) | (( ~ (v15 = 0) | v13 = 0) & ( ~ (v13 = 0) | v15 = 0))))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (lt(v11, v12) = v13) | ~ (ssItem(v11) = 0) | ? [v14] : ? [v15] : (leq(v11, v12) = v15 & ssItem(v12) = v14 & ( ~ (v14 = 0) | (( ~ (v15 = 0) | v13 = 0 | v12 = v11) & ( ~ (v13 = 0) | (v15 = 0 & ~ (v12 = v11))))))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ssList(v11) = 0) | ~ (cons(v12, v11) = v13) | ? [v14] : ? [v15] : (tl(v13) = v15 & ssItem(v12) = v14 & ( ~ (v14 = 0) | v15 = v11))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ssList(v11) = 0) | ~ (cons(v12, v11) = v13) | ? [v14] : ? [v15] : (hd(v13) = v15 & ssItem(v12) = v14 & ( ~ (v14 = 0) | v15 = v12))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ssList(v11) = 0) | ~ (cons(v12, v11) = v13) | ? [v14] : ? [v15] : (ssList(v13) = v15 & ssItem(v12) = v14 & ( ~ (v14 = 0) | v15 = 0))) & ! [v11] : ! [v12] : ! [v13] : ( ~ (ssList(v11) = 0) | ~ (app(v11, v12) = v13) | ? [v14] : ? [v15] : (ssList(v13) = v15 & ssList(v12) = v14 & ( ~ (v14 = 0) | v15 = 0))) & ! [v11] : ! [v12] : (v12 = v11 | ~ (geq(v11, v12) = 0) | ~ (ssItem(v11) = 0) | ? [v13] : ? [v14] : (geq(v12, v11) = v14 & ssItem(v12) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v11] : ! [v12] : (v12 = v11 | ~ (leq(v11, v12) = 0) | ~ (ssItem(v11) = 0) | ? [v13] : ? [v14] : (leq(v12, v11) = v14 & ssItem(v12) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v11] : ! [v12] : (v12 = v11 | ~ (segmentP(v11, v12) = 0) | ~ (ssList(v11) = 0) | ? [v13] : ? [v14] : (segmentP(v12, v11) = v14 & ssList(v12) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v11] : ! [v12] : (v12 = v11 | ~ (rearsegP(v11, v12) = 0) | ~ (ssList(v11) = 0) | ? [v13] : ? [v14] : (rearsegP(v12, v11) = v14 & ssList(v12) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v11] : ! [v12] : (v12 = v11 | ~ (frontsegP(v11, v12) = 0) | ~ (ssList(v11) = 0) | ? [v13] : ? [v14] : (frontsegP(v12, v11) = v14 & ssList(v12) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v11] : ! [v12] : (v12 = v11 | ~ (app(v11, nil) = v12) | ? [v13] : ( ~ (v13 = 0) & ssList(v11) = v13)) & ! [v11] : ! [v12] : (v12 = v11 | ~ (app(nil, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & ssList(v11) = v13)) & ! [v11] : ! [v12] : (v12 = nil | ~ (ssList(v11) = 0) | ~ (app(v11, v12) = nil) | ? [v13] : ( ~ (v13 = 0) & ssList(v12) = v13)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (geq(v11, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & ssItem(v11) = v13)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (equalelemsP(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v23 = v11 & v20 = 0 & v18 = 0 & v16 = 0 & v14 = 0 & ~ (v15 = v13) & ssList(v19) = 0 & ssList(v17) = 0 & cons(v15, v19) = v21 & cons(v13, v21) = v22 & app(v17, v22) = v11 & ssItem(v15) = 0 & ssItem(v13) = 0) | ( ~ (v13 = 0) & ssList(v11) = v13))) & ! [v11] : ! [v12] : (v12 = 0 | ~ (duplicatefreeP(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ((v26 = v11 & v24 = 0 & v20 = 0 & v18 = 0 & v16 = 0 & v15 = v13 & v14 = 0 & ssList(v23) = 0 & ssList(v19) = 0 & ssList(v17) = 0 & cons(v13, v23) = v25 & cons(v13, v19) = v21 & app(v22, v25) = v11 & app(v17, v21) = v22 & ssItem(v13) = 0) | ( ~ (v13 = 0) & ssList(v11) = v13))) & ! [v11] : ! [v12] : (v12 = 0 | ~ (strictorderedP(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ((v27 = v11 & v25 = 0 & v21 = 0 & v19 = 0 & v16 = 0 & v14 = 0 & ~ (v17 = 0) & lt(v13, v15) = v17 & ssList(v24) = 0 & ssList(v20) = 0 & ssList(v18) = 0 & cons(v15, v24) = v26 & cons(v13, v20) = v22 & app(v23, v26) = v11 & app(v18, v22) = v23 & ssItem(v15) = 0 & ssItem(v13) = 0) | ( ~ (v13 = 0) & ssList(v11) = v13))) & ! [v11] : ! [v12] : (v12 = 0 | ~ (totalorderedP(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ((v27 = v11 & v25 = 0 & v21 = 0 & v19 = 0 & v16 = 0 & v14 = 0 & ~ (v17 = 0) & leq(v13, v15) = v17 & ssList(v24) = 0 & ssList(v20) = 0 & ssList(v18) = 0 & cons(v15, v24) = v26 & cons(v13, v20) = v22 & app(v23, v26) = v11 & app(v18, v22) = v23 & ssItem(v15) = 0 & ssItem(v13) = 0) | ( ~ (v13 = 0) & ssList(v11) = v13))) & ! [v11] : ! [v12] : (v12 = 0 | ~ (strictorderP(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ((v28 = v11 & v26 = 0 & v22 = 0 & v20 = 0 & v16 = 0 & v14 = 0 & ~ (v18 = 0) & ~ (v17 = 0) & lt(v15, v13) = v18 & lt(v13, v15) = v17 & ssList(v25) = 0 & ssList(v21) = 0 & ssList(v19) = 0 & cons(v15, v25) = v27 & cons(v13, v21) = v23 & app(v24, v27) = v11 & app(v19, v23) = v24 & ssItem(v15) = 0 & ssItem(v13) = 0) | ( ~ (v13 = 0) & ssList(v11) = v13))) & ! [v11] : ! [v12] : (v12 = 0 | ~ (totalorderP(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ((v28 = v11 & v26 = 0 & v22 = 0 & v20 = 0 & v16 = 0 & v14 = 0 & ~ (v18 = 0) & ~ (v17 = 0) & leq(v15, v13) = v18 & leq(v13, v15) = v17 & ssList(v25) = 0 & ssList(v21) = 0 & ssList(v19) = 0 & cons(v15, v25) = v27 & cons(v13, v21) = v23 & app(v24, v27) = v11 & app(v19, v23) = v24 & ssItem(v15) = 0 & ssItem(v13) = 0) | ( ~ (v13 = 0) & ssList(v11) = v13))) & ! [v11] : ! [v12] : (v12 = 0 | ~ (cyclefreeP(v11) = v12) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ? [v26] : ? [v27] : ? [v28] : ((v28 = v11 & v26 = 0 & v22 = 0 & v20 = 0 & v18 = 0 & v17 = 0 & v16 = 0 & v14 = 0 & leq(v15, v13) = 0 & leq(v13, v15) = 0 & ssList(v25) = 0 & ssList(v21) = 0 & ssList(v19) = 0 & cons(v15, v25) = v27 & cons(v13, v21) = v23 & app(v24, v27) = v11 & app(v19, v23) = v24 & ssItem(v15) = 0 & ssItem(v13) = 0) | ( ~ (v13 = 0) & ssList(v11) = v13))) & ! [v11] : ! [v12] : (v12 = 0 | ~ (leq(v11, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & ssItem(v11) = v13)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (segmentP(v11, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & ssList(v11) = v13)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (segmentP(v11, nil) = v12) | ? [v13] : ( ~ (v13 = 0) & ssList(v11) = v13)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (rearsegP(v11, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & ssList(v11) = v13)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (rearsegP(v11, nil) = v12) | ? [v13] : ( ~ (v13 = 0) & ssList(v11) = v13)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (frontsegP(v11, v11) = v12) | ? [v13] : ( ~ (v13 = 0) & ssList(v11) = v13)) & ! [v11] : ! [v12] : (v12 = 0 | ~ (frontsegP(v11, nil) = v12) | ? [v13] : ( ~ (v13 = 0) & ssList(v11) = v13)) & ! [v11] : ! [v12] : (v11 = nil | ~ (tl(v11) = v12) | ? [v13] : ? [v14] : (ssList(v12) = v14 & ssList(v11) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v11] : ! [v12] : (v11 = nil | ~ (tl(v11) = v12) | ? [v13] : ? [v14] : ((v14 = 0 & v13 = v12 & ssList(v12) = 0) | ( ~ (v13 = 0) & ssList(v11) = v13))) & ! [v11] : ! [v12] : (v11 = nil | ~ (hd(v11) = v12) | ? [v13] : ? [v14] : (ssList(v11) = v13 & ssItem(v12) = v14 & ( ~ (v13 = 0) | v14 = 0))) & ! [v11] : ! [v12] : (v11 = nil | ~ (hd(v11) = v12) | ? [v13] : ? [v14] : ((v14 = 0 & v13 = v12 & ssItem(v12) = 0) | ( ~ (v13 = 0) & ssList(v11) = v13))) & ! [v11] : ! [v12] : (v11 = nil | ~ (ssList(v11) = 0) | ~ (app(v11, v12) = nil) | ? [v13] : ( ~ (v13 = 0) & ssList(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (gt(v11, v12) = 0) | ~ (ssItem(v11) = 0) | ? [v13] : ? [v14] : (gt(v12, v11) = v14 & ssItem(v12) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v11] : ! [v12] : ( ~ (tl(v11) = v12) | ? [v13] : ? [v14] : (hd(v11) = v14 & ssList(v11) = v13 & ( ~ (v13 = 0) | ! [v15] : (v15 = v11 | v15 = nil | v11 = nil | ~ (tl(v15) = v12) | ? [v16] : ? [v17] : (hd(v15) = v17 & ssList(v15) = v16 & ( ~ (v17 = v14) | ~ (v16 = 0))))))) & ! [v11] : ! [v12] : ( ~ (lt(v11, v12) = 0) | ~ (ssItem(v11) = 0) | ? [v13] : ? [v14] : (lt(v12, v11) = v14 & ssItem(v12) = v13 & ( ~ (v14 = 0) | ~ (v13 = 0)))) & ! [v11] : ! [v12] : ( ~ (segmentP(v11, v12) = 0) | ~ (ssList(v11) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = v11 & v17 = 0 & v14 = 0 & ssList(v16) = 0 & ssList(v13) = 0 & app(v15, v16) = v11 & app(v13, v12) = v15) | ( ~ (v13 = 0) & ssList(v12) = v13))) & ! [v11] : ! [v12] : ( ~ (rearsegP(v11, v12) = 0) | ~ (ssList(v11) = 0) | ? [v13] : ? [v14] : ? [v15] : ((v15 = v11 & v14 = 0 & ssList(v13) = 0 & app(v13, v12) = v11) | ( ~ (v13 = 0) & ssList(v12) = v13))) & ! [v11] : ! [v12] : ( ~ (frontsegP(v11, v12) = 0) | ~ (ssList(v11) = 0) | ? [v13] : ? [v14] : ? [v15] : ((v15 = v11 & v14 = 0 & ssList(v13) = 0 & app(v12, v13) = v11) | ( ~ (v13 = 0) & ssList(v12) = v13))) & ! [v11] : ! [v12] : ( ~ (memberP(v11, v12) = 0) | ~ (ssList(v11) = 0) | ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ((v18 = v11 & v16 = 0 & v14 = 0 & ssList(v15) = 0 & ssList(v13) = 0 & cons(v12, v15) = v17 & app(v13, v17) = v11) | ( ~ (v13 = 0) & ssItem(v12) = v13))) & ! [v11] : ! [v12] : ( ~ (ssList(v11) = 0) | ~ (cons(v12, v11) = v11) | ? [v13] : ( ~ (v13 = 0) & ssItem(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (ssList(v11) = 0) | ~ (cons(v12, v11) = nil) | ? [v13] : ( ~ (v13 = 0) & ssItem(v12) = v13)) & ! [v11] : ! [v12] : ( ~ (cons(v11, nil) = v12) | ? [v13] : ? [v14] : (equalelemsP(v12) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v11] : ! [v12] : ( ~ (cons(v11, nil) = v12) | ? [v13] : ? [v14] : (duplicatefreeP(v12) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v11] : ! [v12] : ( ~ (cons(v11, nil) = v12) | ? [v13] : ? [v14] : (strictorderedP(v12) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v11] : ! [v12] : ( ~ (cons(v11, nil) = v12) | ? [v13] : ? [v14] : (totalorderedP(v12) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v11] : ! [v12] : ( ~ (cons(v11, nil) = v12) | ? [v13] : ? [v14] : (strictorderP(v12) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v11] : ! [v12] : ( ~ (cons(v11, nil) = v12) | ? [v13] : ? [v14] : (totalorderP(v12) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v11] : ! [v12] : ( ~ (cons(v11, nil) = v12) | ? [v13] : ? [v14] : (cyclefreeP(v12) = v14 & ssItem(v11) = v13 & ( ~ (v13 = 0) | v14 = 0))) & ! [v11] : (v11 = nil | ~ (segmentP(nil, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & ssList(v11) = v12)) & ! [v11] : (v11 = nil | ~ (rearsegP(nil, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & ssList(v11) = v12)) & ! [v11] : (v11 = nil | ~ (frontsegP(nil, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & ssList(v11) = v12)) & ! [v11] : (v11 = nil | ~ (ssList(v11) = 0) | ? [v12] : ? [v13] : (ssList(v12) = 0 & cons(v13, v12) = v11 & ssItem(v13) = 0)) & ! [v11] : (v11 = nil | ~ (app(nil, nil) = v11)) & ! [v11] : (v11 = 0 | ~ (segmentP(nil, nil) = v11)) & ! [v11] : (v11 = 0 | ~ (rearsegP(nil, nil) = v11)) & ! [v11] : (v11 = 0 | ~ (frontsegP(nil, nil) = v11)) & ! [v11] : ( ~ (lt(v11, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & ssItem(v11) = v12)) & ! [v11] : ( ~ (singletonP(v11) = 0) | ? [v12] : ? [v13] : ? [v14] : ((v14 = v11 & v13 = 0 & cons(v12, nil) = v11 & ssItem(v12) = 0) | ( ~ (v12 = 0) & ssList(v11) = v12))) & ! [v11] : ( ~ (memberP(nil, v11) = 0) | ? [v12] : ( ~ (v12 = 0) & ssItem(v11) = v12)) & ! [v11] : ( ~ (ssList(v11) = 0) | ~ (neq(v11, v11) = 0)) & ! [v11] : ( ~ (neq(v11, v11) = 0) | ~ (ssItem(v11) = 0)) & ! [v11] : ( ~ (neq(v11, nil) = 0) | ? [v12] : ? [v13] : ? [v14] : (segmentP(v2, v11) = v13 & segmentP(v1, v11) = v14 & ssList(v11) = v12 & ( ~ (v14 = 0) | ~ (v13 = 0) | ~ (v12 = 0)))) & ( ~ (v3 = 0) | (v8 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & segmentP(v2, v4) = 0 & segmentP(v1, v4) = 0 & ssList(v4) = 0 & neq(v4, nil) = 0)) & ( ~ (v2 = nil) | ~ (v1 = nil)) & ( ~ (v2 = nil) | v1 = nil))
% 23.30/6.95 | 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, all_0_10_10 yields:
% 23.30/6.95 | (1) ~ (all_0_0_0 = all_0_1_1) & ~ (all_0_10_10 = 0) & equalelemsP(nil) = 0 & duplicatefreeP(nil) = 0 & strictorderedP(nil) = 0 & totalorderedP(nil) = 0 & strictorderP(nil) = 0 & totalorderP(nil) = 0 & cyclefreeP(nil) = 0 & singletonP(nil) = all_0_10_10 & ssList(all_0_8_8) = 0 & ssList(all_0_9_9) = 0 & ssList(nil) = 0 & neq(all_0_8_8, nil) = all_0_7_7 & ssItem(all_0_0_0) = 0 & ssItem(all_0_1_1) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v3 = 0 | ~ (strictorderedP(v0) = 0) | ~ (lt(v1, v2) = v3) | ~ (ssList(v4) = 0) | ~ (cons(v2, v8) = v9) | ~ (cons(v1, v5) = v6) | ~ (app(v7, v9) = v0) | ~ (app(v4, v6) = v7) | ~ (ssItem(v1) = 0) | ? [v10] : (( ~ (v10 = 0) & ssList(v8) = v10) | ( ~ (v10 = 0) & ssList(v5) = v10) | ( ~ (v10 = 0) & ssList(v0) = v10) | ( ~ (v10 = 0) & ssItem(v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v3 = 0 | ~ (totalorderedP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssList(v4) = 0) | ~ (cons(v2, v8) = v9) | ~ (cons(v1, v5) = v6) | ~ (app(v7, v9) = v0) | ~ (app(v4, v6) = v7) | ~ (ssItem(v1) = 0) | ? [v10] : (( ~ (v10 = 0) & ssList(v8) = v10) | ( ~ (v10 = 0) & ssList(v5) = v10) | ( ~ (v10 = 0) & ssList(v0) = v10) | ( ~ (v10 = 0) & ssItem(v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (duplicatefreeP(v0) = 0) | ~ (ssList(v2) = 0) | ~ (cons(v1, v6) = v7) | ~ (cons(v1, v3) = v4) | ~ (app(v5, v7) = v0) | ~ (app(v2, v4) = v5) | ~ (ssItem(v1) = 0) | ? [v8] : (( ~ (v8 = 0) & ssList(v6) = v8) | ( ~ (v8 = 0) & ssList(v3) = v8) | ( ~ (v8 = 0) & ssList(v0) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (segmentP(v5, v1) = v6) | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v3, v4) = v5) | ~ (app(v2, v0) = v3) | ? [v7] : (( ~ (v7 = 0) & ssList(v4) = v7) | ( ~ (v7 = 0) & ssList(v2) = v7) | ( ~ (v7 = 0) & ssList(v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (equalelemsP(v0) = 0) | ~ (ssList(v3) = 0) | ~ (cons(v2, v4) = v5) | ~ (cons(v1, v5) = v6) | ~ (app(v3, v6) = v0) | ~ (ssItem(v2) = 0) | ~ (ssItem(v1) = 0) | ? [v7] : (( ~ (v7 = 0) & ssList(v4) = v7) | ( ~ (v7 = 0) & ssList(v0) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (frontsegP(v3, v5) = v6) | ~ (cons(v1, v4) = v5) | ~ (cons(v0, v2) = v3) | ~ (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ? [v7] : ? [v8] : (( ~ (v7 = 0) & ssList(v2) = v7) | (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 = 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = 0 | ~ (segmentP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v4, v5) = v0) | ~ (app(v3, v1) = v4) | ? [v6] : (( ~ (v6 = 0) & ssList(v5) = v6) | ( ~ (v6 = 0) & ssList(v3) = v6) | ( ~ (v6 = 0) & ssList(v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = 0 | ~ (memberP(v0, v1) = v2) | ~ (ssList(v3) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v1, v4) = v5) | ~ (app(v3, v5) = v0) | ? [v6] : (( ~ (v6 = 0) & ssList(v4) = v6) | ( ~ (v6 = 0) & ssItem(v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (memberP(v4, v0) = v5) | ~ (memberP(v1, v0) = v2) | ~ (app(v1, v3) = v4) | ~ (ssItem(v0) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & ssList(v1) = v6) | (memberP(v3, v0) = v7 & ssList(v3) = v6 & ( ~ (v6 = 0) | (( ~ (v5 = 0) | v7 = 0 | v2 = 0) & (v5 = 0 | ( ~ (v7 = 0) & ~ (v2 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ssList(v0) = 0) | ~ (cons(v3, v1) = v4) | ~ (app(v4, v0) = v5) | ~ (app(v1, v0) = v2) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & ssList(v1) = v6) | (cons(v3, v2) = v7 & ssItem(v3) = v6 & ( ~ (v6 = 0) | v7 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssItem(v4) = v5) | ( ~ (v5 = 0) & ssItem(v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (rearsegP(v3, v1) = v4) | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssList(v2) = v5) | ( ~ (v5 = 0) & ssList(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (frontsegP(v3, v1) = v4) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v0, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & ssList(v2) = v5) | ( ~ (v5 = 0) & ssList(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssItem(v4) = v5) | ( ~ (v5 = 0) & ssItem(v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (memberP(v3, v0) = v4) | ~ (cons(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ? [v5] : ? [v6] : (memberP(v2, v0) = v6 & ssList(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | v6 = 0 | v1 = v0) & (v4 = 0 | ( ~ (v6 = 0) & ~ (v1 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ssList(v0) = 0) | ~ (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & ssList(v1) = v5) | (ssList(v3) = v5 & app(v1, v3) = v6 & app(v0, v6) = v7 & ( ~ (v5 = 0) | v7 = v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & ssList(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ssList(v0) = 0) | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (gt(v0, v2) = v3) | ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (gt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (geq(v0, v2) = v3) | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (geq(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lt(v0, v2) = v3) | ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (lt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lt(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (lt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (leq(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (segmentP(v0, v2) = v3) | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (segmentP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (rearsegP(v0, v2) = v3) | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (rearsegP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (frontsegP(v0, v2) = v3) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (frontsegP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (rearsegP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v3, v1) = v0) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (frontsegP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v0) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & ssList(v0) = v4) | (tl(v5) = v6 & ssList(v2) = v4 & app(v0, v2) = v5 & ( ~ (v4 = 0) | v6 = v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (hd(v3) = v5 & ssList(v2) = v4 & ( ~ (v4 = 0) | v5 = v1)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (hd(v1) = v2) | ~ (lt(v0, v2) = v3) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (strictorderedP(v5) = v6 & strictorderedP(v1) = v7 & ssList(v1) = v4 & cons(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v1 = nil | (v7 = 0 & v3 = 0)) & (v6 = 0 | ( ~ (v1 = nil) & ( ~ (v7 = 0) | ~ (v3 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (hd(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (totalorderedP(v5) = v6 & totalorderedP(v1) = v7 & ssList(v1) = v4 & cons(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v1 = nil | (v7 = 0 & v3 = 0)) & (v6 = 0 | ( ~ (v1 = nil) & ( ~ (v7 = 0) | ~ (v3 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (strictorderP(v0) = 0) | ~ (lt(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (lt(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v5 = 0 | v3 = 0 | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (totalorderP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (leq(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v5 = 0 | v3 = 0 | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cyclefreeP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (leq(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (v5 = 0) | ~ (v3 = 0) | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ? [v4] : ? [v5] : (cons(v1, v0) = v5 & ssItem(v1) = v4 & ( ~ (v4 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (lt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v0, v1) = v4 & ssItem(v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (ssList(v0) = 0) | ~ (neq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & ssList(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (neq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & ssItem(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | ~ (equalelemsP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | ~ (duplicatefreeP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderP(v2) = v1) | ~ (strictorderP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ (totalorderP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ (cyclefreeP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (singletonP(v0) = v1) | ~ (cons(v2, nil) = v0) | ? [v3] : (( ~ (v3 = 0) & ssList(v0) = v3) | ( ~ (v3 = 0) & ssItem(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (gt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (lt(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (geq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (lt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v0, v1) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0 | v1 = v0) & ( ~ (v2 = 0) | (v4 = 0 & ~ (v1 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (tl(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (app(v0, v1) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (geq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (leq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (frontsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (equalelemsP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v0 & v9 = 0 & v7 = 0 & v5 = 0 & v3 = 0 & ~ (v4 = v2) & ssList(v8) = 0 & ssList(v6) = 0 & cons(v4, v8) = v10 & cons(v2, v10) = v11 & app(v6, v11) = v0 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (duplicatefreeP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v15 = v0 & v13 = 0 & v9 = 0 & v7 = 0 & v5 = 0 & v4 = v2 & v3 = 0 & ssList(v12) = 0 & ssList(v8) = 0 & ssList(v6) = 0 & cons(v2, v12) = v14 & cons(v2, v8) = v10 & app(v11, v14) = v0 & app(v6, v10) = v11 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (strictorderedP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v0 & v14 = 0 & v10 = 0 & v8 = 0 & v5 = 0 & v3 = 0 & ~ (v6 = 0) & lt(v2, v4) = v6 & ssList(v13) = 0 & ssList(v9) = 0 & ssList(v7) = 0 & cons(v4, v13) = v15 & cons(v2, v9) = v11 & app(v12, v15) = v0 & app(v7, v11) = v12 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (totalorderedP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v0 & v14 = 0 & v10 = 0 & v8 = 0 & v5 = 0 & v3 = 0 & ~ (v6 = 0) & leq(v2, v4) = v6 & ssList(v13) = 0 & ssList(v9) = 0 & ssList(v7) = 0 & cons(v4, v13) = v15 & cons(v2, v9) = v11 & app(v12, v15) = v0 & app(v7, v11) = v12 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (strictorderP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v5 = 0 & v3 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & lt(v4, v2) = v7 & lt(v2, v4) = v6 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (totalorderP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v5 = 0 & v3 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & leq(v4, v2) = v7 & leq(v2, v4) = v6 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cyclefreeP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & v3 = 0 & leq(v4, v2) = 0 & leq(v2, v4) = 0 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (ssList(v1) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssList(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : (ssList(v0) = v2 & ssItem(v1) = v3 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssItem(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v0 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (gt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (hd(v0) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : (v4 = v0 | v4 = nil | v0 = nil | ~ (tl(v4) = v1) | ? [v5] : ? [v6] : (hd(v4) = v6 & ssList(v4) = v5 & ( ~ (v6 = v3) | ~ (v5 = 0))))))) & ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (lt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v0 & v6 = 0 & v3 = 0 & ssList(v5) = 0 & ssList(v2) = 0 & app(v4, v5) = v0 & app(v2, v1) = v4) | ( ~ (v2 = 0) & ssList(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & v3 = 0 & ssList(v2) = 0 & app(v2, v1) = v0) | ( ~ (v2 = 0) & ssList(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & v3 = 0 & ssList(v2) = 0 & app(v1, v2) = v0) | ( ~ (v2 = 0) & ssList(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (memberP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v0 & v5 = 0 & v3 = 0 & ssList(v4) = 0 & ssList(v2) = 0 & cons(v1, v4) = v6 & app(v2, v6) = v0) | ( ~ (v2 = 0) & ssItem(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v0) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = nil) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : (v0 = nil | ~ (segmentP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1)) & ! [v0] : (v0 = nil | ~ (rearsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1)) & ! [v0] : (v0 = nil | ~ (frontsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1)) & ! [v0] : (v0 = nil | ~ (ssList(v0) = 0) | ? [v1] : ? [v2] : (ssList(v1) = 0 & cons(v2, v1) = v0 & ssItem(v2) = 0)) & ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0)) & ! [v0] : (v0 = 0 | ~ (segmentP(nil, nil) = v0)) & ! [v0] : (v0 = 0 | ~ (rearsegP(nil, nil) = v0)) & ! [v0] : (v0 = 0 | ~ (frontsegP(nil, nil) = v0)) & ! [v0] : ( ~ (lt(v0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1)) & ! [v0] : ( ~ (singletonP(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v0 & v2 = 0 & cons(v1, nil) = v0 & ssItem(v1) = 0) | ( ~ (v1 = 0) & ssList(v0) = v1))) & ! [v0] : ( ~ (memberP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1)) & ! [v0] : ( ~ (ssList(v0) = 0) | ~ (neq(v0, v0) = 0)) & ! [v0] : ( ~ (neq(v0, v0) = 0) | ~ (ssItem(v0) = 0)) & ! [v0] : ( ~ (neq(v0, nil) = 0) | ? [v1] : ? [v2] : ? [v3] : (segmentP(all_0_8_8, v0) = v2 & segmentP(all_0_9_9, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0)))) & ( ~ (all_0_7_7 = 0) | (all_0_2_2 = 0 & all_0_3_3 = 0 & all_0_4_4 = 0 & all_0_5_5 = 0 & segmentP(all_0_8_8, all_0_6_6) = 0 & segmentP(all_0_9_9, all_0_6_6) = 0 & ssList(all_0_6_6) = 0 & neq(all_0_6_6, nil) = 0)) & ( ~ (all_0_8_8 = nil) | ~ (all_0_9_9 = nil)) & ( ~ (all_0_8_8 = nil) | all_0_9_9 = nil)
% 23.48/6.98 |
% 23.48/6.98 | Applying alpha-rule on (1) yields:
% 23.48/6.98 | (2) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = 0 | ~ (memberP(v0, v1) = v2) | ~ (ssList(v3) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v1, v4) = v5) | ~ (app(v3, v5) = v0) | ? [v6] : (( ~ (v6 = 0) & ssList(v4) = v6) | ( ~ (v6 = 0) & ssItem(v1) = v6)))
% 23.48/6.98 | (3) ~ (all_0_0_0 = all_0_1_1)
% 23.48/6.98 | (4) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v3 = 0 | ~ (totalorderedP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssList(v4) = 0) | ~ (cons(v2, v8) = v9) | ~ (cons(v1, v5) = v6) | ~ (app(v7, v9) = v0) | ~ (app(v4, v6) = v7) | ~ (ssItem(v1) = 0) | ? [v10] : (( ~ (v10 = 0) & ssList(v8) = v10) | ( ~ (v10 = 0) & ssList(v5) = v10) | ( ~ (v10 = 0) & ssList(v0) = v10) | ( ~ (v10 = 0) & ssItem(v2) = v10)))
% 23.48/6.98 | (5) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0))
% 23.48/6.98 | (6) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (tl(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v0)))
% 23.48/6.98 | (7) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.48/6.98 | (8) ! [v0] : (v0 = 0 | ~ (rearsegP(nil, nil) = v0))
% 23.48/6.98 | (9) strictorderP(nil) = 0
% 23.48/6.98 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (totalorderedP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v0 & v14 = 0 & v10 = 0 & v8 = 0 & v5 = 0 & v3 = 0 & ~ (v6 = 0) & leq(v2, v4) = v6 & ssList(v13) = 0 & ssList(v9) = 0 & ssList(v7) = 0 & cons(v4, v13) = v15 & cons(v2, v9) = v11 & app(v12, v15) = v0 & app(v7, v11) = v12 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 23.48/6.98 | (11) ! [v0] : ! [v1] : (v1 = v0 | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 23.48/6.98 | (12) duplicatefreeP(nil) = 0
% 23.48/6.98 | (13) ! [v0] : ( ~ (neq(v0, nil) = 0) | ? [v1] : ? [v2] : ? [v3] : (segmentP(all_0_8_8, v0) = v2 & segmentP(all_0_9_9, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))
% 23.48/6.98 | (14) ~ (all_0_8_8 = nil) | ~ (all_0_9_9 = nil)
% 23.48/6.98 | (15) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = nil) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 23.48/6.99 | (16) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lt(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (lt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 23.48/6.99 | (17) ! [v0] : ! [v1] : (v1 = 0 | ~ (totalorderP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v5 = 0 & v3 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & leq(v4, v2) = v7 & leq(v2, v4) = v6 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 23.48/6.99 | (18) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ? [v4] : ? [v5] : (cons(v1, v0) = v5 & ssItem(v1) = v4 & ( ~ (v4 = 0) | v5 = v3)))
% 23.48/6.99 | (19) ! [v0] : ( ~ (singletonP(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v0 & v2 = 0 & cons(v1, nil) = v0 & ssItem(v1) = 0) | ( ~ (v1 = 0) & ssList(v0) = v1)))
% 23.48/6.99 | (20) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & ssList(v0) = v4))
% 23.48/6.99 | (21) ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0))
% 23.48/6.99 | (22) ! [v0] : ! [v1] : (v1 = 0 | ~ (duplicatefreeP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v15 = v0 & v13 = 0 & v9 = 0 & v7 = 0 & v5 = 0 & v4 = v2 & v3 = 0 & ssList(v12) = 0 & ssList(v8) = 0 & ssList(v6) = 0 & cons(v2, v12) = v14 & cons(v2, v8) = v10 & app(v11, v14) = v0 & app(v6, v10) = v11 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 23.48/6.99 | (23) ssItem(all_0_0_0) = 0
% 23.48/6.99 | (24) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lt(v0, v2) = v3) | ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (lt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 23.48/6.99 | (25) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.48/6.99 | (26) singletonP(nil) = all_0_10_10
% 23.48/6.99 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 23.48/6.99 | (28) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 23.48/6.99 | (29) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.48/6.99 | (30) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) = v0))
% 23.48/6.99 | (31) ! [v0] : (v0 = nil | ~ (rearsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 23.48/6.99 | (32) ~ (all_0_10_10 = 0)
% 23.48/6.99 | (33) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.48/6.99 | (34) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v1)))
% 23.48/6.99 | (35) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0))
% 23.48/6.99 | (36) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (app(v0, v1) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 23.48/6.99 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0))
% 23.48/6.99 | (38) ! [v0] : (v0 = nil | ~ (ssList(v0) = 0) | ? [v1] : ? [v2] : (ssList(v1) = 0 & cons(v2, v1) = v0 & ssItem(v2) = 0))
% 23.48/6.99 | (39) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | ~ (equalelemsP(v2) = v0))
% 23.48/6.99 | (40) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (hd(v1) = v2) | ~ (lt(v0, v2) = v3) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (strictorderedP(v5) = v6 & strictorderedP(v1) = v7 & ssList(v1) = v4 & cons(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v1 = nil | (v7 = 0 & v3 = 0)) & (v6 = 0 | ( ~ (v1 = nil) & ( ~ (v7 = 0) | ~ (v3 = 0))))))))
% 23.48/6.99 | (41) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (hd(v3) = v5 & ssList(v2) = v4 & ( ~ (v4 = 0) | v5 = v1))))
% 23.48/6.99 | (42) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.48/6.99 | (43) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (neq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & ssItem(v1) = v3))
% 23.48/6.99 | (44) ! [v0] : ! [v1] : ( ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (hd(v0) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : (v4 = v0 | v4 = nil | v0 = nil | ~ (tl(v4) = v1) | ? [v5] : ? [v6] : (hd(v4) = v6 & ssList(v4) = v5 & ( ~ (v6 = v3) | ~ (v5 = 0)))))))
% 23.48/6.99 | (45) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (frontsegP(v3, v1) = v4) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v0, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & ssList(v2) = v5) | ( ~ (v5 = 0) & ssList(v1) = v5)))
% 23.48/6.99 | (46) ! [v0] : ! [v1] : (v1 = 0 | ~ (strictorderedP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v0 & v14 = 0 & v10 = 0 & v8 = 0 & v5 = 0 & v3 = 0 & ~ (v6 = 0) & lt(v2, v4) = v6 & ssList(v13) = 0 & ssList(v9) = 0 & ssList(v7) = 0 & cons(v4, v13) = v15 & cons(v2, v9) = v11 & app(v12, v15) = v0 & app(v7, v11) = v12 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 23.48/6.99 | (47) ! [v0] : ( ~ (lt(v0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 23.48/6.99 | (48) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.48/6.99 | (49) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (rearsegP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v3, v1) = v0) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4)))
% 23.48/6.99 | (50) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (equalelemsP(v0) = 0) | ~ (ssList(v3) = 0) | ~ (cons(v2, v4) = v5) | ~ (cons(v1, v5) = v6) | ~ (app(v3, v6) = v0) | ~ (ssItem(v2) = 0) | ~ (ssItem(v1) = 0) | ? [v7] : (( ~ (v7 = 0) & ssList(v4) = v7) | ( ~ (v7 = 0) & ssList(v0) = v7)))
% 23.48/7.00 | (51) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (singletonP(v0) = v1) | ~ (cons(v2, nil) = v0) | ? [v3] : (( ~ (v3 = 0) & ssList(v0) = v3) | ( ~ (v3 = 0) & ssItem(v2) = v3)))
% 23.48/7.00 | (52) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.48/7.00 | (53) neq(all_0_8_8, nil) = all_0_7_7
% 23.48/7.00 | (54) ssList(all_0_9_9) = 0
% 23.48/7.00 | (55) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (ssList(v0) = 0) | ~ (neq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & ssList(v1) = v3))
% 23.48/7.00 | (56) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.48/7.00 | (57) ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (geq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 23.48/7.00 | (58) ! [v0] : ! [v1] : ( ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & v3 = 0 & ssList(v2) = 0 & app(v1, v2) = v0) | ( ~ (v2 = 0) & ssList(v1) = v2)))
% 23.48/7.00 | (59) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = v0))
% 23.48/7.00 | (60) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cyclefreeP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (leq(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (v5 = 0) | ~ (v3 = 0) | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12)))))))
% 23.48/7.00 | (61) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssItem(v4) = v5) | ( ~ (v5 = 0) & ssItem(v2) = v5)))
% 23.48/7.00 | (62) ! [v0] : ! [v1] : ( ~ (memberP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v0 & v5 = 0 & v3 = 0 & ssList(v4) = 0 & ssList(v2) = 0 & cons(v1, v4) = v6 & app(v2, v6) = v0) | ( ~ (v2 = 0) & ssItem(v1) = v2)))
% 23.48/7.00 | (63) ~ (all_0_7_7 = 0) | (all_0_2_2 = 0 & all_0_3_3 = 0 & all_0_4_4 = 0 & all_0_5_5 = 0 & segmentP(all_0_8_8, all_0_6_6) = 0 & segmentP(all_0_9_9, all_0_6_6) = 0 & ssList(all_0_6_6) = 0 & neq(all_0_6_6, nil) = 0)
% 23.48/7.00 | (64) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (ssList(v1) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.48/7.00 | (65) ! [v0] : (v0 = 0 | ~ (segmentP(nil, nil) = v0))
% 23.48/7.00 | (66) ssList(nil) = 0
% 23.48/7.00 | (67) strictorderedP(nil) = 0
% 23.48/7.00 | (68) ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (lt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 23.48/7.00 | (69) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ssList(v0) = 0) | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4)))
% 23.48/7.00 | (70) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : (ssList(v0) = v2 & ssItem(v1) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 23.48/7.00 | (71) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssItem(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 23.48/7.00 | (72) ! [v0] : ! [v1] : (v1 = 0 | ~ (equalelemsP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v0 & v9 = 0 & v7 = 0 & v5 = 0 & v3 = 0 & ~ (v4 = v2) & ssList(v8) = 0 & ssList(v6) = 0 & cons(v4, v8) = v10 & cons(v2, v10) = v11 & app(v6, v11) = v0 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 23.48/7.00 | (73) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssList(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 23.48/7.00 | (74) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (memberP(v4, v0) = v5) | ~ (memberP(v1, v0) = v2) | ~ (app(v1, v3) = v4) | ~ (ssItem(v0) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & ssList(v1) = v6) | (memberP(v3, v0) = v7 & ssList(v3) = v6 & ( ~ (v6 = 0) | (( ~ (v5 = 0) | v7 = 0 | v2 = 0) & (v5 = 0 | ( ~ (v7 = 0) & ~ (v2 = 0))))))))
% 23.48/7.00 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = 0 | ~ (segmentP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v4, v5) = v0) | ~ (app(v3, v1) = v4) | ? [v6] : (( ~ (v6 = 0) & ssList(v5) = v6) | ( ~ (v6 = 0) & ssList(v3) = v6) | ( ~ (v6 = 0) & ssList(v1) = v6)))
% 23.48/7.00 | (76) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 23.48/7.00 | (77) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 23.48/7.00 | (78) ! [v0] : (v0 = 0 | ~ (frontsegP(nil, nil) = v0))
% 23.48/7.00 | (79) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (memberP(v3, v0) = v4) | ~ (cons(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ? [v5] : ? [v6] : (memberP(v2, v0) = v6 & ssList(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | v6 = 0 | v1 = v0) & (v4 = 0 | ( ~ (v6 = 0) & ~ (v1 = v0)))))))
% 23.48/7.00 | (80) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | ~ (duplicatefreeP(v2) = v0))
% 23.48/7.00 | (81) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0))
% 23.48/7.00 | (82) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.48/7.00 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (lt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v0, v1) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0 | v1 = v0) & ( ~ (v2 = 0) | (v4 = 0 & ~ (v1 = v0)))))))
% 23.48/7.00 | (84) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (totalorderP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (leq(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v5 = 0 | v3 = 0 | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12)))))))
% 23.48/7.00 | (85) ! [v0] : ! [v1] : ! [v2] : ( ~ (gt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (lt(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))))
% 23.48/7.00 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssItem(v4) = v5) | ( ~ (v5 = 0) & ssItem(v2) = v5)))
% 23.48/7.00 | (87) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 23.48/7.00 | (88) totalorderedP(nil) = 0
% 23.48/7.00 | (89) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderP(v2) = v1) | ~ (strictorderP(v2) = v0))
% 23.48/7.01 | (90) ! [v0] : ( ~ (ssList(v0) = 0) | ~ (neq(v0, v0) = 0))
% 23.48/7.01 | (91) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (segmentP(v5, v1) = v6) | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v3, v4) = v5) | ~ (app(v2, v0) = v3) | ? [v7] : (( ~ (v7 = 0) & ssList(v4) = v7) | ( ~ (v7 = 0) & ssList(v2) = v7) | ( ~ (v7 = 0) & ssList(v1) = v7)))
% 23.48/7.01 | (92) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v0) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 23.48/7.01 | (93) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.48/7.01 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0))
% 23.48/7.01 | (95) ssItem(all_0_1_1) = 0
% 23.48/7.01 | (96) ! [v0] : ! [v1] : (v0 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 23.48/7.01 | (97) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (leq(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 23.48/7.01 | (98) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (rearsegP(v0, v2) = v3) | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (rearsegP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 23.48/7.01 | (99) ! [v0] : ! [v1] : (v1 = v0 | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (frontsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 23.48/7.01 | (100) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.48/7.01 | (101) ! [v0] : ! [v1] : ! [v2] : ( ~ (geq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0)))))
% 23.48/7.01 | (102) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 23.48/7.01 | (103) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.48/7.01 | (104) totalorderP(nil) = 0
% 23.48/7.01 | (105) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (lt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v0, v1) = v4 & ssItem(v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0))))
% 23.48/7.01 | (106) ! [v0] : ! [v1] : (v1 = v0 | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 23.48/7.01 | (107) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0))
% 23.48/7.01 | (108) ! [v0] : ! [v1] : ( ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & v3 = 0 & ssList(v2) = 0 & app(v2, v1) = v0) | ( ~ (v2 = 0) & ssList(v1) = v2)))
% 23.48/7.01 | (109) ! [v0] : ! [v1] : (v1 = 0 | ~ (strictorderP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v5 = 0 & v3 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & lt(v4, v2) = v7 & lt(v2, v4) = v6 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 23.48/7.01 | (110) ! [v0] : (v0 = nil | ~ (frontsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 23.48/7.01 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (frontsegP(v3, v5) = v6) | ~ (cons(v1, v4) = v5) | ~ (cons(v0, v2) = v3) | ~ (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ? [v7] : ? [v8] : (( ~ (v7 = 0) & ssList(v2) = v7) | (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 = 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 = v0)))))))
% 23.48/7.01 | (112) ! [v0] : ( ~ (neq(v0, v0) = 0) | ~ (ssItem(v0) = 0))
% 23.48/7.01 | (113) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (strictorderP(v0) = 0) | ~ (lt(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (lt(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v5 = 0 | v3 = 0 | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12)))))))
% 23.48/7.01 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0))
% 23.48/7.01 | (115) ! [v0] : ! [v1] : ( ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (gt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 23.48/7.01 | (116) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 23.48/7.01 | (117) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ssList(v0) = 0) | ~ (cons(v3, v1) = v4) | ~ (app(v4, v0) = v5) | ~ (app(v1, v0) = v2) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & ssList(v1) = v6) | (cons(v3, v2) = v7 & ssItem(v3) = v6 & ( ~ (v6 = 0) | v7 = v5))))
% 23.48/7.01 | (118) ! [v0] : ( ~ (memberP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 23.48/7.01 | (119) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ (cyclefreeP(v2) = v0))
% 23.48/7.01 | (120) ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (leq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 23.48/7.01 | (121) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0))
% 23.48/7.01 | (122) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (segmentP(v0, v2) = v3) | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (segmentP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 23.48/7.01 | (123) equalelemsP(nil) = 0
% 23.48/7.01 | (124) ssList(all_0_8_8) = 0
% 23.48/7.01 | (125) ! [v0] : ! [v1] : (v1 = 0 | ~ (cyclefreeP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & v3 = 0 & leq(v4, v2) = 0 & leq(v2, v4) = 0 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 23.48/7.01 | (126) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 23.48/7.01 | (127) ! [v0] : ! [v1] : (v1 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 23.48/7.02 | (128) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 23.48/7.02 | (129) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4)))
% 23.48/7.02 | (130) cyclefreeP(nil) = 0
% 23.48/7.02 | (131) ~ (all_0_8_8 = nil) | all_0_9_9 = nil
% 23.48/7.02 | (132) ! [v0] : ! [v1] : ( ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v0 & v6 = 0 & v3 = 0 & ssList(v5) = 0 & ssList(v2) = 0 & app(v4, v5) = v0 & app(v2, v1) = v4) | ( ~ (v2 = 0) & ssList(v1) = v2)))
% 23.48/7.02 | (133) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.48/7.02 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (geq(v0, v2) = v3) | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (geq(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 23.48/7.02 | (135) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ssList(v0) = 0) | ~ (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & ssList(v1) = v5) | (ssList(v3) = v5 & app(v1, v3) = v6 & app(v0, v6) = v7 & ( ~ (v5 = 0) | v7 = v4))))
% 23.48/7.02 | (136) ! [v0] : (v0 = nil | ~ (segmentP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 23.48/7.02 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (hd(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (totalorderedP(v5) = v6 & totalorderedP(v1) = v7 & ssList(v1) = v4 & cons(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v1 = nil | (v7 = 0 & v3 = 0)) & (v6 = 0 | ( ~ (v1 = nil) & ( ~ (v7 = 0) | ~ (v3 = 0))))))))
% 23.48/7.02 | (138) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0))
% 23.48/7.02 | (139) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 23.48/7.02 | (140) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v3 = 0 | ~ (strictorderedP(v0) = 0) | ~ (lt(v1, v2) = v3) | ~ (ssList(v4) = 0) | ~ (cons(v2, v8) = v9) | ~ (cons(v1, v5) = v6) | ~ (app(v7, v9) = v0) | ~ (app(v4, v6) = v7) | ~ (ssItem(v1) = 0) | ? [v10] : (( ~ (v10 = 0) & ssList(v8) = v10) | ( ~ (v10 = 0) & ssList(v5) = v10) | ( ~ (v10 = 0) & ssList(v0) = v10) | ( ~ (v10 = 0) & ssItem(v2) = v10)))
% 23.48/7.02 | (141) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0))
% 23.48/7.02 | (142) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (duplicatefreeP(v0) = 0) | ~ (ssList(v2) = 0) | ~ (cons(v1, v6) = v7) | ~ (cons(v1, v3) = v4) | ~ (app(v5, v7) = v0) | ~ (app(v2, v4) = v5) | ~ (ssItem(v1) = 0) | ? [v8] : (( ~ (v8 = 0) & ssList(v6) = v8) | ( ~ (v8 = 0) & ssList(v3) = v8) | ( ~ (v8 = 0) & ssList(v0) = v8)))
% 23.48/7.02 | (143) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ (totalorderP(v2) = v0))
% 23.48/7.02 | (144) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (frontsegP(v0, v2) = v3) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (frontsegP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 23.48/7.02 | (145) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & ssList(v0) = v4) | (tl(v5) = v6 & ssList(v2) = v4 & app(v0, v2) = v5 & ( ~ (v4 = 0) | v6 = v3))))
% 23.48/7.02 | (146) ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 23.48/7.02 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (rearsegP(v3, v1) = v4) | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssList(v2) = v5) | ( ~ (v5 = 0) & ssList(v1) = v5)))
% 23.48/7.02 | (148) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (frontsegP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v0) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4)))
% 23.48/7.02 | (149) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (gt(v0, v2) = v3) | ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (gt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0)))))
% 23.48/7.02 |
% 23.48/7.02 | Instantiating formula (55) with all_0_7_7, nil, all_0_8_8 and discharging atoms ssList(all_0_8_8) = 0, neq(all_0_8_8, nil) = all_0_7_7, yields:
% 23.48/7.02 | (150) all_0_7_7 = 0 | all_0_8_8 = nil | ? [v0] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 23.48/7.02 |
% 23.48/7.02 +-Applying beta-rule and splitting (63), into two cases.
% 23.48/7.02 |-Branch one:
% 23.48/7.02 | (151) ~ (all_0_7_7 = 0)
% 23.48/7.02 |
% 23.48/7.02 +-Applying beta-rule and splitting (150), into two cases.
% 23.48/7.02 |-Branch one:
% 23.48/7.02 | (152) all_0_8_8 = nil
% 23.48/7.02 |
% 23.48/7.02 +-Applying beta-rule and splitting (131), into two cases.
% 23.48/7.02 |-Branch one:
% 23.48/7.02 | (153) ~ (all_0_8_8 = nil)
% 23.48/7.02 |
% 23.48/7.02 | Equations (152) can reduce 153 to:
% 23.48/7.02 | (154) $false
% 23.48/7.02 |
% 23.48/7.02 |-The branch is then unsatisfiable
% 23.48/7.02 |-Branch two:
% 23.48/7.02 | (152) all_0_8_8 = nil
% 23.48/7.02 | (156) all_0_9_9 = nil
% 23.48/7.02 |
% 23.48/7.02 +-Applying beta-rule and splitting (14), into two cases.
% 23.48/7.02 |-Branch one:
% 23.48/7.02 | (153) ~ (all_0_8_8 = nil)
% 23.48/7.02 |
% 23.48/7.02 | Equations (152) can reduce 153 to:
% 23.48/7.02 | (154) $false
% 23.48/7.02 |
% 23.48/7.02 |-The branch is then unsatisfiable
% 23.48/7.02 |-Branch two:
% 23.48/7.02 | (152) all_0_8_8 = nil
% 23.48/7.02 | (160) ~ (all_0_9_9 = nil)
% 23.48/7.02 |
% 23.48/7.02 | Equations (156) can reduce 160 to:
% 23.48/7.02 | (154) $false
% 23.48/7.02 |
% 23.48/7.02 |-The branch is then unsatisfiable
% 23.48/7.02 |-Branch two:
% 23.48/7.02 | (153) ~ (all_0_8_8 = nil)
% 23.48/7.02 | (163) all_0_7_7 = 0 | ? [v0] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 23.48/7.02 |
% 23.48/7.02 +-Applying beta-rule and splitting (163), into two cases.
% 23.48/7.02 |-Branch one:
% 23.48/7.02 | (164) all_0_7_7 = 0
% 23.48/7.02 |
% 23.48/7.02 | Equations (164) can reduce 151 to:
% 23.48/7.02 | (154) $false
% 23.48/7.02 |
% 23.48/7.02 |-The branch is then unsatisfiable
% 23.48/7.02 |-Branch two:
% 23.48/7.02 | (151) ~ (all_0_7_7 = 0)
% 23.48/7.02 | (167) ? [v0] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 23.48/7.03 |
% 23.48/7.03 | Instantiating (167) with all_18_0_11 yields:
% 23.48/7.03 | (168) ~ (all_18_0_11 = 0) & ssList(nil) = all_18_0_11
% 23.48/7.03 |
% 23.48/7.03 | Applying alpha-rule on (168) yields:
% 23.48/7.03 | (169) ~ (all_18_0_11 = 0)
% 23.48/7.03 | (170) ssList(nil) = all_18_0_11
% 23.48/7.03 |
% 23.48/7.03 | Instantiating formula (128) with nil, all_18_0_11, 0 and discharging atoms ssList(nil) = all_18_0_11, ssList(nil) = 0, yields:
% 23.48/7.03 | (171) all_18_0_11 = 0
% 23.48/7.03 |
% 23.48/7.03 | Equations (171) can reduce 169 to:
% 23.48/7.03 | (154) $false
% 23.48/7.03 |
% 23.48/7.03 |-The branch is then unsatisfiable
% 23.48/7.03 |-Branch two:
% 23.48/7.03 | (164) all_0_7_7 = 0
% 23.48/7.03 | (174) all_0_2_2 = 0 & all_0_3_3 = 0 & all_0_4_4 = 0 & all_0_5_5 = 0 & segmentP(all_0_8_8, all_0_6_6) = 0 & segmentP(all_0_9_9, all_0_6_6) = 0 & ssList(all_0_6_6) = 0 & neq(all_0_6_6, nil) = 0
% 23.48/7.03 |
% 23.48/7.03 | Applying alpha-rule on (174) yields:
% 23.48/7.03 | (175) all_0_5_5 = 0
% 23.48/7.03 | (176) all_0_3_3 = 0
% 23.48/7.03 | (177) segmentP(all_0_8_8, all_0_6_6) = 0
% 23.48/7.03 | (178) neq(all_0_6_6, nil) = 0
% 23.48/7.03 | (179) ssList(all_0_6_6) = 0
% 23.48/7.03 | (180) segmentP(all_0_9_9, all_0_6_6) = 0
% 23.48/7.03 | (181) all_0_4_4 = 0
% 23.48/7.03 | (182) all_0_2_2 = 0
% 23.48/7.03 |
% 23.48/7.03 | Instantiating formula (13) with all_0_6_6 and discharging atoms neq(all_0_6_6, nil) = 0, yields:
% 23.48/7.03 | (183) ? [v0] : ? [v1] : ? [v2] : (segmentP(all_0_8_8, all_0_6_6) = v1 & segmentP(all_0_9_9, all_0_6_6) = v2 & ssList(all_0_6_6) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 23.48/7.03 |
% 23.48/7.03 | Instantiating (183) with all_25_0_17, all_25_1_18, all_25_2_19 yields:
% 23.48/7.03 | (184) segmentP(all_0_8_8, all_0_6_6) = all_25_1_18 & segmentP(all_0_9_9, all_0_6_6) = all_25_0_17 & ssList(all_0_6_6) = all_25_2_19 & ( ~ (all_25_0_17 = 0) | ~ (all_25_1_18 = 0) | ~ (all_25_2_19 = 0))
% 23.48/7.03 |
% 23.48/7.03 | Applying alpha-rule on (184) yields:
% 23.48/7.03 | (185) segmentP(all_0_8_8, all_0_6_6) = all_25_1_18
% 23.48/7.03 | (186) segmentP(all_0_9_9, all_0_6_6) = all_25_0_17
% 23.48/7.03 | (187) ssList(all_0_6_6) = all_25_2_19
% 23.48/7.03 | (188) ~ (all_25_0_17 = 0) | ~ (all_25_1_18 = 0) | ~ (all_25_2_19 = 0)
% 23.48/7.03 |
% 23.48/7.03 | Instantiating formula (94) with all_0_8_8, all_0_6_6, all_25_1_18, 0 and discharging atoms segmentP(all_0_8_8, all_0_6_6) = all_25_1_18, segmentP(all_0_8_8, all_0_6_6) = 0, yields:
% 23.48/7.03 | (189) all_25_1_18 = 0
% 23.48/7.03 |
% 23.48/7.03 | Instantiating formula (94) with all_0_9_9, all_0_6_6, all_25_0_17, 0 and discharging atoms segmentP(all_0_9_9, all_0_6_6) = all_25_0_17, segmentP(all_0_9_9, all_0_6_6) = 0, yields:
% 23.48/7.03 | (190) all_25_0_17 = 0
% 23.48/7.03 |
% 23.48/7.03 | Instantiating formula (128) with all_0_6_6, all_25_2_19, 0 and discharging atoms ssList(all_0_6_6) = all_25_2_19, ssList(all_0_6_6) = 0, yields:
% 23.48/7.03 | (191) all_25_2_19 = 0
% 23.48/7.03 |
% 23.48/7.03 +-Applying beta-rule and splitting (188), into two cases.
% 23.48/7.03 |-Branch one:
% 23.48/7.03 | (192) ~ (all_25_0_17 = 0)
% 23.48/7.03 |
% 23.48/7.03 | Equations (190) can reduce 192 to:
% 23.48/7.03 | (154) $false
% 23.48/7.03 |
% 23.48/7.03 |-The branch is then unsatisfiable
% 23.48/7.03 |-Branch two:
% 23.48/7.03 | (190) all_25_0_17 = 0
% 23.48/7.03 | (195) ~ (all_25_1_18 = 0) | ~ (all_25_2_19 = 0)
% 23.48/7.03 |
% 23.48/7.03 +-Applying beta-rule and splitting (195), into two cases.
% 23.48/7.03 |-Branch one:
% 23.48/7.03 | (196) ~ (all_25_1_18 = 0)
% 23.48/7.03 |
% 23.48/7.03 | Equations (189) can reduce 196 to:
% 23.48/7.03 | (154) $false
% 23.48/7.03 |
% 23.48/7.03 |-The branch is then unsatisfiable
% 23.48/7.03 |-Branch two:
% 23.48/7.03 | (189) all_25_1_18 = 0
% 23.48/7.03 | (199) ~ (all_25_2_19 = 0)
% 23.48/7.03 |
% 23.48/7.03 | Equations (191) can reduce 199 to:
% 23.48/7.03 | (154) $false
% 23.48/7.03 |
% 23.48/7.03 |-The branch is then unsatisfiable
% 23.48/7.03 % SZS output end Proof for theBenchmark
% 23.48/7.03
% 23.48/7.03 6442ms
%------------------------------------------------------------------------------