TSTP Solution File: SWC388+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWC388+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n016.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 20:17:52 EDT 2022
% Result : Theorem 22.33s 6.69s
% Output : Proof 34.73s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWC388+1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13 % Command : ePrincess-casc -timeout=%d %s
% 0.14/0.34 % Computer : n016.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sun Jun 12 07:12:27 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.53/0.59 ____ _
% 0.53/0.59 ___ / __ \_____(_)___ ________ __________
% 0.53/0.59 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.53/0.59 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.53/0.59 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.53/0.59
% 0.53/0.59 A Theorem Prover for First-Order Logic
% 0.53/0.59 (ePrincess v.1.0)
% 0.53/0.59
% 0.53/0.59 (c) Philipp Rümmer, 2009-2015
% 0.53/0.59 (c) Peter Backeman, 2014-2015
% 0.53/0.59 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.53/0.59 Free software under GNU Lesser General Public License (LGPL).
% 0.53/0.59 Bug reports to peter@backeman.se
% 0.53/0.59
% 0.53/0.59 For more information, visit http://user.uu.se/~petba168/breu/
% 0.53/0.59
% 0.53/0.59 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.73/0.64 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.36/1.11 Prover 0: Preprocessing ...
% 4.93/1.70 Prover 0: Constructing countermodel ...
% 19.02/5.93 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.41/6.05 Prover 1: Preprocessing ...
% 20.82/6.32 Prover 1: Constructing countermodel ...
% 22.33/6.69 Prover 1: proved (757ms)
% 22.33/6.69 Prover 0: stopped
% 22.33/6.69
% 22.33/6.69 No countermodel exists, formula is valid
% 22.33/6.69 % SZS status Theorem for theBenchmark
% 22.33/6.69
% 22.33/6.69 Generating proof ... found it (size 359)
% 33.70/9.34
% 33.70/9.34 % SZS output start Proof for theBenchmark
% 33.70/9.34 Assumed formulas after preprocessing and simplification:
% 33.70/9.35 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ( ~ (v6 = v5) & ~ (v0 = 0) & equalelemsP(nil) = 0 & duplicatefreeP(nil) = 0 & strictorderedP(nil) = 0 & totalorderedP(nil) = 0 & strictorderP(nil) = 0 & totalorderP(nil) = 0 & cyclefreeP(nil) = 0 & segmentP(v2, v1) = 0 & singletonP(v1) = v3 & singletonP(nil) = v0 & ssList(v2) = 0 & ssList(v1) = 0 & ssList(nil) = 0 & neq(v2, nil) = v4 & ssItem(v6) = 0 & ssItem(v5) = 0 & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v10 = 0 | ~ (strictorderedP(v7) = 0) | ~ (lt(v8, v9) = v10) | ~ (ssList(v11) = 0) | ~ (cons(v9, v15) = v16) | ~ (cons(v8, v12) = v13) | ~ (app(v14, v16) = v7) | ~ (app(v11, v13) = v14) | ~ (ssItem(v8) = 0) | ? [v17] : (( ~ (v17 = 0) & ssList(v15) = v17) | ( ~ (v17 = 0) & ssList(v12) = v17) | ( ~ (v17 = 0) & ssList(v7) = v17) | ( ~ (v17 = 0) & ssItem(v9) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : (v10 = 0 | ~ (totalorderedP(v7) = 0) | ~ (leq(v8, v9) = v10) | ~ (ssList(v11) = 0) | ~ (cons(v9, v15) = v16) | ~ (cons(v8, v12) = v13) | ~ (app(v14, v16) = v7) | ~ (app(v11, v13) = v14) | ~ (ssItem(v8) = 0) | ? [v17] : (( ~ (v17 = 0) & ssList(v15) = v17) | ( ~ (v17 = 0) & ssList(v12) = v17) | ( ~ (v17 = 0) & ssList(v7) = v17) | ( ~ (v17 = 0) & ssItem(v9) = v17))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (duplicatefreeP(v7) = 0) | ~ (ssList(v9) = 0) | ~ (cons(v8, v13) = v14) | ~ (cons(v8, v10) = v11) | ~ (app(v12, v14) = v7) | ~ (app(v9, v11) = v12) | ~ (ssItem(v8) = 0) | ? [v15] : (( ~ (v15 = 0) & ssList(v13) = v15) | ( ~ (v15 = 0) & ssList(v10) = v15) | ( ~ (v15 = 0) & ssList(v7) = v15))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v13 = 0 | ~ (segmentP(v12, v8) = v13) | ~ (segmentP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ~ (app(v10, v11) = v12) | ~ (app(v9, v7) = v10) | ? [v14] : (( ~ (v14 = 0) & ssList(v11) = v14) | ( ~ (v14 = 0) & ssList(v9) = v14) | ( ~ (v14 = 0) & ssList(v8) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v9 = v8 | ~ (equalelemsP(v7) = 0) | ~ (ssList(v10) = 0) | ~ (cons(v9, v11) = v12) | ~ (cons(v8, v12) = v13) | ~ (app(v10, v13) = v7) | ~ (ssItem(v9) = 0) | ~ (ssItem(v8) = 0) | ? [v14] : (( ~ (v14 = 0) & ssList(v11) = v14) | ( ~ (v14 = 0) & ssList(v7) = v14))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (frontsegP(v10, v12) = v13) | ~ (cons(v8, v11) = v12) | ~ (cons(v7, v9) = v10) | ~ (ssItem(v8) = 0) | ~ (ssItem(v7) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssList(v9) = v14) | (frontsegP(v9, v11) = v15 & ssList(v11) = v14 & ( ~ (v14 = 0) | (( ~ (v15 = 0) | ~ (v8 = v7) | v13 = 0) & ( ~ (v13 = 0) | (v15 = 0 & v8 = v7))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = 0 | ~ (segmentP(v7, v8) = v9) | ~ (ssList(v7) = 0) | ~ (app(v11, v12) = v7) | ~ (app(v10, v8) = v11) | ? [v13] : (( ~ (v13 = 0) & ssList(v12) = v13) | ( ~ (v13 = 0) & ssList(v10) = v13) | ( ~ (v13 = 0) & ssList(v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = 0 | ~ (memberP(v7, v8) = v9) | ~ (ssList(v10) = 0) | ~ (ssList(v7) = 0) | ~ (cons(v8, v11) = v12) | ~ (app(v10, v12) = v7) | ? [v13] : (( ~ (v13 = 0) & ssList(v11) = v13) | ( ~ (v13 = 0) & ssItem(v8) = v13))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (memberP(v11, v7) = v12) | ~ (memberP(v8, v7) = v9) | ~ (app(v8, v10) = v11) | ~ (ssItem(v7) = 0) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssList(v8) = v13) | (memberP(v10, v7) = v14 & ssList(v10) = v13 & ( ~ (v13 = 0) | (( ~ (v12 = 0) | v14 = 0 | v9 = 0) & (v12 = 0 | ( ~ (v14 = 0) & ~ (v9 = 0)))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (ssList(v7) = 0) | ~ (cons(v10, v8) = v11) | ~ (app(v11, v7) = v12) | ~ (app(v8, v7) = v9) | ? [v13] : ? [v14] : (( ~ (v13 = 0) & ssList(v8) = v13) | (cons(v10, v9) = v14 & ssItem(v10) = v13 & ( ~ (v13 = 0) | v14 = v12)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v9 | ~ (ssList(v8) = 0) | ~ (ssList(v7) = 0) | ~ (cons(v11, v8) = v10) | ~ (cons(v9, v7) = v10) | ? [v12] : (( ~ (v12 = 0) & ssItem(v11) = v12) | ( ~ (v12 = 0) & ssItem(v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (rearsegP(v10, v8) = v11) | ~ (rearsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ~ (app(v9, v7) = v10) | ? [v12] : (( ~ (v12 = 0) & ssList(v9) = v12) | ( ~ (v12 = 0) & ssList(v8) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (frontsegP(v10, v8) = v11) | ~ (frontsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ~ (app(v7, v9) = v10) | ? [v12] : (( ~ (v12 = 0) & ssList(v9) = v12) | ( ~ (v12 = 0) & ssList(v8) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = v7 | ~ (ssList(v8) = 0) | ~ (ssList(v7) = 0) | ~ (cons(v11, v8) = v10) | ~ (cons(v9, v7) = v10) | ? [v12] : (( ~ (v12 = 0) & ssItem(v11) = v12) | ( ~ (v12 = 0) & ssItem(v9) = v12))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (memberP(v10, v7) = v11) | ~ (cons(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ~ (ssItem(v7) = 0) | ? [v12] : ? [v13] : (memberP(v9, v7) = v13 & ssList(v9) = v12 & ( ~ (v12 = 0) | (( ~ (v11 = 0) | v13 = 0 | v8 = v7) & (v11 = 0 | ( ~ (v13 = 0) & ~ (v8 = v7))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (ssList(v7) = 0) | ~ (app(v9, v10) = v11) | ~ (app(v7, v8) = v9) | ? [v12] : ? [v13] : ? [v14] : (( ~ (v12 = 0) & ssList(v8) = v12) | (ssList(v10) = v12 & app(v8, v10) = v13 & app(v7, v13) = v14 & ( ~ (v12 = 0) | v14 = v11)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | v7 = nil | ~ (tl(v7) = v9) | ~ (hd(v7) = v8) | ~ (cons(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & ssList(v7) = v11)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (ssList(v7) = 0) | ~ (app(v10, v8) = v9) | ~ (app(v7, v8) = v9) | ? [v11] : (( ~ (v11 = 0) & ssList(v10) = v11) | ( ~ (v11 = 0) & ssList(v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = v7 | ~ (ssList(v7) = 0) | ~ (app(v8, v10) = v9) | ~ (app(v8, v7) = v9) | ? [v11] : (( ~ (v11 = 0) & ssList(v10) = v11) | ( ~ (v11 = 0) & ssList(v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (gt(v7, v9) = v10) | ~ (gt(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssItem(v8) = v11) | (gt(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (geq(v7, v9) = v10) | ~ (geq(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssItem(v8) = v11) | (geq(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (lt(v7, v9) = v10) | ~ (lt(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssItem(v8) = v11) | (lt(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (lt(v7, v9) = v10) | ~ (leq(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssItem(v8) = v11) | (lt(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (leq(v7, v9) = v10) | ~ (leq(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssItem(v8) = v11) | (leq(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (segmentP(v7, v9) = v10) | ~ (segmentP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssList(v8) = v11) | (segmentP(v8, v9) = v12 & ssList(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (rearsegP(v7, v9) = v10) | ~ (rearsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssList(v8) = v11) | (rearsegP(v8, v9) = v12 & ssList(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | ~ (frontsegP(v7, v9) = v10) | ~ (frontsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssList(v8) = v11) | (frontsegP(v8, v9) = v12 & ssList(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (rearsegP(v7, v8) = v9) | ~ (ssList(v7) = 0) | ~ (app(v10, v8) = v7) | ? [v11] : (( ~ (v11 = 0) & ssList(v10) = v11) | ( ~ (v11 = 0) & ssList(v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (frontsegP(v7, v8) = v9) | ~ (ssList(v7) = 0) | ~ (app(v8, v10) = v7) | ? [v11] : (( ~ (v11 = 0) & ssList(v10) = v11) | ( ~ (v11 = 0) & ssList(v8) = v11))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (gt(v10, v9) = v8) | ~ (gt(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (geq(v10, v9) = v8) | ~ (geq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (lt(v10, v9) = v8) | ~ (lt(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (leq(v10, v9) = v8) | ~ (leq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (segmentP(v10, v9) = v8) | ~ (segmentP(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (rearsegP(v10, v9) = v8) | ~ (rearsegP(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (frontsegP(v10, v9) = v8) | ~ (frontsegP(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (memberP(v10, v9) = v8) | ~ (memberP(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (cons(v10, v9) = v8) | ~ (cons(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (app(v10, v9) = v8) | ~ (app(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v8 = v7 | ~ (neq(v10, v9) = v8) | ~ (neq(v10, v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = nil | ~ (tl(v7) = v8) | ~ (app(v8, v9) = v10) | ? [v11] : ? [v12] : ? [v13] : (( ~ (v11 = 0) & ssList(v7) = v11) | (tl(v12) = v13 & ssList(v9) = v11 & app(v7, v9) = v12 & ( ~ (v11 = 0) | v13 = v10)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : (v7 = nil | ~ (hd(v7) = v8) | ~ (app(v7, v9) = v10) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssList(v7) = v11) | (hd(v10) = v12 & ssList(v9) = v11 & ( ~ (v11 = 0) | v12 = v8)))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (hd(v8) = v9) | ~ (lt(v7, v9) = v10) | ~ (ssItem(v7) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (strictorderedP(v12) = v13 & strictorderedP(v8) = v14 & ssList(v8) = v11 & cons(v7, v8) = v12 & ( ~ (v11 = 0) | (( ~ (v13 = 0) | v8 = nil | (v14 = 0 & v10 = 0)) & (v13 = 0 | ( ~ (v8 = nil) & ( ~ (v14 = 0) | ~ (v10 = 0)))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (hd(v8) = v9) | ~ (leq(v7, v9) = v10) | ~ (ssItem(v7) = 0) | ? [v11] : ? [v12] : ? [v13] : ? [v14] : (totalorderedP(v12) = v13 & totalorderedP(v8) = v14 & ssList(v8) = v11 & cons(v7, v8) = v12 & ( ~ (v11 = 0) | (( ~ (v13 = 0) | v8 = nil | (v14 = 0 & v10 = 0)) & (v13 = 0 | ( ~ (v8 = nil) & ( ~ (v14 = 0) | ~ (v10 = 0)))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (strictorderP(v7) = 0) | ~ (lt(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssList(v7) = v11) | (lt(v9, v8) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v12 = 0 | v10 = 0 | ~ (ssList(v13) = 0) | ~ (cons(v9, v17) = v18) | ~ (cons(v8, v14) = v15) | ~ (app(v16, v18) = v7) | ~ (app(v13, v15) = v16) | ? [v19] : (( ~ (v19 = 0) & ssList(v17) = v19) | ( ~ (v19 = 0) & ssList(v14) = v19))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (totalorderP(v7) = 0) | ~ (leq(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssList(v7) = v11) | (leq(v9, v8) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : (v12 = 0 | v10 = 0 | ~ (ssList(v13) = 0) | ~ (cons(v9, v17) = v18) | ~ (cons(v8, v14) = v15) | ~ (app(v16, v18) = v7) | ~ (app(v13, v15) = v16) | ? [v19] : (( ~ (v19 = 0) & ssList(v17) = v19) | ( ~ (v19 = 0) & ssList(v14) = v19))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (cyclefreeP(v7) = 0) | ~ (leq(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (( ~ (v11 = 0) & ssList(v7) = v11) | (leq(v9, v8) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ( ~ (v12 = 0) | ~ (v10 = 0) | ~ (ssList(v13) = 0) | ~ (cons(v9, v17) = v18) | ~ (cons(v8, v14) = v15) | ~ (app(v16, v18) = v7) | ~ (app(v13, v15) = v16) | ? [v19] : (( ~ (v19 = 0) & ssList(v17) = v19) | ( ~ (v19 = 0) & ssList(v14) = v19))))))) & ! [v7] : ! [v8] : ! [v9] : ! [v10] : ( ~ (ssList(v7) = 0) | ~ (cons(v8, nil) = v9) | ~ (app(v9, v7) = v10) | ? [v11] : ? [v12] : (cons(v8, v7) = v12 & ssItem(v8) = v11 & ( ~ (v11 = 0) | v12 = v10))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = v7 | ~ (lt(v7, v8) = v9) | ~ (ssItem(v7) = 0) | ? [v10] : ? [v11] : (leq(v7, v8) = v11 & ssItem(v8) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = v7 | ~ (ssList(v7) = 0) | ~ (neq(v7, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v9 = 0 | v8 = v7 | ~ (neq(v7, v8) = v9) | ~ (ssItem(v7) = 0) | ? [v10] : ( ~ (v10 = 0) & ssItem(v8) = v10)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (tl(v9) = v8) | ~ (tl(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (hd(v9) = v8) | ~ (hd(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (equalelemsP(v9) = v8) | ~ (equalelemsP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (duplicatefreeP(v9) = v8) | ~ (duplicatefreeP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (strictorderedP(v9) = v8) | ~ (strictorderedP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (totalorderedP(v9) = v8) | ~ (totalorderedP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (strictorderP(v9) = v8) | ~ (strictorderP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (totalorderP(v9) = v8) | ~ (totalorderP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (cyclefreeP(v9) = v8) | ~ (cyclefreeP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (singletonP(v9) = v8) | ~ (singletonP(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (ssList(v9) = v8) | ~ (ssList(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = v7 | ~ (ssItem(v9) = v8) | ~ (ssItem(v9) = v7)) & ! [v7] : ! [v8] : ! [v9] : (v8 = 0 | ~ (singletonP(v7) = v8) | ~ (cons(v9, nil) = v7) | ? [v10] : (( ~ (v10 = 0) & ssList(v7) = v10) | ( ~ (v10 = 0) & ssItem(v9) = v10))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (gt(v7, v8) = v9) | ~ (ssItem(v7) = 0) | ? [v10] : ? [v11] : (lt(v8, v7) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | (( ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (geq(v7, v8) = v9) | ~ (ssItem(v7) = 0) | ? [v10] : ? [v11] : (leq(v8, v7) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | (( ~ (v11 = 0) | v9 = 0) & ( ~ (v9 = 0) | v11 = 0))))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (lt(v7, v8) = v9) | ~ (ssItem(v7) = 0) | ? [v10] : ? [v11] : (leq(v7, v8) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | (( ~ (v11 = 0) | v9 = 0 | v8 = v7) & ( ~ (v9 = 0) | (v11 = 0 & ~ (v8 = v7))))))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ssList(v7) = 0) | ~ (cons(v8, v7) = v9) | ? [v10] : ? [v11] : (tl(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = v7))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ssList(v7) = 0) | ~ (cons(v8, v7) = v9) | ? [v10] : ? [v11] : (hd(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = v8))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ssList(v7) = 0) | ~ (cons(v8, v7) = v9) | ? [v10] : ? [v11] : (ssList(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v7] : ! [v8] : ! [v9] : ( ~ (ssList(v7) = 0) | ~ (app(v7, v8) = v9) | ? [v10] : ? [v11] : (ssList(v9) = v11 & ssList(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (geq(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v9] : ? [v10] : (geq(v8, v7) = v10 & ssItem(v8) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (leq(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v9] : ? [v10] : (leq(v8, v7) = v10 & ssItem(v8) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (segmentP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v9] : ? [v10] : (segmentP(v8, v7) = v10 & ssList(v8) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (rearsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v9] : ? [v10] : (rearsegP(v8, v7) = v10 & ssList(v8) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (frontsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v9] : ? [v10] : (frontsegP(v8, v7) = v10 & ssList(v8) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : (v8 = v7 | ~ (app(v7, nil) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v8 = v7 | ~ (app(nil, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v8 = nil | ~ (ssList(v7) = 0) | ~ (app(v7, v8) = nil) | ? [v9] : ( ~ (v9 = 0) & ssList(v8) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (geq(v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & ssItem(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (equalelemsP(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ((v19 = v7 & v16 = 0 & v14 = 0 & v12 = 0 & v10 = 0 & ~ (v11 = v9) & ssList(v15) = 0 & ssList(v13) = 0 & cons(v11, v15) = v17 & cons(v9, v17) = v18 & app(v13, v18) = v7 & ssItem(v11) = 0 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (duplicatefreeP(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ((v22 = v7 & v20 = 0 & v16 = 0 & v14 = 0 & v12 = 0 & v11 = v9 & v10 = 0 & ssList(v19) = 0 & ssList(v15) = 0 & ssList(v13) = 0 & cons(v9, v19) = v21 & cons(v9, v15) = v17 & app(v18, v21) = v7 & app(v13, v17) = v18 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (strictorderedP(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v23 = v7 & v21 = 0 & v17 = 0 & v15 = 0 & v12 = 0 & v10 = 0 & ~ (v13 = 0) & lt(v9, v11) = v13 & ssList(v20) = 0 & ssList(v16) = 0 & ssList(v14) = 0 & cons(v11, v20) = v22 & cons(v9, v16) = v18 & app(v19, v22) = v7 & app(v14, v18) = v19 & ssItem(v11) = 0 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (totalorderedP(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v23 = v7 & v21 = 0 & v17 = 0 & v15 = 0 & v12 = 0 & v10 = 0 & ~ (v13 = 0) & leq(v9, v11) = v13 & ssList(v20) = 0 & ssList(v16) = 0 & ssList(v14) = 0 & cons(v11, v20) = v22 & cons(v9, v16) = v18 & app(v19, v22) = v7 & app(v14, v18) = v19 & ssItem(v11) = 0 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (strictorderP(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v24 = v7 & v22 = 0 & v18 = 0 & v16 = 0 & v12 = 0 & v10 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & lt(v11, v9) = v14 & lt(v9, v11) = v13 & ssList(v21) = 0 & ssList(v17) = 0 & ssList(v15) = 0 & cons(v11, v21) = v23 & cons(v9, v17) = v19 & app(v20, v23) = v7 & app(v15, v19) = v20 & ssItem(v11) = 0 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (totalorderP(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v24 = v7 & v22 = 0 & v18 = 0 & v16 = 0 & v12 = 0 & v10 = 0 & ~ (v14 = 0) & ~ (v13 = 0) & leq(v11, v9) = v14 & leq(v9, v11) = v13 & ssList(v21) = 0 & ssList(v17) = 0 & ssList(v15) = 0 & cons(v11, v21) = v23 & cons(v9, v17) = v19 & app(v20, v23) = v7 & app(v15, v19) = v20 & ssItem(v11) = 0 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (cyclefreeP(v7) = v8) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v24 = v7 & v22 = 0 & v18 = 0 & v16 = 0 & v14 = 0 & v13 = 0 & v12 = 0 & v10 = 0 & leq(v11, v9) = 0 & leq(v9, v11) = 0 & ssList(v21) = 0 & ssList(v17) = 0 & ssList(v15) = 0 & cons(v11, v21) = v23 & cons(v9, v17) = v19 & app(v20, v23) = v7 & app(v15, v19) = v20 & ssItem(v11) = 0 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v8 = 0 | ~ (leq(v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & ssItem(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (segmentP(v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (segmentP(v7, nil) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (rearsegP(v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (rearsegP(v7, nil) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (frontsegP(v7, v7) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v8 = 0 | ~ (frontsegP(v7, nil) = v8) | ? [v9] : ( ~ (v9 = 0) & ssList(v7) = v9)) & ! [v7] : ! [v8] : (v7 = nil | ~ (tl(v7) = v8) | ? [v9] : ? [v10] : (ssList(v8) = v10 & ssList(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : (v7 = nil | ~ (tl(v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = v8 & ssList(v8) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v7 = nil | ~ (hd(v7) = v8) | ? [v9] : ? [v10] : (ssList(v7) = v9 & ssItem(v8) = v10 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : (v7 = nil | ~ (hd(v7) = v8) | ? [v9] : ? [v10] : ((v10 = 0 & v9 = v8 & ssItem(v8) = 0) | ( ~ (v9 = 0) & ssList(v7) = v9))) & ! [v7] : ! [v8] : (v7 = nil | ~ (ssList(v7) = 0) | ~ (app(v7, v8) = nil) | ? [v9] : ( ~ (v9 = 0) & ssList(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (gt(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v9] : ? [v10] : (gt(v8, v7) = v10 & ssItem(v8) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : ( ~ (tl(v7) = v8) | ? [v9] : ? [v10] : (hd(v7) = v10 & ssList(v7) = v9 & ( ~ (v9 = 0) | ! [v11] : (v11 = v7 | v11 = nil | v7 = nil | ~ (tl(v11) = v8) | ? [v12] : ? [v13] : (hd(v11) = v13 & ssList(v11) = v12 & ( ~ (v13 = v10) | ~ (v12 = 0))))))) & ! [v7] : ! [v8] : ( ~ (lt(v7, v8) = 0) | ~ (ssItem(v7) = 0) | ? [v9] : ? [v10] : (lt(v8, v7) = v10 & ssItem(v8) = v9 & ( ~ (v10 = 0) | ~ (v9 = 0)))) & ! [v7] : ! [v8] : ( ~ (segmentP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = v7 & v13 = 0 & v10 = 0 & ssList(v12) = 0 & ssList(v9) = 0 & app(v11, v12) = v7 & app(v9, v8) = v11) | ( ~ (v9 = 0) & ssList(v8) = v9))) & ! [v7] : ! [v8] : ( ~ (rearsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = v7 & v10 = 0 & ssList(v9) = 0 & app(v9, v8) = v7) | ( ~ (v9 = 0) & ssList(v8) = v9))) & ! [v7] : ! [v8] : ( ~ (frontsegP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = v7 & v10 = 0 & ssList(v9) = 0 & app(v8, v9) = v7) | ( ~ (v9 = 0) & ssList(v8) = v9))) & ! [v7] : ! [v8] : ( ~ (memberP(v7, v8) = 0) | ~ (ssList(v7) = 0) | ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ((v14 = v7 & v12 = 0 & v10 = 0 & ssList(v11) = 0 & ssList(v9) = 0 & cons(v8, v11) = v13 & app(v9, v13) = v7) | ( ~ (v9 = 0) & ssItem(v8) = v9))) & ! [v7] : ! [v8] : ( ~ (ssList(v7) = 0) | ~ (cons(v8, v7) = v7) | ? [v9] : ( ~ (v9 = 0) & ssItem(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (ssList(v7) = 0) | ~ (cons(v8, v7) = nil) | ? [v9] : ( ~ (v9 = 0) & ssItem(v8) = v9)) & ! [v7] : ! [v8] : ( ~ (cons(v7, nil) = v8) | ? [v9] : ? [v10] : (equalelemsP(v8) = v10 & ssItem(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : ( ~ (cons(v7, nil) = v8) | ? [v9] : ? [v10] : (duplicatefreeP(v8) = v10 & ssItem(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : ( ~ (cons(v7, nil) = v8) | ? [v9] : ? [v10] : (strictorderedP(v8) = v10 & ssItem(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : ( ~ (cons(v7, nil) = v8) | ? [v9] : ? [v10] : (totalorderedP(v8) = v10 & ssItem(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : ( ~ (cons(v7, nil) = v8) | ? [v9] : ? [v10] : (strictorderP(v8) = v10 & ssItem(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : ( ~ (cons(v7, nil) = v8) | ? [v9] : ? [v10] : (totalorderP(v8) = v10 & ssItem(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : ! [v8] : ( ~ (cons(v7, nil) = v8) | ? [v9] : ? [v10] : (cyclefreeP(v8) = v10 & ssItem(v7) = v9 & ( ~ (v9 = 0) | v10 = 0))) & ! [v7] : (v7 = nil | ~ (segmentP(nil, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & ssList(v7) = v8)) & ! [v7] : (v7 = nil | ~ (rearsegP(nil, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & ssList(v7) = v8)) & ! [v7] : (v7 = nil | ~ (frontsegP(nil, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & ssList(v7) = v8)) & ! [v7] : (v7 = nil | ~ (ssList(v7) = 0) | ? [v8] : ? [v9] : (ssList(v8) = 0 & cons(v9, v8) = v7 & ssItem(v9) = 0)) & ! [v7] : (v7 = nil | ~ (app(nil, nil) = v7)) & ! [v7] : (v7 = 0 | ~ (segmentP(nil, nil) = v7)) & ! [v7] : (v7 = 0 | ~ (rearsegP(nil, nil) = v7)) & ! [v7] : (v7 = 0 | ~ (frontsegP(nil, nil) = v7)) & ! [v7] : ( ~ (lt(v7, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & ssItem(v7) = v8)) & ! [v7] : ( ~ (singletonP(v7) = 0) | ? [v8] : ? [v9] : ? [v10] : ((v10 = v7 & v9 = 0 & cons(v8, nil) = v7 & ssItem(v8) = 0) | ( ~ (v8 = 0) & ssList(v7) = v8))) & ! [v7] : ( ~ (memberP(nil, v7) = 0) | ? [v8] : ( ~ (v8 = 0) & ssItem(v7) = v8)) & ! [v7] : ( ~ (ssList(v7) = 0) | ~ (neq(v7, v7) = 0)) & ! [v7] : ( ~ (cons(v7, nil) = v1) | ? [v8] : ? [v9] : (memberP(v2, v7) = v9 & ssItem(v7) = v8 & ( ~ (v9 = 0) | ~ (v8 = 0)))) & ! [v7] : ( ~ (neq(v7, v7) = 0) | ~ (ssItem(v7) = 0)) & ( ~ (v4 = 0) | v3 = 0) & ( ~ (v2 = nil) | ~ (v1 = nil)))
% 34.04/9.43 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6 yields:
% 34.04/9.43 | (1) ~ (all_0_0_0 = all_0_1_1) & ~ (all_0_6_6 = 0) & equalelemsP(nil) = 0 & duplicatefreeP(nil) = 0 & strictorderedP(nil) = 0 & totalorderedP(nil) = 0 & strictorderP(nil) = 0 & totalorderP(nil) = 0 & cyclefreeP(nil) = 0 & segmentP(all_0_4_4, all_0_5_5) = 0 & singletonP(all_0_5_5) = all_0_3_3 & singletonP(nil) = all_0_6_6 & ssList(all_0_4_4) = 0 & ssList(all_0_5_5) = 0 & ssList(nil) = 0 & neq(all_0_4_4, nil) = all_0_2_2 & ssItem(all_0_0_0) = 0 & ssItem(all_0_1_1) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v3 = 0 | ~ (strictorderedP(v0) = 0) | ~ (lt(v1, v2) = v3) | ~ (ssList(v4) = 0) | ~ (cons(v2, v8) = v9) | ~ (cons(v1, v5) = v6) | ~ (app(v7, v9) = v0) | ~ (app(v4, v6) = v7) | ~ (ssItem(v1) = 0) | ? [v10] : (( ~ (v10 = 0) & ssList(v8) = v10) | ( ~ (v10 = 0) & ssList(v5) = v10) | ( ~ (v10 = 0) & ssList(v0) = v10) | ( ~ (v10 = 0) & ssItem(v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v3 = 0 | ~ (totalorderedP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssList(v4) = 0) | ~ (cons(v2, v8) = v9) | ~ (cons(v1, v5) = v6) | ~ (app(v7, v9) = v0) | ~ (app(v4, v6) = v7) | ~ (ssItem(v1) = 0) | ? [v10] : (( ~ (v10 = 0) & ssList(v8) = v10) | ( ~ (v10 = 0) & ssList(v5) = v10) | ( ~ (v10 = 0) & ssList(v0) = v10) | ( ~ (v10 = 0) & ssItem(v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (duplicatefreeP(v0) = 0) | ~ (ssList(v2) = 0) | ~ (cons(v1, v6) = v7) | ~ (cons(v1, v3) = v4) | ~ (app(v5, v7) = v0) | ~ (app(v2, v4) = v5) | ~ (ssItem(v1) = 0) | ? [v8] : (( ~ (v8 = 0) & ssList(v6) = v8) | ( ~ (v8 = 0) & ssList(v3) = v8) | ( ~ (v8 = 0) & ssList(v0) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (segmentP(v5, v1) = v6) | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v3, v4) = v5) | ~ (app(v2, v0) = v3) | ? [v7] : (( ~ (v7 = 0) & ssList(v4) = v7) | ( ~ (v7 = 0) & ssList(v2) = v7) | ( ~ (v7 = 0) & ssList(v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (equalelemsP(v0) = 0) | ~ (ssList(v3) = 0) | ~ (cons(v2, v4) = v5) | ~ (cons(v1, v5) = v6) | ~ (app(v3, v6) = v0) | ~ (ssItem(v2) = 0) | ~ (ssItem(v1) = 0) | ? [v7] : (( ~ (v7 = 0) & ssList(v4) = v7) | ( ~ (v7 = 0) & ssList(v0) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (frontsegP(v3, v5) = v6) | ~ (cons(v1, v4) = v5) | ~ (cons(v0, v2) = v3) | ~ (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ? [v7] : ? [v8] : (( ~ (v7 = 0) & ssList(v2) = v7) | (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 = 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = 0 | ~ (segmentP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v4, v5) = v0) | ~ (app(v3, v1) = v4) | ? [v6] : (( ~ (v6 = 0) & ssList(v5) = v6) | ( ~ (v6 = 0) & ssList(v3) = v6) | ( ~ (v6 = 0) & ssList(v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = 0 | ~ (memberP(v0, v1) = v2) | ~ (ssList(v3) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v1, v4) = v5) | ~ (app(v3, v5) = v0) | ? [v6] : (( ~ (v6 = 0) & ssList(v4) = v6) | ( ~ (v6 = 0) & ssItem(v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (memberP(v4, v0) = v5) | ~ (memberP(v1, v0) = v2) | ~ (app(v1, v3) = v4) | ~ (ssItem(v0) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & ssList(v1) = v6) | (memberP(v3, v0) = v7 & ssList(v3) = v6 & ( ~ (v6 = 0) | (( ~ (v5 = 0) | v7 = 0 | v2 = 0) & (v5 = 0 | ( ~ (v7 = 0) & ~ (v2 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ssList(v0) = 0) | ~ (cons(v3, v1) = v4) | ~ (app(v4, v0) = v5) | ~ (app(v1, v0) = v2) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & ssList(v1) = v6) | (cons(v3, v2) = v7 & ssItem(v3) = v6 & ( ~ (v6 = 0) | v7 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssItem(v4) = v5) | ( ~ (v5 = 0) & ssItem(v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (rearsegP(v3, v1) = v4) | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssList(v2) = v5) | ( ~ (v5 = 0) & ssList(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (frontsegP(v3, v1) = v4) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v0, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & ssList(v2) = v5) | ( ~ (v5 = 0) & ssList(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssItem(v4) = v5) | ( ~ (v5 = 0) & ssItem(v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (memberP(v3, v0) = v4) | ~ (cons(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ? [v5] : ? [v6] : (memberP(v2, v0) = v6 & ssList(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | v6 = 0 | v1 = v0) & (v4 = 0 | ( ~ (v6 = 0) & ~ (v1 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ssList(v0) = 0) | ~ (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & ssList(v1) = v5) | (ssList(v3) = v5 & app(v1, v3) = v6 & app(v0, v6) = v7 & ( ~ (v5 = 0) | v7 = v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & ssList(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ssList(v0) = 0) | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (gt(v0, v2) = v3) | ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (gt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (geq(v0, v2) = v3) | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (geq(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lt(v0, v2) = v3) | ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (lt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lt(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (lt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (leq(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (segmentP(v0, v2) = v3) | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (segmentP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (rearsegP(v0, v2) = v3) | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (rearsegP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (frontsegP(v0, v2) = v3) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (frontsegP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (rearsegP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v3, v1) = v0) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (frontsegP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v0) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & ssList(v0) = v4) | (tl(v5) = v6 & ssList(v2) = v4 & app(v0, v2) = v5 & ( ~ (v4 = 0) | v6 = v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (hd(v3) = v5 & ssList(v2) = v4 & ( ~ (v4 = 0) | v5 = v1)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (hd(v1) = v2) | ~ (lt(v0, v2) = v3) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (strictorderedP(v5) = v6 & strictorderedP(v1) = v7 & ssList(v1) = v4 & cons(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v1 = nil | (v7 = 0 & v3 = 0)) & (v6 = 0 | ( ~ (v1 = nil) & ( ~ (v7 = 0) | ~ (v3 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (hd(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (totalorderedP(v5) = v6 & totalorderedP(v1) = v7 & ssList(v1) = v4 & cons(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v1 = nil | (v7 = 0 & v3 = 0)) & (v6 = 0 | ( ~ (v1 = nil) & ( ~ (v7 = 0) | ~ (v3 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (strictorderP(v0) = 0) | ~ (lt(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (lt(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v5 = 0 | v3 = 0 | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (totalorderP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (leq(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v5 = 0 | v3 = 0 | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cyclefreeP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (leq(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (v5 = 0) | ~ (v3 = 0) | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ? [v4] : ? [v5] : (cons(v1, v0) = v5 & ssItem(v1) = v4 & ( ~ (v4 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (lt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v0, v1) = v4 & ssItem(v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (ssList(v0) = 0) | ~ (neq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & ssList(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (neq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & ssItem(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | ~ (equalelemsP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | ~ (duplicatefreeP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderP(v2) = v1) | ~ (strictorderP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ (totalorderP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ (cyclefreeP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (singletonP(v0) = v1) | ~ (cons(v2, nil) = v0) | ? [v3] : (( ~ (v3 = 0) & ssList(v0) = v3) | ( ~ (v3 = 0) & ssItem(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (gt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (lt(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (geq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (lt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v0, v1) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0 | v1 = v0) & ( ~ (v2 = 0) | (v4 = 0 & ~ (v1 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (tl(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (app(v0, v1) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (geq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (leq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (frontsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (equalelemsP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v0 & v9 = 0 & v7 = 0 & v5 = 0 & v3 = 0 & ~ (v4 = v2) & ssList(v8) = 0 & ssList(v6) = 0 & cons(v4, v8) = v10 & cons(v2, v10) = v11 & app(v6, v11) = v0 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (duplicatefreeP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v15 = v0 & v13 = 0 & v9 = 0 & v7 = 0 & v5 = 0 & v4 = v2 & v3 = 0 & ssList(v12) = 0 & ssList(v8) = 0 & ssList(v6) = 0 & cons(v2, v12) = v14 & cons(v2, v8) = v10 & app(v11, v14) = v0 & app(v6, v10) = v11 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (strictorderedP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v0 & v14 = 0 & v10 = 0 & v8 = 0 & v5 = 0 & v3 = 0 & ~ (v6 = 0) & lt(v2, v4) = v6 & ssList(v13) = 0 & ssList(v9) = 0 & ssList(v7) = 0 & cons(v4, v13) = v15 & cons(v2, v9) = v11 & app(v12, v15) = v0 & app(v7, v11) = v12 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (totalorderedP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v0 & v14 = 0 & v10 = 0 & v8 = 0 & v5 = 0 & v3 = 0 & ~ (v6 = 0) & leq(v2, v4) = v6 & ssList(v13) = 0 & ssList(v9) = 0 & ssList(v7) = 0 & cons(v4, v13) = v15 & cons(v2, v9) = v11 & app(v12, v15) = v0 & app(v7, v11) = v12 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (strictorderP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v5 = 0 & v3 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & lt(v4, v2) = v7 & lt(v2, v4) = v6 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (totalorderP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v5 = 0 & v3 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & leq(v4, v2) = v7 & leq(v2, v4) = v6 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cyclefreeP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & v3 = 0 & leq(v4, v2) = 0 & leq(v2, v4) = 0 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (ssList(v1) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssList(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : (ssList(v0) = v2 & ssItem(v1) = v3 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssItem(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v0 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (gt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (hd(v0) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : (v4 = v0 | v4 = nil | v0 = nil | ~ (tl(v4) = v1) | ? [v5] : ? [v6] : (hd(v4) = v6 & ssList(v4) = v5 & ( ~ (v6 = v3) | ~ (v5 = 0))))))) & ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (lt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v0 & v6 = 0 & v3 = 0 & ssList(v5) = 0 & ssList(v2) = 0 & app(v4, v5) = v0 & app(v2, v1) = v4) | ( ~ (v2 = 0) & ssList(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & v3 = 0 & ssList(v2) = 0 & app(v2, v1) = v0) | ( ~ (v2 = 0) & ssList(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & v3 = 0 & ssList(v2) = 0 & app(v1, v2) = v0) | ( ~ (v2 = 0) & ssList(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (memberP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v0 & v5 = 0 & v3 = 0 & ssList(v4) = 0 & ssList(v2) = 0 & cons(v1, v4) = v6 & app(v2, v6) = v0) | ( ~ (v2 = 0) & ssItem(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v0) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = nil) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : (v0 = nil | ~ (segmentP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1)) & ! [v0] : (v0 = nil | ~ (rearsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1)) & ! [v0] : (v0 = nil | ~ (frontsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1)) & ! [v0] : (v0 = nil | ~ (ssList(v0) = 0) | ? [v1] : ? [v2] : (ssList(v1) = 0 & cons(v2, v1) = v0 & ssItem(v2) = 0)) & ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0)) & ! [v0] : (v0 = 0 | ~ (segmentP(nil, nil) = v0)) & ! [v0] : (v0 = 0 | ~ (rearsegP(nil, nil) = v0)) & ! [v0] : (v0 = 0 | ~ (frontsegP(nil, nil) = v0)) & ! [v0] : ( ~ (lt(v0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1)) & ! [v0] : ( ~ (singletonP(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v0 & v2 = 0 & cons(v1, nil) = v0 & ssItem(v1) = 0) | ( ~ (v1 = 0) & ssList(v0) = v1))) & ! [v0] : ( ~ (memberP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1)) & ! [v0] : ( ~ (ssList(v0) = 0) | ~ (neq(v0, v0) = 0)) & ! [v0] : ( ~ (cons(v0, nil) = all_0_5_5) | ? [v1] : ? [v2] : (memberP(all_0_4_4, v0) = v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0)))) & ! [v0] : ( ~ (neq(v0, v0) = 0) | ~ (ssItem(v0) = 0)) & ( ~ (all_0_2_2 = 0) | all_0_3_3 = 0) & ( ~ (all_0_4_4 = nil) | ~ (all_0_5_5 = nil))
% 34.34/9.47 |
% 34.34/9.47 | Applying alpha-rule on (1) yields:
% 34.34/9.47 | (2) ! [v0] : ! [v1] : (v0 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 34.34/9.47 | (3) ! [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)))))
% 34.34/9.47 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 34.34/9.47 | (5) singletonP(nil) = all_0_6_6
% 34.34/9.47 | (6) ! [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)))
% 34.34/9.47 | (7) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 34.34/9.47 | (8) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 34.34/9.47 | (9) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssList(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 34.34/9.47 | (10) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (app(v0, v1) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 34.34/9.47 | (11) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) = v0))
% 34.34/9.47 | (12) ! [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))))
% 34.34/9.48 | (13) ! [v0] : ! [v1] : ( ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (gt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 34.34/9.48 | (14) ! [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)))))
% 34.34/9.48 | (15) ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (leq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 34.34/9.48 | (16) ! [v0] : ( ~ (neq(v0, v0) = 0) | ~ (ssItem(v0) = 0))
% 34.34/9.48 | (17) ! [v0] : (v0 = nil | ~ (frontsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 34.34/9.48 | (18) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 34.34/9.48 | (19) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 34.34/9.48 | (20) ~ (all_0_0_0 = all_0_1_1)
% 34.34/9.48 | (21) ! [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)))))
% 34.34/9.48 | (22) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ (totalorderP(v2) = v0))
% 34.34/9.48 | (23) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0))
% 34.34/9.48 | (24) ! [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))))
% 34.34/9.48 | (25) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 34.34/9.48 | (26) ! [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)))))
% 34.34/9.48 | (27) ! [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)))
% 34.34/9.48 | (28) ! [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))))
% 34.34/9.48 | (29) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssItem(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 34.34/9.48 | (30) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 34.34/9.48 | (31) totalorderedP(nil) = 0
% 34.34/9.48 | (32) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | ~ (equalelemsP(v2) = v0))
% 34.34/9.48 | (33) ssItem(all_0_0_0) = 0
% 34.34/9.48 | (34) ! [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)))))
% 34.34/9.48 | (35) singletonP(all_0_5_5) = all_0_3_3
% 34.34/9.48 | (36) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0))
% 34.34/9.48 | (37) ! [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)))
% 34.34/9.48 | (38) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (neq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & ssItem(v1) = v3))
% 34.34/9.48 | (39) ! [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)))
% 34.34/9.48 | (40) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 34.34/9.48 | (41) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (ssList(v1) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 34.34/9.48 | (42) ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 34.34/9.48 | (43) ! [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)))
% 34.34/9.48 | (44) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0))
% 34.34/9.48 | (45) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 34.34/9.48 | (46) ! [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)))
% 34.34/9.49 | (47) ssItem(all_0_1_1) = 0
% 34.34/9.49 | (48) ! [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)))
% 34.34/9.49 | (49) ! [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)))
% 34.34/9.49 | (50) ! [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)))))))
% 34.34/9.49 | (51) ! [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)))
% 34.34/9.49 | (52) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = nil) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 34.34/9.49 | (53) ! [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))))))))
% 34.34/9.49 | (54) ! [v0] : (v0 = nil | ~ (segmentP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 34.34/9.49 | (55) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 34.34/9.49 | (56) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v1)))
% 34.34/9.49 | (57) ! [v0] : ( ~ (cons(v0, nil) = all_0_5_5) | ? [v1] : ? [v2] : (memberP(all_0_4_4, v0) = v2 & ssItem(v0) = v1 & ( ~ (v2 = 0) | ~ (v1 = 0))))
% 34.34/9.49 | (58) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 34.34/9.49 | (59) ! [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)))
% 34.34/9.49 | (60) ! [v0] : ( ~ (lt(v0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 34.34/9.49 | (61) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderP(v2) = v1) | ~ (strictorderP(v2) = v0))
% 34.34/9.49 | (62) ~ (all_0_4_4 = nil) | ~ (all_0_5_5 = nil)
% 34.34/9.49 | (63) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0))
% 34.34/9.49 | (64) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ (cyclefreeP(v2) = v0))
% 34.34/9.49 | (65) ! [v0] : (v0 = nil | ~ (rearsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 34.34/9.49 | (66) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (tl(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v0)))
% 34.34/9.49 | (67) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & ssList(v0) = v4))
% 34.34/9.49 | (68) ~ (all_0_2_2 = 0) | all_0_3_3 = 0
% 34.34/9.49 | (69) ! [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)))))
% 34.34/9.49 | (70) ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (equalelemsP(v0) = 0) | ~ (ssList(v3) = 0) | ~ (cons(v2, v4) = v5) | ~ (cons(v1, v5) = v6) | ~ (app(v3, v6) = v0) | ~ (ssItem(v2) = 0) | ~ (ssItem(v1) = 0) | ? [v7] : (( ~ (v7 = 0) & ssList(v4) = v7) | ( ~ (v7 = 0) & ssList(v0) = v7)))
% 34.34/9.49 | (71) strictorderedP(nil) = 0
% 34.34/9.49 | (72) ! [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)))
% 34.34/9.49 | (73) ! [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))))))))
% 34.34/9.49 | (74) ! [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)))))
% 34.34/9.49 | (75) ! [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))))))))
% 34.34/9.49 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = v0))
% 34.34/9.49 | (77) equalelemsP(nil) = 0
% 34.34/9.49 | (78) ! [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)))
% 34.34/9.49 | (79) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 34.34/9.49 | (80) ! [v0] : ! [v1] : (v1 = v0 | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (frontsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 34.34/9.50 | (81) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | ~ (duplicatefreeP(v2) = v0))
% 34.34/9.50 | (82) ! [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)))))
% 34.34/9.50 | (83) ! [v0] : ! [v1] : (v1 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 34.34/9.50 | (84) ! [v0] : ( ~ (ssList(v0) = 0) | ~ (neq(v0, v0) = 0))
% 34.34/9.50 | (85) totalorderP(nil) = 0
% 34.34/9.50 | (86) ! [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))))
% 34.34/9.50 | (87) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0))
% 34.34/9.50 | (88) ! [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)))
% 34.34/9.50 | (89) ssList(nil) = 0
% 34.34/9.50 | (90) ! [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)))
% 34.34/9.50 | (91) ! [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)))))
% 34.34/9.50 | (92) ! [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)))))))
% 34.34/9.50 | (93) ! [v0] : (v0 = 0 | ~ (frontsegP(nil, nil) = v0))
% 34.34/9.50 | (94) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0))
% 34.34/9.50 | (95) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 34.34/9.50 | (96) ! [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)))))))
% 34.34/9.50 | (97) strictorderP(nil) = 0
% 34.34/9.50 | (98) ! [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)))))))
% 34.34/9.50 | (99) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (singletonP(v0) = v1) | ~ (cons(v2, nil) = v0) | ? [v3] : (( ~ (v3 = 0) & ssList(v0) = v3) | ( ~ (v3 = 0) & ssItem(v2) = v3)))
% 34.34/9.50 | (100) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 34.34/9.50 | (101) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 34.34/9.50 | (102) ! [v0] : (v0 = 0 | ~ (segmentP(nil, nil) = v0))
% 34.34/9.50 | (103) duplicatefreeP(nil) = 0
% 34.34/9.50 | (104) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : (ssList(v0) = v2 & ssItem(v1) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 34.34/9.50 | (105) ! [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)))
% 34.34/9.50 | (106) ! [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)))))
% 34.34/9.50 | (107) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0))
% 34.34/9.50 | (108) ssList(all_0_4_4) = 0
% 34.34/9.50 | (109) ! [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)))
% 34.34/9.50 | (110) ! [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)))
% 34.34/9.50 | (111) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 34.34/9.50 | (112) ! [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)))
% 34.34/9.50 | (113) ssList(all_0_5_5) = 0
% 34.34/9.50 | (114) ! [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)))
% 34.34/9.50 | (115) ! [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)))
% 34.34/9.50 | (116) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 34.34/9.50 | (117) ~ (all_0_6_6 = 0)
% 34.34/9.50 | (118) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (ssList(v0) = 0) | ~ (neq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & ssList(v1) = v3))
% 34.34/9.51 | (119) ! [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)))
% 34.34/9.51 | (120) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0))
% 34.34/9.51 | (121) ! [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)))
% 34.34/9.51 | (122) ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0))
% 34.34/9.51 | (123) ! [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))))
% 34.34/9.51 | (124) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 34.34/9.51 | (125) ! [v0] : ( ~ (singletonP(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v0 & v2 = 0 & cons(v1, nil) = v0 & ssItem(v1) = 0) | ( ~ (v1 = 0) & ssList(v0) = v1)))
% 34.34/9.51 | (126) ! [v0] : ! [v1] : (v1 = v0 | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 34.34/9.51 | (127) ! [v0] : ( ~ (memberP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 34.34/9.51 | (128) ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (geq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 34.34/9.51 | (129) cyclefreeP(nil) = 0
% 34.34/9.51 | (130) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 34.34/9.51 | (131) ! [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)))
% 34.34/9.51 | (132) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0))
% 34.34/9.51 | (133) ! [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)))
% 34.34/9.51 | (134) neq(all_0_4_4, nil) = all_0_2_2
% 34.34/9.51 | (135) ! [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)))
% 34.34/9.51 | (136) ! [v0] : ! [v1] : (v1 = v0 | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 34.34/9.51 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4)))
% 34.34/9.51 | (138) ! [v0] : (v0 = 0 | ~ (rearsegP(nil, nil) = v0))
% 34.34/9.51 | (139) ! [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)))))))
% 34.34/9.51 | (140) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 34.34/9.51 | (141) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 34.34/9.51 | (142) ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (lt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 34.34/9.51 | (143) ! [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)))))))
% 34.34/9.51 | (144) ! [v0] : (v0 = nil | ~ (ssList(v0) = 0) | ? [v1] : ? [v2] : (ssList(v1) = 0 & cons(v2, v1) = v0 & ssItem(v2) = 0))
% 34.34/9.51 | (145) segmentP(all_0_4_4, all_0_5_5) = 0
% 34.34/9.51 | (146) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 34.34/9.51 | (147) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0))
% 34.34/9.51 | (148) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 34.34/9.51 | (149) ! [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)))))))
% 34.34/9.51 | (150) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v0) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 34.34/9.51 |
% 34.34/9.51 | Instantiating formula (54) with all_0_5_5 yields:
% 34.34/9.51 | (151) all_0_5_5 = nil | ~ (segmentP(nil, all_0_5_5) = 0) | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_5_5) = v0)
% 34.34/9.51 |
% 34.34/9.51 | Instantiating formula (125) with all_0_5_5 yields:
% 34.34/9.51 | (152) ~ (singletonP(all_0_5_5) = 0) | ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_5_5 & v1 = 0 & cons(v0, nil) = all_0_5_5 & ssItem(v0) = 0) | ( ~ (v0 = 0) & ssList(all_0_5_5) = v0))
% 34.34/9.51 |
% 34.34/9.51 | Instantiating formula (126) with all_0_5_5, all_0_4_4 and discharging atoms segmentP(all_0_4_4, all_0_5_5) = 0, ssList(all_0_4_4) = 0, yields:
% 34.34/9.51 | (153) all_0_4_4 = all_0_5_5 | ? [v0] : ? [v1] : (segmentP(all_0_5_5, all_0_4_4) = v1 & ssList(all_0_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 34.34/9.51 |
% 34.34/9.51 | Instantiating formula (51) with all_0_5_5, all_0_4_4 and discharging atoms segmentP(all_0_4_4, all_0_5_5) = 0, ssList(all_0_4_4) = 0, yields:
% 34.34/9.51 | (154) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = all_0_4_4 & v4 = 0 & v1 = 0 & ssList(v3) = 0 & ssList(v0) = 0 & app(v2, v3) = all_0_4_4 & app(v0, all_0_5_5) = v2) | ( ~ (v0 = 0) & ssList(all_0_5_5) = v0))
% 34.34/9.51 |
% 34.34/9.51 | Instantiating formula (144) with all_0_4_4 and discharging atoms ssList(all_0_4_4) = 0, yields:
% 34.34/9.51 | (155) all_0_4_4 = nil | ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_4_4 & ssItem(v1) = 0)
% 34.34/9.51 |
% 34.34/9.51 | Instantiating formula (144) with all_0_5_5 and discharging atoms ssList(all_0_5_5) = 0, yields:
% 34.34/9.51 | (156) all_0_5_5 = nil | ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_5_5 & ssItem(v1) = 0)
% 34.34/9.51 |
% 34.34/9.51 | Instantiating formula (118) with all_0_2_2, nil, all_0_4_4 and discharging atoms ssList(all_0_4_4) = 0, neq(all_0_4_4, nil) = all_0_2_2, yields:
% 34.34/9.52 | (157) all_0_2_2 = 0 | all_0_4_4 = nil | ? [v0] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 34.34/9.52 |
% 34.34/9.52 | Instantiating (154) with all_8_0_7, all_8_1_8, all_8_2_9, all_8_3_10, all_8_4_11, all_8_5_12 yields:
% 34.34/9.52 | (158) (all_8_0_7 = all_0_4_4 & all_8_1_8 = 0 & all_8_4_11 = 0 & ssList(all_8_2_9) = 0 & ssList(all_8_5_12) = 0 & app(all_8_3_10, all_8_2_9) = all_0_4_4 & app(all_8_5_12, all_0_5_5) = all_8_3_10) | ( ~ (all_8_5_12 = 0) & ssList(all_0_5_5) = all_8_5_12)
% 34.34/9.52 |
% 34.34/9.52 +-Applying beta-rule and splitting (62), into two cases.
% 34.34/9.52 |-Branch one:
% 34.34/9.52 | (159) ~ (all_0_4_4 = nil)
% 34.34/9.52 |
% 34.34/9.52 +-Applying beta-rule and splitting (158), into two cases.
% 34.34/9.52 |-Branch one:
% 34.34/9.52 | (160) all_8_0_7 = all_0_4_4 & all_8_1_8 = 0 & all_8_4_11 = 0 & ssList(all_8_2_9) = 0 & ssList(all_8_5_12) = 0 & app(all_8_3_10, all_8_2_9) = all_0_4_4 & app(all_8_5_12, all_0_5_5) = all_8_3_10
% 34.34/9.52 |
% 34.34/9.52 | Applying alpha-rule on (160) yields:
% 34.34/9.52 | (161) all_8_0_7 = all_0_4_4
% 34.34/9.52 | (162) ssList(all_8_5_12) = 0
% 34.34/9.52 | (163) all_8_1_8 = 0
% 34.34/9.52 | (164) ssList(all_8_2_9) = 0
% 34.34/9.52 | (165) app(all_8_5_12, all_0_5_5) = all_8_3_10
% 34.34/9.52 | (166) app(all_8_3_10, all_8_2_9) = all_0_4_4
% 34.34/9.52 | (167) all_8_4_11 = 0
% 34.34/9.52 |
% 34.34/9.52 +-Applying beta-rule and splitting (157), into two cases.
% 34.34/9.52 |-Branch one:
% 34.34/9.52 | (168) all_0_4_4 = nil
% 34.34/9.52 |
% 34.34/9.52 | Equations (168) can reduce 159 to:
% 34.34/9.52 | (169) $false
% 34.34/9.52 |
% 34.34/9.52 |-The branch is then unsatisfiable
% 34.34/9.52 |-Branch two:
% 34.34/9.52 | (159) ~ (all_0_4_4 = nil)
% 34.34/9.52 | (171) all_0_2_2 = 0 | ? [v0] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 34.34/9.52 |
% 34.34/9.52 +-Applying beta-rule and splitting (155), into two cases.
% 34.34/9.52 |-Branch one:
% 34.34/9.52 | (168) all_0_4_4 = nil
% 34.34/9.52 |
% 34.34/9.52 | Equations (168) can reduce 159 to:
% 34.34/9.52 | (169) $false
% 34.34/9.52 |
% 34.34/9.52 |-The branch is then unsatisfiable
% 34.34/9.52 |-Branch two:
% 34.34/9.52 | (159) ~ (all_0_4_4 = nil)
% 34.34/9.52 | (175) ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_4_4 & ssItem(v1) = 0)
% 34.34/9.52 |
% 34.34/9.52 | Instantiating (175) with all_22_0_13, all_22_1_14 yields:
% 34.34/9.52 | (176) ssList(all_22_1_14) = 0 & cons(all_22_0_13, all_22_1_14) = all_0_4_4 & ssItem(all_22_0_13) = 0
% 34.34/9.52 |
% 34.34/9.52 | Applying alpha-rule on (176) yields:
% 34.34/9.52 | (177) ssList(all_22_1_14) = 0
% 34.34/9.52 | (178) cons(all_22_0_13, all_22_1_14) = all_0_4_4
% 34.34/9.52 | (179) ssItem(all_22_0_13) = 0
% 34.34/9.52 |
% 34.34/9.52 +-Applying beta-rule and splitting (171), into two cases.
% 34.34/9.52 |-Branch one:
% 34.34/9.52 | (180) all_0_2_2 = 0
% 34.34/9.52 |
% 34.34/9.52 +-Applying beta-rule and splitting (68), into two cases.
% 34.34/9.52 |-Branch one:
% 34.34/9.52 | (181) ~ (all_0_2_2 = 0)
% 34.34/9.52 |
% 34.34/9.52 | Equations (180) can reduce 181 to:
% 34.34/9.52 | (169) $false
% 34.34/9.52 |
% 34.34/9.52 |-The branch is then unsatisfiable
% 34.34/9.52 |-Branch two:
% 34.34/9.52 | (180) all_0_2_2 = 0
% 34.34/9.52 | (184) all_0_3_3 = 0
% 34.34/9.52 |
% 34.34/9.52 | From (184) and (35) follows:
% 34.34/9.52 | (185) singletonP(all_0_5_5) = 0
% 34.34/9.52 |
% 34.34/9.52 +-Applying beta-rule and splitting (152), into two cases.
% 34.34/9.52 |-Branch one:
% 34.34/9.52 | (186) ~ (singletonP(all_0_5_5) = 0)
% 34.34/9.52 |
% 34.34/9.52 | Using (185) and (186) yields:
% 34.34/9.52 | (187) $false
% 34.34/9.52 |
% 34.34/9.52 |-The branch is then unsatisfiable
% 34.34/9.52 |-Branch two:
% 34.34/9.52 | (185) singletonP(all_0_5_5) = 0
% 34.34/9.52 | (189) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_5_5 & v1 = 0 & cons(v0, nil) = all_0_5_5 & ssItem(v0) = 0) | ( ~ (v0 = 0) & ssList(all_0_5_5) = v0))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating (189) with all_36_0_15, all_36_1_16, all_36_2_17 yields:
% 34.34/9.52 | (190) (all_36_0_15 = all_0_5_5 & all_36_1_16 = 0 & cons(all_36_2_17, nil) = all_0_5_5 & ssItem(all_36_2_17) = 0) | ( ~ (all_36_2_17 = 0) & ssList(all_0_5_5) = all_36_2_17)
% 34.34/9.52 |
% 34.34/9.52 +-Applying beta-rule and splitting (190), into two cases.
% 34.34/9.52 |-Branch one:
% 34.34/9.52 | (191) all_36_0_15 = all_0_5_5 & all_36_1_16 = 0 & cons(all_36_2_17, nil) = all_0_5_5 & ssItem(all_36_2_17) = 0
% 34.34/9.52 |
% 34.34/9.52 | Applying alpha-rule on (191) yields:
% 34.34/9.52 | (192) all_36_0_15 = all_0_5_5
% 34.34/9.52 | (193) all_36_1_16 = 0
% 34.34/9.52 | (194) cons(all_36_2_17, nil) = all_0_5_5
% 34.34/9.52 | (195) ssItem(all_36_2_17) = 0
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (66) with nil, all_36_2_17, nil and discharging atoms ssList(nil) = 0, yields:
% 34.34/9.52 | (196) ~ (cons(all_36_2_17, nil) = nil) | ? [v0] : ? [v1] : (tl(nil) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v0 = 0) | v1 = nil))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (56) with nil, all_36_2_17, nil and discharging atoms ssList(nil) = 0, yields:
% 34.34/9.52 | (197) ~ (cons(all_36_2_17, nil) = nil) | ? [v0] : ? [v1] : (hd(nil) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v0 = 0) | v1 = all_36_2_17))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (66) with all_0_5_5, all_36_2_17, nil and discharging atoms ssList(nil) = 0, cons(all_36_2_17, nil) = all_0_5_5, yields:
% 34.34/9.52 | (198) ? [v0] : ? [v1] : (tl(all_0_5_5) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v0 = 0) | v1 = nil))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (56) with all_0_5_5, all_36_2_17, nil and discharging atoms ssList(nil) = 0, cons(all_36_2_17, nil) = all_0_5_5, yields:
% 34.34/9.52 | (199) ? [v0] : ? [v1] : (hd(all_0_5_5) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v0 = 0) | v1 = all_36_2_17))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (57) with all_36_2_17 and discharging atoms cons(all_36_2_17, nil) = all_0_5_5, yields:
% 34.34/9.52 | (200) ? [v0] : ? [v1] : (memberP(all_0_4_4, all_36_2_17) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (55) with all_0_5_5, all_36_2_17 and discharging atoms cons(all_36_2_17, nil) = all_0_5_5, yields:
% 34.34/9.52 | (201) ? [v0] : ? [v1] : (equalelemsP(all_0_5_5) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (7) with all_0_5_5, all_36_2_17 and discharging atoms cons(all_36_2_17, nil) = all_0_5_5, yields:
% 34.34/9.52 | (202) ? [v0] : ? [v1] : (duplicatefreeP(all_0_5_5) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (40) with all_0_5_5, all_36_2_17 and discharging atoms cons(all_36_2_17, nil) = all_0_5_5, yields:
% 34.34/9.52 | (203) ? [v0] : ? [v1] : (strictorderedP(all_0_5_5) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (100) with all_0_5_5, all_36_2_17 and discharging atoms cons(all_36_2_17, nil) = all_0_5_5, yields:
% 34.34/9.52 | (204) ? [v0] : ? [v1] : (totalorderedP(all_0_5_5) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (141) with all_0_5_5, all_36_2_17 and discharging atoms cons(all_36_2_17, nil) = all_0_5_5, yields:
% 34.34/9.52 | (205) ? [v0] : ? [v1] : (strictorderP(all_0_5_5) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (148) with all_0_5_5, all_36_2_17 and discharging atoms cons(all_36_2_17, nil) = all_0_5_5, yields:
% 34.34/9.52 | (206) ? [v0] : ? [v1] : (totalorderP(all_0_5_5) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (140) with all_0_5_5, all_36_2_17 and discharging atoms cons(all_36_2_17, nil) = all_0_5_5, yields:
% 34.34/9.52 | (207) ? [v0] : ? [v1] : (cyclefreeP(all_0_5_5) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (52) with all_36_2_17, nil and discharging atoms ssList(nil) = 0, yields:
% 34.34/9.52 | (208) ~ (cons(all_36_2_17, nil) = nil) | ? [v0] : ( ~ (v0 = 0) & ssItem(all_36_2_17) = v0)
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (66) with all_0_4_4, all_22_0_13, all_22_1_14 and discharging atoms ssList(all_22_1_14) = 0, cons(all_22_0_13, all_22_1_14) = all_0_4_4, yields:
% 34.34/9.52 | (209) ? [v0] : ? [v1] : (tl(all_0_4_4) = v1 & ssItem(all_22_0_13) = v0 & ( ~ (v0 = 0) | v1 = all_22_1_14))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (56) with all_0_4_4, all_22_0_13, all_22_1_14 and discharging atoms ssList(all_22_1_14) = 0, cons(all_22_0_13, all_22_1_14) = all_0_4_4, yields:
% 34.34/9.52 | (210) ? [v0] : ? [v1] : (hd(all_0_4_4) = v1 & ssItem(all_22_0_13) = v0 & ( ~ (v0 = 0) | v1 = all_22_0_13))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (24) with all_0_4_4, all_8_2_9, all_8_3_10, all_0_5_5, all_8_5_12 and discharging atoms ssList(all_8_5_12) = 0, app(all_8_3_10, all_8_2_9) = all_0_4_4, app(all_8_5_12, all_0_5_5) = all_8_3_10, yields:
% 34.34/9.52 | (211) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & ssList(all_0_5_5) = v0) | (ssList(all_8_2_9) = v0 & app(all_8_5_12, v1) = v2 & app(all_0_5_5, all_8_2_9) = v1 & ( ~ (v0 = 0) | v2 = all_0_4_4)))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating formula (10) with all_8_3_10, all_0_5_5, all_8_5_12 and discharging atoms ssList(all_8_5_12) = 0, app(all_8_5_12, all_0_5_5) = all_8_3_10, yields:
% 34.34/9.52 | (212) ? [v0] : ? [v1] : (ssList(all_8_3_10) = v1 & ssList(all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 34.34/9.52 |
% 34.34/9.52 | Instantiating (212) with all_46_0_18, all_46_1_19 yields:
% 34.34/9.52 | (213) ssList(all_8_3_10) = all_46_0_18 & ssList(all_0_5_5) = all_46_1_19 & ( ~ (all_46_1_19 = 0) | all_46_0_18 = 0)
% 34.34/9.53 |
% 34.34/9.53 | Applying alpha-rule on (213) yields:
% 34.34/9.53 | (214) ssList(all_8_3_10) = all_46_0_18
% 34.34/9.53 | (215) ssList(all_0_5_5) = all_46_1_19
% 34.34/9.53 | (216) ~ (all_46_1_19 = 0) | all_46_0_18 = 0
% 34.34/9.53 |
% 34.34/9.53 | Instantiating (210) with all_48_0_20, all_48_1_21 yields:
% 34.34/9.53 | (217) hd(all_0_4_4) = all_48_0_20 & ssItem(all_22_0_13) = all_48_1_21 & ( ~ (all_48_1_21 = 0) | all_48_0_20 = all_22_0_13)
% 34.34/9.53 |
% 34.34/9.53 | Applying alpha-rule on (217) yields:
% 34.34/9.53 | (218) hd(all_0_4_4) = all_48_0_20
% 34.34/9.53 | (219) ssItem(all_22_0_13) = all_48_1_21
% 34.34/9.53 | (220) ~ (all_48_1_21 = 0) | all_48_0_20 = all_22_0_13
% 34.34/9.53 |
% 34.34/9.53 | Instantiating (211) with all_50_0_22, all_50_1_23, all_50_2_24 yields:
% 34.34/9.53 | (221) ( ~ (all_50_2_24 = 0) & ssList(all_0_5_5) = all_50_2_24) | (ssList(all_8_2_9) = all_50_2_24 & app(all_8_5_12, all_50_1_23) = all_50_0_22 & app(all_0_5_5, all_8_2_9) = all_50_1_23 & ( ~ (all_50_2_24 = 0) | all_50_0_22 = all_0_4_4))
% 34.34/9.53 |
% 34.34/9.53 | Instantiating (207) with all_51_0_25, all_51_1_26 yields:
% 34.34/9.53 | (222) cyclefreeP(all_0_5_5) = all_51_0_25 & ssItem(all_36_2_17) = all_51_1_26 & ( ~ (all_51_1_26 = 0) | all_51_0_25 = 0)
% 34.34/9.53 |
% 34.34/9.53 | Applying alpha-rule on (222) yields:
% 34.34/9.53 | (223) cyclefreeP(all_0_5_5) = all_51_0_25
% 34.34/9.53 | (224) ssItem(all_36_2_17) = all_51_1_26
% 34.34/9.53 | (225) ~ (all_51_1_26 = 0) | all_51_0_25 = 0
% 34.34/9.53 |
% 34.34/9.53 | Instantiating (205) with all_53_0_27, all_53_1_28 yields:
% 34.34/9.53 | (226) strictorderP(all_0_5_5) = all_53_0_27 & ssItem(all_36_2_17) = all_53_1_28 & ( ~ (all_53_1_28 = 0) | all_53_0_27 = 0)
% 34.34/9.53 |
% 34.34/9.53 | Applying alpha-rule on (226) yields:
% 34.34/9.53 | (227) strictorderP(all_0_5_5) = all_53_0_27
% 34.34/9.53 | (228) ssItem(all_36_2_17) = all_53_1_28
% 34.34/9.53 | (229) ~ (all_53_1_28 = 0) | all_53_0_27 = 0
% 34.34/9.53 |
% 34.34/9.53 | Instantiating (204) with all_55_0_29, all_55_1_30 yields:
% 34.34/9.53 | (230) totalorderedP(all_0_5_5) = all_55_0_29 & ssItem(all_36_2_17) = all_55_1_30 & ( ~ (all_55_1_30 = 0) | all_55_0_29 = 0)
% 34.34/9.53 |
% 34.34/9.53 | Applying alpha-rule on (230) yields:
% 34.34/9.53 | (231) totalorderedP(all_0_5_5) = all_55_0_29
% 34.34/9.53 | (232) ssItem(all_36_2_17) = all_55_1_30
% 34.34/9.53 | (233) ~ (all_55_1_30 = 0) | all_55_0_29 = 0
% 34.34/9.53 |
% 34.34/9.53 | Instantiating (206) with all_57_0_31, all_57_1_32 yields:
% 34.34/9.53 | (234) totalorderP(all_0_5_5) = all_57_0_31 & ssItem(all_36_2_17) = all_57_1_32 & ( ~ (all_57_1_32 = 0) | all_57_0_31 = 0)
% 34.34/9.53 |
% 34.34/9.53 | Applying alpha-rule on (234) yields:
% 34.34/9.53 | (235) totalorderP(all_0_5_5) = all_57_0_31
% 34.34/9.53 | (236) ssItem(all_36_2_17) = all_57_1_32
% 34.34/9.53 | (237) ~ (all_57_1_32 = 0) | all_57_0_31 = 0
% 34.34/9.53 |
% 34.34/9.53 | Instantiating (203) with all_59_0_33, all_59_1_34 yields:
% 34.34/9.53 | (238) strictorderedP(all_0_5_5) = all_59_0_33 & ssItem(all_36_2_17) = all_59_1_34 & ( ~ (all_59_1_34 = 0) | all_59_0_33 = 0)
% 34.34/9.53 |
% 34.34/9.53 | Applying alpha-rule on (238) yields:
% 34.34/9.53 | (239) strictorderedP(all_0_5_5) = all_59_0_33
% 34.34/9.53 | (240) ssItem(all_36_2_17) = all_59_1_34
% 34.34/9.53 | (241) ~ (all_59_1_34 = 0) | all_59_0_33 = 0
% 34.34/9.53 |
% 34.34/9.53 | Instantiating (202) with all_61_0_35, all_61_1_36 yields:
% 34.34/9.53 | (242) duplicatefreeP(all_0_5_5) = all_61_0_35 & ssItem(all_36_2_17) = all_61_1_36 & ( ~ (all_61_1_36 = 0) | all_61_0_35 = 0)
% 34.34/9.53 |
% 34.34/9.53 | Applying alpha-rule on (242) yields:
% 34.34/9.53 | (243) duplicatefreeP(all_0_5_5) = all_61_0_35
% 34.34/9.53 | (244) ssItem(all_36_2_17) = all_61_1_36
% 34.34/9.53 | (245) ~ (all_61_1_36 = 0) | all_61_0_35 = 0
% 34.34/9.53 |
% 34.34/9.53 | Instantiating (201) with all_63_0_37, all_63_1_38 yields:
% 34.34/9.53 | (246) equalelemsP(all_0_5_5) = all_63_0_37 & ssItem(all_36_2_17) = all_63_1_38 & ( ~ (all_63_1_38 = 0) | all_63_0_37 = 0)
% 34.34/9.53 |
% 34.34/9.53 | Applying alpha-rule on (246) yields:
% 34.34/9.53 | (247) equalelemsP(all_0_5_5) = all_63_0_37
% 34.34/9.53 | (248) ssItem(all_36_2_17) = all_63_1_38
% 34.34/9.53 | (249) ~ (all_63_1_38 = 0) | all_63_0_37 = 0
% 34.34/9.53 |
% 34.34/9.53 | Instantiating (200) with all_65_0_39, all_65_1_40 yields:
% 34.34/9.53 | (250) memberP(all_0_4_4, all_36_2_17) = all_65_0_39 & ssItem(all_36_2_17) = all_65_1_40 & ( ~ (all_65_0_39 = 0) | ~ (all_65_1_40 = 0))
% 34.34/9.53 |
% 34.34/9.53 | Applying alpha-rule on (250) yields:
% 34.34/9.53 | (251) memberP(all_0_4_4, all_36_2_17) = all_65_0_39
% 34.34/9.53 | (252) ssItem(all_36_2_17) = all_65_1_40
% 34.34/9.53 | (253) ~ (all_65_0_39 = 0) | ~ (all_65_1_40 = 0)
% 34.34/9.53 |
% 34.34/9.53 | Instantiating (199) with all_67_0_41, all_67_1_42 yields:
% 34.34/9.53 | (254) hd(all_0_5_5) = all_67_0_41 & ssItem(all_36_2_17) = all_67_1_42 & ( ~ (all_67_1_42 = 0) | all_67_0_41 = all_36_2_17)
% 34.34/9.53 |
% 34.34/9.53 | Applying alpha-rule on (254) yields:
% 34.34/9.53 | (255) hd(all_0_5_5) = all_67_0_41
% 34.34/9.53 | (256) ssItem(all_36_2_17) = all_67_1_42
% 34.34/9.53 | (257) ~ (all_67_1_42 = 0) | all_67_0_41 = all_36_2_17
% 34.34/9.53 |
% 34.34/9.53 | Instantiating (209) with all_69_0_43, all_69_1_44 yields:
% 34.34/9.53 | (258) tl(all_0_4_4) = all_69_0_43 & ssItem(all_22_0_13) = all_69_1_44 & ( ~ (all_69_1_44 = 0) | all_69_0_43 = all_22_1_14)
% 34.34/9.53 |
% 34.34/9.53 | Applying alpha-rule on (258) yields:
% 34.34/9.53 | (259) tl(all_0_4_4) = all_69_0_43
% 34.34/9.53 | (260) ssItem(all_22_0_13) = all_69_1_44
% 34.34/9.53 | (261) ~ (all_69_1_44 = 0) | all_69_0_43 = all_22_1_14
% 34.34/9.53 |
% 34.34/9.53 | Instantiating (198) with all_71_0_45, all_71_1_46 yields:
% 34.34/9.53 | (262) tl(all_0_5_5) = all_71_0_45 & ssItem(all_36_2_17) = all_71_1_46 & ( ~ (all_71_1_46 = 0) | all_71_0_45 = nil)
% 34.34/9.53 |
% 34.34/9.53 | Applying alpha-rule on (262) yields:
% 34.34/9.53 | (263) tl(all_0_5_5) = all_71_0_45
% 34.34/9.53 | (264) ssItem(all_36_2_17) = all_71_1_46
% 34.34/9.53 | (265) ~ (all_71_1_46 = 0) | all_71_0_45 = nil
% 34.34/9.53 |
% 34.34/9.53 | Instantiating formula (130) with all_0_5_5, all_46_1_19, 0 and discharging atoms ssList(all_0_5_5) = all_46_1_19, ssList(all_0_5_5) = 0, yields:
% 34.34/9.53 | (266) all_46_1_19 = 0
% 34.34/9.53 |
% 34.34/9.53 | Instantiating formula (79) with all_36_2_17, all_71_1_46, 0 and discharging atoms ssItem(all_36_2_17) = all_71_1_46, ssItem(all_36_2_17) = 0, yields:
% 34.34/9.53 | (267) all_71_1_46 = 0
% 34.34/9.53 |
% 34.34/9.53 | Instantiating formula (79) with all_36_2_17, all_65_1_40, all_67_1_42 and discharging atoms ssItem(all_36_2_17) = all_67_1_42, ssItem(all_36_2_17) = all_65_1_40, yields:
% 34.34/9.53 | (268) all_67_1_42 = all_65_1_40
% 34.34/9.53 |
% 34.34/9.53 | Instantiating formula (79) with all_36_2_17, all_61_1_36, all_67_1_42 and discharging atoms ssItem(all_36_2_17) = all_67_1_42, ssItem(all_36_2_17) = all_61_1_36, yields:
% 34.34/9.53 | (269) all_67_1_42 = all_61_1_36
% 34.34/9.53 |
% 34.34/9.53 | Instantiating formula (79) with all_36_2_17, all_61_1_36, all_63_1_38 and discharging atoms ssItem(all_36_2_17) = all_63_1_38, ssItem(all_36_2_17) = all_61_1_36, yields:
% 34.34/9.53 | (270) all_63_1_38 = all_61_1_36
% 34.34/9.53 |
% 34.34/9.53 | Instantiating formula (79) with all_36_2_17, all_59_1_34, all_67_1_42 and discharging atoms ssItem(all_36_2_17) = all_67_1_42, ssItem(all_36_2_17) = all_59_1_34, yields:
% 34.34/9.53 | (271) all_67_1_42 = all_59_1_34
% 34.34/9.53 |
% 34.34/9.53 | Instantiating formula (79) with all_36_2_17, all_57_1_32, all_71_1_46 and discharging atoms ssItem(all_36_2_17) = all_71_1_46, ssItem(all_36_2_17) = all_57_1_32, yields:
% 34.34/9.53 | (272) all_71_1_46 = all_57_1_32
% 34.34/9.53 |
% 34.34/9.53 | Instantiating formula (79) with all_36_2_17, all_55_1_30, all_71_1_46 and discharging atoms ssItem(all_36_2_17) = all_71_1_46, ssItem(all_36_2_17) = all_55_1_30, yields:
% 34.34/9.53 | (273) all_71_1_46 = all_55_1_30
% 34.34/9.53 |
% 34.34/9.53 | Instantiating formula (79) with all_36_2_17, all_53_1_28, all_71_1_46 and discharging atoms ssItem(all_36_2_17) = all_71_1_46, ssItem(all_36_2_17) = all_53_1_28, yields:
% 34.34/9.53 | (274) all_71_1_46 = all_53_1_28
% 34.34/9.53 |
% 34.34/9.53 | Instantiating formula (79) with all_36_2_17, all_53_1_28, all_61_1_36 and discharging atoms ssItem(all_36_2_17) = all_61_1_36, ssItem(all_36_2_17) = all_53_1_28, yields:
% 34.34/9.53 | (275) all_61_1_36 = all_53_1_28
% 34.34/9.53 |
% 34.34/9.53 | Instantiating formula (79) with all_36_2_17, all_51_1_26, all_63_1_38 and discharging atoms ssItem(all_36_2_17) = all_63_1_38, ssItem(all_36_2_17) = all_51_1_26, yields:
% 34.34/9.53 | (276) all_63_1_38 = all_51_1_26
% 34.34/9.53 |
% 34.34/9.53 | Instantiating formula (79) with all_22_0_13, all_69_1_44, 0 and discharging atoms ssItem(all_22_0_13) = all_69_1_44, ssItem(all_22_0_13) = 0, yields:
% 34.34/9.53 | (277) all_69_1_44 = 0
% 34.34/9.53 |
% 34.34/9.53 | Instantiating formula (79) with all_22_0_13, all_48_1_21, all_69_1_44 and discharging atoms ssItem(all_22_0_13) = all_69_1_44, ssItem(all_22_0_13) = all_48_1_21, yields:
% 34.34/9.53 | (278) all_69_1_44 = all_48_1_21
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (274,272) yields a new equation:
% 34.34/9.53 | (279) all_57_1_32 = all_53_1_28
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (273,272) yields a new equation:
% 34.34/9.53 | (280) all_57_1_32 = all_55_1_30
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (267,272) yields a new equation:
% 34.34/9.53 | (281) all_57_1_32 = 0
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (277,278) yields a new equation:
% 34.34/9.53 | (282) all_48_1_21 = 0
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (271,268) yields a new equation:
% 34.34/9.53 | (283) all_65_1_40 = all_59_1_34
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (269,268) yields a new equation:
% 34.34/9.53 | (284) all_65_1_40 = all_61_1_36
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (284,283) yields a new equation:
% 34.34/9.53 | (285) all_61_1_36 = all_59_1_34
% 34.34/9.53 |
% 34.34/9.53 | Simplifying 285 yields:
% 34.34/9.53 | (286) all_61_1_36 = all_59_1_34
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (270,276) yields a new equation:
% 34.34/9.53 | (287) all_61_1_36 = all_51_1_26
% 34.34/9.53 |
% 34.34/9.53 | Simplifying 287 yields:
% 34.34/9.53 | (288) all_61_1_36 = all_51_1_26
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (275,286) yields a new equation:
% 34.34/9.53 | (289) all_59_1_34 = all_53_1_28
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (288,286) yields a new equation:
% 34.34/9.53 | (290) all_59_1_34 = all_51_1_26
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (289,290) yields a new equation:
% 34.34/9.53 | (291) all_53_1_28 = all_51_1_26
% 34.34/9.53 |
% 34.34/9.53 | Simplifying 291 yields:
% 34.34/9.53 | (292) all_53_1_28 = all_51_1_26
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (281,280) yields a new equation:
% 34.34/9.53 | (293) all_55_1_30 = 0
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (279,280) yields a new equation:
% 34.34/9.53 | (294) all_55_1_30 = all_53_1_28
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (294,293) yields a new equation:
% 34.34/9.53 | (295) all_53_1_28 = 0
% 34.34/9.53 |
% 34.34/9.53 | Simplifying 295 yields:
% 34.34/9.53 | (296) all_53_1_28 = 0
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (296,292) yields a new equation:
% 34.34/9.53 | (297) all_51_1_26 = 0
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (293,280) yields a new equation:
% 34.34/9.53 | (281) all_57_1_32 = 0
% 34.34/9.53 |
% 34.34/9.53 | Combining equations (297,290) yields a new equation:
% 34.34/9.53 | (299) all_59_1_34 = 0
% 34.34/9.54 |
% 34.34/9.54 | Combining equations (299,283) yields a new equation:
% 34.34/9.54 | (300) all_65_1_40 = 0
% 34.34/9.54 |
% 34.34/9.54 | Combining equations (300,268) yields a new equation:
% 34.34/9.54 | (301) all_67_1_42 = 0
% 34.34/9.54 |
% 34.34/9.54 | Combining equations (282,278) yields a new equation:
% 34.34/9.54 | (277) all_69_1_44 = 0
% 34.34/9.54 |
% 34.34/9.54 | Combining equations (281,272) yields a new equation:
% 34.34/9.54 | (267) all_71_1_46 = 0
% 34.34/9.54 |
% 34.34/9.54 | From (266) and (215) follows:
% 34.34/9.54 | (113) ssList(all_0_5_5) = 0
% 34.34/9.54 |
% 34.34/9.54 | From (297) and (224) follows:
% 34.34/9.54 | (195) ssItem(all_36_2_17) = 0
% 34.34/9.54 |
% 34.34/9.54 | From (282) and (219) follows:
% 34.34/9.54 | (179) ssItem(all_22_0_13) = 0
% 34.34/9.54 |
% 34.34/9.54 +-Applying beta-rule and splitting (208), into two cases.
% 34.34/9.54 |-Branch one:
% 34.34/9.54 | (307) ~ (cons(all_36_2_17, nil) = nil)
% 34.34/9.54 |
% 34.34/9.54 +-Applying beta-rule and splitting (253), into two cases.
% 34.34/9.54 |-Branch one:
% 34.34/9.54 | (308) ~ (all_65_0_39 = 0)
% 34.34/9.54 |
% 34.34/9.54 +-Applying beta-rule and splitting (221), into two cases.
% 34.34/9.54 |-Branch one:
% 34.34/9.54 | (309) ~ (all_50_2_24 = 0) & ssList(all_0_5_5) = all_50_2_24
% 34.34/9.54 |
% 34.34/9.54 | Applying alpha-rule on (309) yields:
% 34.34/9.54 | (310) ~ (all_50_2_24 = 0)
% 34.34/9.54 | (311) ssList(all_0_5_5) = all_50_2_24
% 34.34/9.54 |
% 34.34/9.54 | Instantiating formula (130) with all_0_5_5, all_50_2_24, 0 and discharging atoms ssList(all_0_5_5) = all_50_2_24, ssList(all_0_5_5) = 0, yields:
% 34.34/9.54 | (312) all_50_2_24 = 0
% 34.34/9.54 |
% 34.34/9.54 | Equations (312) can reduce 310 to:
% 34.34/9.54 | (169) $false
% 34.34/9.54 |
% 34.34/9.54 |-The branch is then unsatisfiable
% 34.34/9.54 |-Branch two:
% 34.34/9.54 | (314) ssList(all_8_2_9) = all_50_2_24 & app(all_8_5_12, all_50_1_23) = all_50_0_22 & app(all_0_5_5, all_8_2_9) = all_50_1_23 & ( ~ (all_50_2_24 = 0) | all_50_0_22 = all_0_4_4)
% 34.34/9.54 |
% 34.34/9.54 | Applying alpha-rule on (314) yields:
% 34.34/9.54 | (315) ssList(all_8_2_9) = all_50_2_24
% 34.34/9.54 | (316) app(all_8_5_12, all_50_1_23) = all_50_0_22
% 34.34/9.54 | (317) app(all_0_5_5, all_8_2_9) = all_50_1_23
% 34.34/9.54 | (318) ~ (all_50_2_24 = 0) | all_50_0_22 = all_0_4_4
% 34.34/9.54 |
% 34.34/9.54 +-Applying beta-rule and splitting (265), into two cases.
% 34.34/9.54 |-Branch one:
% 34.34/9.54 | (319) ~ (all_71_1_46 = 0)
% 34.34/9.54 |
% 34.34/9.54 | Equations (267) can reduce 319 to:
% 34.34/9.54 | (169) $false
% 34.34/9.54 |
% 34.34/9.54 |-The branch is then unsatisfiable
% 34.34/9.54 |-Branch two:
% 34.34/9.54 | (267) all_71_1_46 = 0
% 34.34/9.54 | (322) all_71_0_45 = nil
% 34.34/9.54 |
% 34.34/9.54 | From (322) and (263) follows:
% 34.34/9.54 | (323) tl(all_0_5_5) = nil
% 34.34/9.54 |
% 34.34/9.54 +-Applying beta-rule and splitting (257), into two cases.
% 34.34/9.54 |-Branch one:
% 34.34/9.54 | (324) ~ (all_67_1_42 = 0)
% 34.34/9.54 |
% 34.34/9.54 | Equations (301) can reduce 324 to:
% 34.34/9.54 | (169) $false
% 34.34/9.54 |
% 34.34/9.54 |-The branch is then unsatisfiable
% 34.34/9.54 |-Branch two:
% 34.34/9.54 | (301) all_67_1_42 = 0
% 34.34/9.54 | (327) all_67_0_41 = all_36_2_17
% 34.34/9.54 |
% 34.34/9.54 | From (327) and (255) follows:
% 34.34/9.54 | (328) hd(all_0_5_5) = all_36_2_17
% 34.34/9.54 |
% 34.34/9.54 +-Applying beta-rule and splitting (261), into two cases.
% 34.34/9.54 |-Branch one:
% 34.34/9.54 | (329) ~ (all_69_1_44 = 0)
% 34.34/9.54 |
% 34.34/9.54 | Equations (277) can reduce 329 to:
% 34.34/9.54 | (169) $false
% 34.34/9.54 |
% 34.34/9.54 |-The branch is then unsatisfiable
% 34.34/9.54 |-Branch two:
% 34.34/9.54 | (277) all_69_1_44 = 0
% 34.34/9.54 | (332) all_69_0_43 = all_22_1_14
% 34.34/9.54 |
% 34.34/9.54 | From (332) and (259) follows:
% 34.34/9.54 | (333) tl(all_0_4_4) = all_22_1_14
% 34.34/9.54 |
% 34.34/9.54 | Instantiating formula (130) with all_8_2_9, all_50_2_24, 0 and discharging atoms ssList(all_8_2_9) = all_50_2_24, ssList(all_8_2_9) = 0, yields:
% 34.34/9.54 | (312) all_50_2_24 = 0
% 34.34/9.54 |
% 34.34/9.54 | Using (194) and (307) yields:
% 34.34/9.54 | (335) ~ (all_0_5_5 = nil)
% 34.34/9.54 |
% 34.34/9.54 | From (312) and (315) follows:
% 34.34/9.54 | (164) ssList(all_8_2_9) = 0
% 34.34/9.54 |
% 34.34/9.54 +-Applying beta-rule and splitting (156), into two cases.
% 34.34/9.54 |-Branch one:
% 34.34/9.54 | (337) all_0_5_5 = nil
% 34.34/9.54 |
% 34.34/9.54 | Equations (337) can reduce 335 to:
% 34.34/9.54 | (169) $false
% 34.34/9.54 |
% 34.34/9.54 |-The branch is then unsatisfiable
% 34.34/9.54 |-Branch two:
% 34.34/9.54 | (335) ~ (all_0_5_5 = nil)
% 34.34/9.54 | (340) ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_5_5 & ssItem(v1) = 0)
% 34.34/9.54 |
% 34.34/9.54 | Instantiating (340) with all_148_0_47, all_148_1_48 yields:
% 34.34/9.54 | (341) ssList(all_148_1_48) = 0 & cons(all_148_0_47, all_148_1_48) = all_0_5_5 & ssItem(all_148_0_47) = 0
% 34.34/9.54 |
% 34.34/9.54 | Applying alpha-rule on (341) yields:
% 34.34/9.54 | (342) ssList(all_148_1_48) = 0
% 34.34/9.54 | (343) cons(all_148_0_47, all_148_1_48) = all_0_5_5
% 34.34/9.54 | (344) ssItem(all_148_0_47) = 0
% 34.34/9.54 |
% 34.34/9.54 +-Applying beta-rule and splitting (318), into two cases.
% 34.34/9.54 |-Branch one:
% 34.34/9.54 | (310) ~ (all_50_2_24 = 0)
% 34.34/9.54 |
% 34.34/9.54 | Equations (312) can reduce 310 to:
% 34.34/9.54 | (169) $false
% 34.34/9.54 |
% 34.34/9.54 |-The branch is then unsatisfiable
% 34.34/9.54 |-Branch two:
% 34.34/9.54 | (312) all_50_2_24 = 0
% 34.34/9.54 | (348) all_50_0_22 = all_0_4_4
% 34.34/9.54 |
% 34.34/9.54 | From (348) and (316) follows:
% 34.34/9.54 | (349) app(all_8_5_12, all_50_1_23) = all_0_4_4
% 34.34/9.54 |
% 34.34/9.54 | Instantiating formula (149) with all_22_1_14, all_0_4_4 and discharging atoms tl(all_0_4_4) = all_22_1_14, yields:
% 34.34/9.54 | (350) ? [v0] : ? [v1] : (hd(all_0_4_4) = v1 & ssList(all_0_4_4) = v0 & ( ~ (v0 = 0) | ! [v2] : (v2 = all_0_4_4 | v2 = nil | all_0_4_4 = nil | ~ (tl(v2) = all_22_1_14) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssList(v2) = v3 & ( ~ (v4 = v1) | ~ (v3 = 0))))))
% 34.34/9.54 |
% 34.34/9.54 | Instantiating formula (149) with nil, all_0_5_5 and discharging atoms tl(all_0_5_5) = nil, yields:
% 34.34/9.54 | (351) ? [v0] : ? [v1] : (hd(all_0_5_5) = v1 & ssList(all_0_5_5) = v0 & ( ~ (v0 = 0) | ! [v2] : (v2 = all_0_5_5 | v2 = nil | all_0_5_5 = nil | ~ (tl(v2) = nil) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssList(v2) = v3 & ( ~ (v4 = v1) | ~ (v3 = 0))))))
% 34.34/9.54 |
% 34.34/9.54 | Instantiating formula (98) with all_65_0_39, all_0_5_5, nil, all_36_2_17, all_36_2_17 and discharging atoms cons(all_36_2_17, nil) = all_0_5_5, ssItem(all_36_2_17) = 0, yields:
% 34.34/9.54 | (352) ~ (memberP(all_0_5_5, all_36_2_17) = all_65_0_39) | ? [v0] : ? [v1] : (memberP(nil, all_36_2_17) = v1 & ssList(nil) = v0 & ( ~ (v0 = 0) | all_65_0_39 = 0))
% 34.34/9.54 |
% 34.34/9.54 | Instantiating formula (98) with all_65_0_39, all_0_4_4, all_22_1_14, all_22_0_13, all_36_2_17 and discharging atoms memberP(all_0_4_4, all_36_2_17) = all_65_0_39, cons(all_22_0_13, all_22_1_14) = all_0_4_4, ssItem(all_36_2_17) = 0, ssItem(all_22_0_13) = 0, yields:
% 34.34/9.54 | (353) ? [v0] : ? [v1] : (memberP(all_22_1_14, all_36_2_17) = v1 & ssList(all_22_1_14) = v0 & ( ~ (v0 = 0) | (( ~ (all_65_0_39 = 0) | v1 = 0 | all_36_2_17 = all_22_0_13) & (all_65_0_39 = 0 | ( ~ (v1 = 0) & ~ (all_36_2_17 = all_22_0_13))))))
% 34.34/9.54 |
% 34.34/9.54 | Instantiating formula (135) with all_36_2_17, all_0_5_5, all_148_0_47, nil, nil and discharging atoms ssList(nil) = 0, cons(all_36_2_17, nil) = all_0_5_5, yields:
% 34.34/9.54 | (354) all_148_0_47 = all_36_2_17 | ~ (cons(all_148_0_47, nil) = all_0_5_5) | ? [v0] : (( ~ (v0 = 0) & ssItem(all_148_0_47) = v0) | ( ~ (v0 = 0) & ssItem(all_36_2_17) = v0))
% 34.34/9.54 |
% 34.34/9.54 | Instantiating formula (66) with all_0_5_5, all_148_0_47, all_148_1_48 and discharging atoms ssList(all_148_1_48) = 0, cons(all_148_0_47, all_148_1_48) = all_0_5_5, yields:
% 34.34/9.54 | (355) ? [v0] : ? [v1] : (tl(all_0_5_5) = v1 & ssItem(all_148_0_47) = v0 & ( ~ (v0 = 0) | v1 = all_148_1_48))
% 34.34/9.54 |
% 34.34/9.54 | Instantiating formula (56) with all_0_5_5, all_148_0_47, all_148_1_48 and discharging atoms ssList(all_148_1_48) = 0, cons(all_148_0_47, all_148_1_48) = all_0_5_5, yields:
% 34.34/9.54 | (356) ? [v0] : ? [v1] : (hd(all_0_5_5) = v1 & ssItem(all_148_0_47) = v0 & ( ~ (v0 = 0) | v1 = all_148_0_47))
% 34.34/9.54 |
% 34.34/9.54 | Instantiating formula (57) with all_148_0_47 yields:
% 34.34/9.54 | (357) ~ (cons(all_148_0_47, nil) = all_0_5_5) | ? [v0] : ? [v1] : (memberP(all_0_4_4, all_148_0_47) = v1 & ssItem(all_148_0_47) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 34.34/9.54 |
% 34.34/9.54 | Instantiating formula (10) with all_0_4_4, all_50_1_23, all_8_5_12 and discharging atoms ssList(all_8_5_12) = 0, app(all_8_5_12, all_50_1_23) = all_0_4_4, yields:
% 34.34/9.54 | (358) ? [v0] : ? [v1] : (ssList(all_50_1_23) = v0 & ssList(all_0_4_4) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 34.34/9.54 |
% 34.34/9.54 | Instantiating formula (49) with all_50_1_23, all_0_5_5, all_36_2_17, all_8_2_9 and discharging atoms ssList(all_8_2_9) = 0, cons(all_36_2_17, nil) = all_0_5_5, app(all_0_5_5, all_8_2_9) = all_50_1_23, yields:
% 34.34/9.54 | (359) ? [v0] : ? [v1] : (cons(all_36_2_17, all_8_2_9) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v0 = 0) | v1 = all_50_1_23))
% 34.34/9.54 |
% 34.34/9.54 | Instantiating formula (10) with all_50_1_23, all_8_2_9, all_0_5_5 and discharging atoms ssList(all_0_5_5) = 0, app(all_0_5_5, all_8_2_9) = all_50_1_23, yields:
% 34.34/9.54 | (360) ? [v0] : ? [v1] : (ssList(all_50_1_23) = v1 & ssList(all_8_2_9) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 34.34/9.54 |
% 34.34/9.54 | Instantiating formula (49) with all_50_1_23, all_0_5_5, all_148_0_47, all_8_2_9 and discharging atoms ssList(all_8_2_9) = 0, app(all_0_5_5, all_8_2_9) = all_50_1_23, yields:
% 34.34/9.54 | (361) ~ (cons(all_148_0_47, nil) = all_0_5_5) | ? [v0] : ? [v1] : (cons(all_148_0_47, all_8_2_9) = v1 & ssItem(all_148_0_47) = v0 & ( ~ (v0 = 0) | v1 = all_50_1_23))
% 34.34/9.54 |
% 34.34/9.54 | Instantiating formula (12) with all_50_1_23, all_8_2_9, all_36_2_17, all_0_5_5 and discharging atoms hd(all_0_5_5) = all_36_2_17, app(all_0_5_5, all_8_2_9) = all_50_1_23, yields:
% 34.34/9.54 | (362) all_0_5_5 = nil | ? [v0] : ? [v1] : (( ~ (v0 = 0) & ssList(all_0_5_5) = v0) | (hd(all_50_1_23) = v1 & ssList(all_8_2_9) = v0 & ( ~ (v0 = 0) | v1 = all_36_2_17)))
% 34.34/9.54 |
% 34.34/9.54 | Instantiating (360) with all_167_0_49, all_167_1_50 yields:
% 34.34/9.54 | (363) ssList(all_50_1_23) = all_167_0_49 & ssList(all_8_2_9) = all_167_1_50 & ( ~ (all_167_1_50 = 0) | all_167_0_49 = 0)
% 34.34/9.54 |
% 34.34/9.54 | Applying alpha-rule on (363) yields:
% 34.34/9.54 | (364) ssList(all_50_1_23) = all_167_0_49
% 34.34/9.54 | (365) ssList(all_8_2_9) = all_167_1_50
% 34.34/9.54 | (366) ~ (all_167_1_50 = 0) | all_167_0_49 = 0
% 34.34/9.54 |
% 34.34/9.54 | Instantiating (359) with all_169_0_51, all_169_1_52 yields:
% 34.34/9.54 | (367) cons(all_36_2_17, all_8_2_9) = all_169_0_51 & ssItem(all_36_2_17) = all_169_1_52 & ( ~ (all_169_1_52 = 0) | all_169_0_51 = all_50_1_23)
% 34.34/9.55 |
% 34.34/9.55 | Applying alpha-rule on (367) yields:
% 34.34/9.55 | (368) cons(all_36_2_17, all_8_2_9) = all_169_0_51
% 34.34/9.55 | (369) ssItem(all_36_2_17) = all_169_1_52
% 34.34/9.55 | (370) ~ (all_169_1_52 = 0) | all_169_0_51 = all_50_1_23
% 34.34/9.55 |
% 34.34/9.55 | Instantiating (358) with all_171_0_53, all_171_1_54 yields:
% 34.34/9.55 | (371) ssList(all_50_1_23) = all_171_1_54 & ssList(all_0_4_4) = all_171_0_53 & ( ~ (all_171_1_54 = 0) | all_171_0_53 = 0)
% 34.34/9.55 |
% 34.34/9.55 | Applying alpha-rule on (371) yields:
% 34.34/9.55 | (372) ssList(all_50_1_23) = all_171_1_54
% 34.34/9.55 | (373) ssList(all_0_4_4) = all_171_0_53
% 34.34/9.55 | (374) ~ (all_171_1_54 = 0) | all_171_0_53 = 0
% 34.34/9.55 |
% 34.34/9.55 | Instantiating (353) with all_173_0_55, all_173_1_56 yields:
% 34.34/9.55 | (375) memberP(all_22_1_14, all_36_2_17) = all_173_0_55 & ssList(all_22_1_14) = all_173_1_56 & ( ~ (all_173_1_56 = 0) | (( ~ (all_65_0_39 = 0) | all_173_0_55 = 0 | all_36_2_17 = all_22_0_13) & (all_65_0_39 = 0 | ( ~ (all_173_0_55 = 0) & ~ (all_36_2_17 = all_22_0_13)))))
% 34.34/9.55 |
% 34.34/9.55 | Applying alpha-rule on (375) yields:
% 34.34/9.55 | (376) memberP(all_22_1_14, all_36_2_17) = all_173_0_55
% 34.34/9.55 | (377) ssList(all_22_1_14) = all_173_1_56
% 34.34/9.55 | (378) ~ (all_173_1_56 = 0) | (( ~ (all_65_0_39 = 0) | all_173_0_55 = 0 | all_36_2_17 = all_22_0_13) & (all_65_0_39 = 0 | ( ~ (all_173_0_55 = 0) & ~ (all_36_2_17 = all_22_0_13))))
% 34.34/9.55 |
% 34.34/9.55 | Instantiating (356) with all_175_0_57, all_175_1_58 yields:
% 34.34/9.55 | (379) hd(all_0_5_5) = all_175_0_57 & ssItem(all_148_0_47) = all_175_1_58 & ( ~ (all_175_1_58 = 0) | all_175_0_57 = all_148_0_47)
% 34.34/9.55 |
% 34.34/9.55 | Applying alpha-rule on (379) yields:
% 34.34/9.55 | (380) hd(all_0_5_5) = all_175_0_57
% 34.34/9.55 | (381) ssItem(all_148_0_47) = all_175_1_58
% 34.34/9.55 | (382) ~ (all_175_1_58 = 0) | all_175_0_57 = all_148_0_47
% 34.34/9.55 |
% 34.34/9.55 | Instantiating (355) with all_177_0_59, all_177_1_60 yields:
% 34.34/9.55 | (383) tl(all_0_5_5) = all_177_0_59 & ssItem(all_148_0_47) = all_177_1_60 & ( ~ (all_177_1_60 = 0) | all_177_0_59 = all_148_1_48)
% 34.34/9.55 |
% 34.34/9.55 | Applying alpha-rule on (383) yields:
% 34.34/9.55 | (384) tl(all_0_5_5) = all_177_0_59
% 34.34/9.55 | (385) ssItem(all_148_0_47) = all_177_1_60
% 34.34/9.55 | (386) ~ (all_177_1_60 = 0) | all_177_0_59 = all_148_1_48
% 34.34/9.55 |
% 34.34/9.55 | Instantiating (351) with all_179_0_61, all_179_1_62 yields:
% 34.34/9.55 | (387) hd(all_0_5_5) = all_179_0_61 & ssList(all_0_5_5) = all_179_1_62 & ( ~ (all_179_1_62 = 0) | ! [v0] : (v0 = all_0_5_5 | v0 = nil | all_0_5_5 = nil | ~ (tl(v0) = nil) | ? [v1] : ? [v2] : (hd(v0) = v2 & ssList(v0) = v1 & ( ~ (v2 = all_179_0_61) | ~ (v1 = 0)))))
% 34.34/9.55 |
% 34.34/9.55 | Applying alpha-rule on (387) yields:
% 34.34/9.55 | (388) hd(all_0_5_5) = all_179_0_61
% 34.34/9.55 | (389) ssList(all_0_5_5) = all_179_1_62
% 34.34/9.55 | (390) ~ (all_179_1_62 = 0) | ! [v0] : (v0 = all_0_5_5 | v0 = nil | all_0_5_5 = nil | ~ (tl(v0) = nil) | ? [v1] : ? [v2] : (hd(v0) = v2 & ssList(v0) = v1 & ( ~ (v2 = all_179_0_61) | ~ (v1 = 0))))
% 34.34/9.55 |
% 34.34/9.55 | Instantiating (350) with all_181_0_63, all_181_1_64 yields:
% 34.34/9.55 | (391) hd(all_0_4_4) = all_181_0_63 & ssList(all_0_4_4) = all_181_1_64 & ( ~ (all_181_1_64 = 0) | ! [v0] : (v0 = all_0_4_4 | v0 = nil | all_0_4_4 = nil | ~ (tl(v0) = all_22_1_14) | ? [v1] : ? [v2] : (hd(v0) = v2 & ssList(v0) = v1 & ( ~ (v2 = all_181_0_63) | ~ (v1 = 0)))))
% 34.34/9.55 |
% 34.34/9.55 | Applying alpha-rule on (391) yields:
% 34.34/9.55 | (392) hd(all_0_4_4) = all_181_0_63
% 34.34/9.55 | (393) ssList(all_0_4_4) = all_181_1_64
% 34.34/9.55 | (394) ~ (all_181_1_64 = 0) | ! [v0] : (v0 = all_0_4_4 | v0 = nil | all_0_4_4 = nil | ~ (tl(v0) = all_22_1_14) | ? [v1] : ? [v2] : (hd(v0) = v2 & ssList(v0) = v1 & ( ~ (v2 = all_181_0_63) | ~ (v1 = 0))))
% 34.34/9.55 |
% 34.34/9.55 +-Applying beta-rule and splitting (352), into two cases.
% 34.34/9.55 |-Branch one:
% 34.34/9.55 | (395) ~ (memberP(all_0_5_5, all_36_2_17) = all_65_0_39)
% 34.34/9.55 |
% 34.34/9.55 +-Applying beta-rule and splitting (362), into two cases.
% 34.34/9.55 |-Branch one:
% 34.34/9.55 | (337) all_0_5_5 = nil
% 34.34/9.55 |
% 34.34/9.55 | Equations (337) can reduce 335 to:
% 34.34/9.55 | (169) $false
% 34.34/9.55 |
% 34.34/9.55 |-The branch is then unsatisfiable
% 34.34/9.55 |-Branch two:
% 34.34/9.55 | (335) ~ (all_0_5_5 = nil)
% 34.34/9.55 | (399) ? [v0] : ? [v1] : (( ~ (v0 = 0) & ssList(all_0_5_5) = v0) | (hd(all_50_1_23) = v1 & ssList(all_8_2_9) = v0 & ( ~ (v0 = 0) | v1 = all_36_2_17)))
% 34.34/9.55 |
% 34.34/9.55 | Instantiating (399) with all_196_0_67, all_196_1_68 yields:
% 34.34/9.55 | (400) ( ~ (all_196_1_68 = 0) & ssList(all_0_5_5) = all_196_1_68) | (hd(all_50_1_23) = all_196_0_67 & ssList(all_8_2_9) = all_196_1_68 & ( ~ (all_196_1_68 = 0) | all_196_0_67 = all_36_2_17))
% 34.34/9.55 |
% 34.34/9.55 | Instantiating formula (107) with all_0_5_5, all_177_0_59, nil and discharging atoms tl(all_0_5_5) = all_177_0_59, tl(all_0_5_5) = nil, yields:
% 34.34/9.55 | (401) all_177_0_59 = nil
% 34.34/9.55 |
% 34.34/9.55 | Instantiating formula (4) with all_0_5_5, all_179_0_61, all_36_2_17 and discharging atoms hd(all_0_5_5) = all_179_0_61, hd(all_0_5_5) = all_36_2_17, yields:
% 34.34/9.55 | (402) all_179_0_61 = all_36_2_17
% 34.34/9.55 |
% 34.34/9.55 | Instantiating formula (4) with all_0_5_5, all_175_0_57, all_179_0_61 and discharging atoms hd(all_0_5_5) = all_179_0_61, hd(all_0_5_5) = all_175_0_57, yields:
% 34.34/9.55 | (403) all_179_0_61 = all_175_0_57
% 34.34/9.55 |
% 34.34/9.55 | Instantiating formula (130) with all_22_1_14, all_173_1_56, 0 and discharging atoms ssList(all_22_1_14) = all_173_1_56, ssList(all_22_1_14) = 0, yields:
% 34.34/9.55 | (404) all_173_1_56 = 0
% 34.34/9.55 |
% 34.34/9.55 | Instantiating formula (130) with all_8_2_9, all_167_1_50, 0 and discharging atoms ssList(all_8_2_9) = all_167_1_50, ssList(all_8_2_9) = 0, yields:
% 34.34/9.55 | (405) all_167_1_50 = 0
% 34.34/9.55 |
% 34.34/9.55 | Instantiating formula (130) with all_0_4_4, all_181_1_64, 0 and discharging atoms ssList(all_0_4_4) = all_181_1_64, ssList(all_0_4_4) = 0, yields:
% 34.34/9.55 | (406) all_181_1_64 = 0
% 34.34/9.55 |
% 34.34/9.55 | Instantiating formula (130) with all_0_4_4, all_171_0_53, all_181_1_64 and discharging atoms ssList(all_0_4_4) = all_181_1_64, ssList(all_0_4_4) = all_171_0_53, yields:
% 34.34/9.55 | (407) all_181_1_64 = all_171_0_53
% 34.34/9.55 |
% 34.34/9.55 | Instantiating formula (130) with all_0_5_5, all_179_1_62, 0 and discharging atoms ssList(all_0_5_5) = all_179_1_62, ssList(all_0_5_5) = 0, yields:
% 34.34/9.55 | (408) all_179_1_62 = 0
% 34.34/9.55 |
% 34.34/9.55 | Instantiating formula (79) with all_148_0_47, all_177_1_60, 0 and discharging atoms ssItem(all_148_0_47) = all_177_1_60, ssItem(all_148_0_47) = 0, yields:
% 34.34/9.55 | (409) all_177_1_60 = 0
% 34.34/9.55 |
% 34.34/9.55 | Instantiating formula (79) with all_148_0_47, all_175_1_58, all_177_1_60 and discharging atoms ssItem(all_148_0_47) = all_177_1_60, ssItem(all_148_0_47) = all_175_1_58, yields:
% 34.34/9.55 | (410) all_177_1_60 = all_175_1_58
% 34.34/9.55 |
% 34.34/9.55 | Instantiating formula (79) with all_36_2_17, all_169_1_52, 0 and discharging atoms ssItem(all_36_2_17) = all_169_1_52, ssItem(all_36_2_17) = 0, yields:
% 34.34/9.55 | (411) all_169_1_52 = 0
% 34.34/9.55 |
% 34.34/9.55 | Using (251) and (395) yields:
% 34.34/9.55 | (412) ~ (all_0_4_4 = all_0_5_5)
% 34.34/9.55 |
% 34.34/9.55 | Combining equations (406,407) yields a new equation:
% 34.34/9.55 | (413) all_171_0_53 = 0
% 34.34/9.55 |
% 34.34/9.55 | Combining equations (402,403) yields a new equation:
% 34.34/9.55 | (414) all_175_0_57 = all_36_2_17
% 34.34/9.55 |
% 34.34/9.55 | Combining equations (409,410) yields a new equation:
% 34.34/9.55 | (415) all_175_1_58 = 0
% 34.34/9.55 |
% 34.34/9.55 | Combining equations (415,410) yields a new equation:
% 34.34/9.55 | (409) all_177_1_60 = 0
% 34.34/9.55 |
% 34.34/9.55 | From (405) and (365) follows:
% 34.34/9.55 | (164) ssList(all_8_2_9) = 0
% 34.34/9.55 |
% 34.34/9.55 | From (413) and (373) follows:
% 34.34/9.55 | (108) ssList(all_0_4_4) = 0
% 34.34/9.55 |
% 34.34/9.55 | From (408) and (389) follows:
% 34.34/9.55 | (113) ssList(all_0_5_5) = 0
% 34.34/9.55 |
% 34.34/9.55 | From (415) and (381) follows:
% 34.34/9.55 | (344) ssItem(all_148_0_47) = 0
% 34.34/9.55 |
% 34.34/9.55 +-Applying beta-rule and splitting (386), into two cases.
% 34.34/9.55 |-Branch one:
% 34.34/9.55 | (421) ~ (all_177_1_60 = 0)
% 34.34/9.55 |
% 34.34/9.55 | Equations (409) can reduce 421 to:
% 34.34/9.55 | (169) $false
% 34.34/9.55 |
% 34.34/9.55 |-The branch is then unsatisfiable
% 34.34/9.55 |-Branch two:
% 34.34/9.55 | (409) all_177_1_60 = 0
% 34.34/9.55 | (424) all_177_0_59 = all_148_1_48
% 34.34/9.55 |
% 34.34/9.55 | Combining equations (424,401) yields a new equation:
% 34.34/9.55 | (425) all_148_1_48 = nil
% 34.34/9.55 |
% 34.34/9.55 | Simplifying 425 yields:
% 34.34/9.55 | (426) all_148_1_48 = nil
% 34.34/9.55 |
% 34.34/9.55 | From (426) and (343) follows:
% 34.34/9.55 | (427) cons(all_148_0_47, nil) = all_0_5_5
% 34.34/9.55 |
% 34.34/9.55 +-Applying beta-rule and splitting (354), into two cases.
% 34.34/9.55 |-Branch one:
% 34.34/9.55 | (428) ~ (cons(all_148_0_47, nil) = all_0_5_5)
% 34.34/9.55 |
% 34.34/9.55 | Using (427) and (428) yields:
% 34.34/9.55 | (187) $false
% 34.34/9.55 |
% 34.34/9.55 |-The branch is then unsatisfiable
% 34.34/9.55 |-Branch two:
% 34.34/9.55 | (427) cons(all_148_0_47, nil) = all_0_5_5
% 34.34/9.55 | (431) all_148_0_47 = all_36_2_17 | ? [v0] : (( ~ (v0 = 0) & ssItem(all_148_0_47) = v0) | ( ~ (v0 = 0) & ssItem(all_36_2_17) = v0))
% 34.34/9.55 |
% 34.34/9.55 +-Applying beta-rule and splitting (361), into two cases.
% 34.34/9.55 |-Branch one:
% 34.34/9.55 | (428) ~ (cons(all_148_0_47, nil) = all_0_5_5)
% 34.34/9.55 |
% 34.34/9.55 | Using (427) and (428) yields:
% 34.34/9.55 | (187) $false
% 34.34/9.55 |
% 34.34/9.55 |-The branch is then unsatisfiable
% 34.34/9.55 |-Branch two:
% 34.34/9.55 | (427) cons(all_148_0_47, nil) = all_0_5_5
% 34.34/9.55 | (435) ? [v0] : ? [v1] : (cons(all_148_0_47, all_8_2_9) = v1 & ssItem(all_148_0_47) = v0 & ( ~ (v0 = 0) | v1 = all_50_1_23))
% 34.34/9.55 |
% 34.34/9.55 | Instantiating (435) with all_221_0_69, all_221_1_70 yields:
% 34.34/9.55 | (436) cons(all_148_0_47, all_8_2_9) = all_221_0_69 & ssItem(all_148_0_47) = all_221_1_70 & ( ~ (all_221_1_70 = 0) | all_221_0_69 = all_50_1_23)
% 34.34/9.55 |
% 34.34/9.55 | Applying alpha-rule on (436) yields:
% 34.34/9.55 | (437) cons(all_148_0_47, all_8_2_9) = all_221_0_69
% 34.34/9.55 | (438) ssItem(all_148_0_47) = all_221_1_70
% 34.34/9.55 | (439) ~ (all_221_1_70 = 0) | all_221_0_69 = all_50_1_23
% 34.34/9.55 |
% 34.34/9.55 +-Applying beta-rule and splitting (382), into two cases.
% 34.34/9.55 |-Branch one:
% 34.34/9.55 | (440) ~ (all_175_1_58 = 0)
% 34.34/9.55 |
% 34.34/9.56 | Equations (415) can reduce 440 to:
% 34.34/9.56 | (169) $false
% 34.34/9.56 |
% 34.34/9.56 |-The branch is then unsatisfiable
% 34.34/9.56 |-Branch two:
% 34.34/9.56 | (415) all_175_1_58 = 0
% 34.34/9.56 | (443) all_175_0_57 = all_148_0_47
% 34.34/9.56 |
% 34.34/9.56 | Combining equations (414,443) yields a new equation:
% 34.34/9.56 | (444) all_148_0_47 = all_36_2_17
% 34.34/9.56 |
% 34.34/9.56 | From (444) and (437) follows:
% 34.34/9.56 | (445) cons(all_36_2_17, all_8_2_9) = all_221_0_69
% 34.34/9.56 |
% 34.34/9.56 | From (444) and (427) follows:
% 34.34/9.56 | (194) cons(all_36_2_17, nil) = all_0_5_5
% 34.34/9.56 |
% 34.34/9.56 | From (444) and (438) follows:
% 34.34/9.56 | (447) ssItem(all_36_2_17) = all_221_1_70
% 34.34/9.56 |
% 34.34/9.56 | From (444) and (344) follows:
% 34.34/9.56 | (195) ssItem(all_36_2_17) = 0
% 34.34/9.56 |
% 34.34/9.56 +-Applying beta-rule and splitting (357), into two cases.
% 34.34/9.56 |-Branch one:
% 34.34/9.56 | (428) ~ (cons(all_148_0_47, nil) = all_0_5_5)
% 34.34/9.56 |
% 34.34/9.56 | From (444) and (428) follows:
% 34.34/9.56 | (450) ~ (cons(all_36_2_17, nil) = all_0_5_5)
% 34.34/9.56 |
% 34.34/9.56 | Using (194) and (450) yields:
% 34.34/9.56 | (187) $false
% 34.34/9.56 |
% 34.34/9.56 |-The branch is then unsatisfiable
% 34.34/9.56 |-Branch two:
% 34.34/9.56 | (427) cons(all_148_0_47, nil) = all_0_5_5
% 34.34/9.56 | (453) ? [v0] : ? [v1] : (memberP(all_0_4_4, all_148_0_47) = v1 & ssItem(all_148_0_47) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 34.34/9.56 |
% 34.34/9.56 | Instantiating (453) with all_230_0_71, all_230_1_72 yields:
% 34.34/9.56 | (454) memberP(all_0_4_4, all_148_0_47) = all_230_0_71 & ssItem(all_148_0_47) = all_230_1_72 & ( ~ (all_230_0_71 = 0) | ~ (all_230_1_72 = 0))
% 34.34/9.56 |
% 34.73/9.56 | Applying alpha-rule on (454) yields:
% 34.73/9.56 | (455) memberP(all_0_4_4, all_148_0_47) = all_230_0_71
% 34.73/9.56 | (456) ssItem(all_148_0_47) = all_230_1_72
% 34.73/9.56 | (457) ~ (all_230_0_71 = 0) | ~ (all_230_1_72 = 0)
% 34.73/9.56 |
% 34.73/9.56 | From (444) and (455) follows:
% 34.73/9.56 | (458) memberP(all_0_4_4, all_36_2_17) = all_230_0_71
% 34.73/9.56 |
% 34.73/9.56 | From (444) and (456) follows:
% 34.73/9.56 | (459) ssItem(all_36_2_17) = all_230_1_72
% 34.73/9.56 |
% 34.73/9.56 +-Applying beta-rule and splitting (400), into two cases.
% 34.73/9.56 |-Branch one:
% 34.73/9.56 | (460) ~ (all_196_1_68 = 0) & ssList(all_0_5_5) = all_196_1_68
% 34.73/9.56 |
% 34.73/9.56 | Applying alpha-rule on (460) yields:
% 34.73/9.56 | (461) ~ (all_196_1_68 = 0)
% 34.73/9.56 | (462) ssList(all_0_5_5) = all_196_1_68
% 34.73/9.56 |
% 34.73/9.56 +-Applying beta-rule and splitting (153), into two cases.
% 34.73/9.56 |-Branch one:
% 34.73/9.56 | (463) all_0_4_4 = all_0_5_5
% 34.73/9.56 |
% 34.73/9.56 | Equations (463) can reduce 412 to:
% 34.73/9.56 | (169) $false
% 34.73/9.56 |
% 34.73/9.56 |-The branch is then unsatisfiable
% 34.73/9.56 |-Branch two:
% 34.73/9.56 | (412) ~ (all_0_4_4 = all_0_5_5)
% 34.73/9.56 | (466) ? [v0] : ? [v1] : (segmentP(all_0_5_5, all_0_4_4) = v1 & ssList(all_0_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 34.73/9.56 |
% 34.73/9.56 | Instantiating (466) with all_243_0_73, all_243_1_74 yields:
% 34.73/9.56 | (467) segmentP(all_0_5_5, all_0_4_4) = all_243_0_73 & ssList(all_0_5_5) = all_243_1_74 & ( ~ (all_243_0_73 = 0) | ~ (all_243_1_74 = 0))
% 34.73/9.56 |
% 34.73/9.56 | Applying alpha-rule on (467) yields:
% 34.73/9.56 | (468) segmentP(all_0_5_5, all_0_4_4) = all_243_0_73
% 34.73/9.56 | (469) ssList(all_0_5_5) = all_243_1_74
% 34.73/9.56 | (470) ~ (all_243_0_73 = 0) | ~ (all_243_1_74 = 0)
% 34.73/9.56 |
% 34.73/9.56 | Instantiating formula (130) with all_0_5_5, all_243_1_74, 0 and discharging atoms ssList(all_0_5_5) = all_243_1_74, ssList(all_0_5_5) = 0, yields:
% 34.73/9.56 | (471) all_243_1_74 = 0
% 34.73/9.56 |
% 34.73/9.56 | Instantiating formula (130) with all_0_5_5, all_196_1_68, all_243_1_74 and discharging atoms ssList(all_0_5_5) = all_243_1_74, ssList(all_0_5_5) = all_196_1_68, yields:
% 34.73/9.56 | (472) all_243_1_74 = all_196_1_68
% 34.73/9.56 |
% 34.73/9.56 | Combining equations (472,471) yields a new equation:
% 34.73/9.56 | (473) all_196_1_68 = 0
% 34.73/9.56 |
% 34.73/9.56 | Simplifying 473 yields:
% 34.73/9.56 | (474) all_196_1_68 = 0
% 34.73/9.56 |
% 34.73/9.56 | Equations (474) can reduce 461 to:
% 34.73/9.56 | (169) $false
% 34.73/9.56 |
% 34.73/9.56 |-The branch is then unsatisfiable
% 34.73/9.56 |-Branch two:
% 34.73/9.56 | (476) hd(all_50_1_23) = all_196_0_67 & ssList(all_8_2_9) = all_196_1_68 & ( ~ (all_196_1_68 = 0) | all_196_0_67 = all_36_2_17)
% 34.73/9.56 |
% 34.73/9.56 | Applying alpha-rule on (476) yields:
% 34.73/9.56 | (477) hd(all_50_1_23) = all_196_0_67
% 34.73/9.56 | (478) ssList(all_8_2_9) = all_196_1_68
% 34.73/9.56 | (479) ~ (all_196_1_68 = 0) | all_196_0_67 = all_36_2_17
% 34.73/9.56 |
% 34.73/9.56 +-Applying beta-rule and splitting (378), into two cases.
% 34.73/9.56 |-Branch one:
% 34.73/9.56 | (480) ~ (all_173_1_56 = 0)
% 34.73/9.56 |
% 34.73/9.56 | Equations (404) can reduce 480 to:
% 34.73/9.56 | (169) $false
% 34.73/9.56 |
% 34.73/9.56 |-The branch is then unsatisfiable
% 34.73/9.56 |-Branch two:
% 34.73/9.56 | (404) all_173_1_56 = 0
% 34.73/9.56 | (483) ( ~ (all_65_0_39 = 0) | all_173_0_55 = 0 | all_36_2_17 = all_22_0_13) & (all_65_0_39 = 0 | ( ~ (all_173_0_55 = 0) & ~ (all_36_2_17 = all_22_0_13)))
% 34.73/9.56 |
% 34.73/9.56 | Applying alpha-rule on (483) yields:
% 34.73/9.56 | (484) ~ (all_65_0_39 = 0) | all_173_0_55 = 0 | all_36_2_17 = all_22_0_13
% 34.73/9.56 | (485) all_65_0_39 = 0 | ( ~ (all_173_0_55 = 0) & ~ (all_36_2_17 = all_22_0_13))
% 34.73/9.56 |
% 34.73/9.56 +-Applying beta-rule and splitting (370), into two cases.
% 34.73/9.56 |-Branch one:
% 34.73/9.56 | (486) ~ (all_169_1_52 = 0)
% 34.73/9.56 |
% 34.73/9.56 | Equations (411) can reduce 486 to:
% 34.73/9.56 | (169) $false
% 34.73/9.56 |
% 34.73/9.56 |-The branch is then unsatisfiable
% 34.73/9.56 |-Branch two:
% 34.73/9.56 | (411) all_169_1_52 = 0
% 34.73/9.56 | (489) all_169_0_51 = all_50_1_23
% 34.73/9.56 |
% 34.73/9.56 | From (489) and (368) follows:
% 34.73/9.56 | (490) cons(all_36_2_17, all_8_2_9) = all_50_1_23
% 34.73/9.56 |
% 34.73/9.56 +-Applying beta-rule and splitting (485), into two cases.
% 34.73/9.56 |-Branch one:
% 34.73/9.56 | (491) all_65_0_39 = 0
% 34.73/9.56 |
% 34.73/9.56 | Equations (491) can reduce 308 to:
% 34.73/9.56 | (169) $false
% 34.73/9.56 |
% 34.73/9.56 |-The branch is then unsatisfiable
% 34.73/9.56 |-Branch two:
% 34.73/9.56 | (308) ~ (all_65_0_39 = 0)
% 34.73/9.56 | (494) ~ (all_173_0_55 = 0) & ~ (all_36_2_17 = all_22_0_13)
% 34.73/9.56 |
% 34.73/9.56 | Instantiating formula (94) with all_0_4_4, all_36_2_17, all_230_0_71, all_65_0_39 and discharging atoms memberP(all_0_4_4, all_36_2_17) = all_230_0_71, memberP(all_0_4_4, all_36_2_17) = all_65_0_39, yields:
% 34.73/9.56 | (495) all_230_0_71 = all_65_0_39
% 34.73/9.56 |
% 34.73/9.56 | Instantiating formula (130) with all_8_2_9, all_196_1_68, 0 and discharging atoms ssList(all_8_2_9) = all_196_1_68, ssList(all_8_2_9) = 0, yields:
% 34.73/9.56 | (474) all_196_1_68 = 0
% 34.73/9.56 |
% 34.73/9.56 | Instantiating formula (147) with all_36_2_17, all_8_2_9, all_50_1_23, all_221_0_69 and discharging atoms cons(all_36_2_17, all_8_2_9) = all_221_0_69, cons(all_36_2_17, all_8_2_9) = all_50_1_23, yields:
% 34.73/9.56 | (497) all_221_0_69 = all_50_1_23
% 34.73/9.56 |
% 34.73/9.56 | Instantiating formula (79) with all_36_2_17, all_230_1_72, 0 and discharging atoms ssItem(all_36_2_17) = all_230_1_72, ssItem(all_36_2_17) = 0, yields:
% 34.73/9.56 | (498) all_230_1_72 = 0
% 34.73/9.56 |
% 34.73/9.56 | Instantiating formula (79) with all_36_2_17, all_221_1_70, all_230_1_72 and discharging atoms ssItem(all_36_2_17) = all_230_1_72, ssItem(all_36_2_17) = all_221_1_70, yields:
% 34.73/9.56 | (499) all_230_1_72 = all_221_1_70
% 34.73/9.56 |
% 34.73/9.56 | Combining equations (499,498) yields a new equation:
% 34.73/9.56 | (500) all_221_1_70 = 0
% 34.73/9.56 |
% 34.73/9.56 | Simplifying 500 yields:
% 34.73/9.56 | (501) all_221_1_70 = 0
% 34.73/9.56 |
% 34.73/9.56 | From (495) and (458) follows:
% 34.73/9.56 | (251) memberP(all_0_4_4, all_36_2_17) = all_65_0_39
% 34.73/9.56 |
% 34.73/9.56 | From (474) and (478) follows:
% 34.73/9.56 | (164) ssList(all_8_2_9) = 0
% 34.73/9.56 |
% 34.73/9.56 | From (497) and (445) follows:
% 34.73/9.56 | (490) cons(all_36_2_17, all_8_2_9) = all_50_1_23
% 34.73/9.56 |
% 34.73/9.56 | From (501) and (447) follows:
% 34.73/9.56 | (195) ssItem(all_36_2_17) = 0
% 34.73/9.56 |
% 34.73/9.56 | Instantiating formula (119) with all_50_1_23, all_8_2_9, all_8_5_12, all_65_0_39, all_36_2_17, all_0_4_4 and discharging atoms memberP(all_0_4_4, all_36_2_17) = all_65_0_39, ssList(all_8_5_12) = 0, ssList(all_0_4_4) = 0, cons(all_36_2_17, all_8_2_9) = all_50_1_23, app(all_8_5_12, all_50_1_23) = all_0_4_4, yields:
% 34.73/9.56 | (506) all_65_0_39 = 0 | ? [v0] : (( ~ (v0 = 0) & ssList(all_8_2_9) = v0) | ( ~ (v0 = 0) & ssItem(all_36_2_17) = v0))
% 34.73/9.56 |
% 34.73/9.56 | Instantiating formula (66) with all_50_1_23, all_36_2_17, all_8_2_9 and discharging atoms ssList(all_8_2_9) = 0, cons(all_36_2_17, all_8_2_9) = all_50_1_23, yields:
% 34.73/9.56 | (507) ? [v0] : ? [v1] : (tl(all_50_1_23) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v0 = 0) | v1 = all_8_2_9))
% 34.73/9.56 |
% 34.73/9.56 | Instantiating (507) with all_480_0_85, all_480_1_86 yields:
% 34.73/9.56 | (508) tl(all_50_1_23) = all_480_0_85 & ssItem(all_36_2_17) = all_480_1_86 & ( ~ (all_480_1_86 = 0) | all_480_0_85 = all_8_2_9)
% 34.73/9.56 |
% 34.73/9.56 | Applying alpha-rule on (508) yields:
% 34.73/9.56 | (509) tl(all_50_1_23) = all_480_0_85
% 34.73/9.56 | (510) ssItem(all_36_2_17) = all_480_1_86
% 34.73/9.56 | (511) ~ (all_480_1_86 = 0) | all_480_0_85 = all_8_2_9
% 34.73/9.56 |
% 34.73/9.56 +-Applying beta-rule and splitting (506), into two cases.
% 34.73/9.56 |-Branch one:
% 34.73/9.57 | (491) all_65_0_39 = 0
% 34.73/9.57 |
% 34.73/9.57 | Equations (491) can reduce 308 to:
% 34.73/9.57 | (169) $false
% 34.73/9.57 |
% 34.73/9.57 |-The branch is then unsatisfiable
% 34.73/9.57 |-Branch two:
% 34.73/9.57 | (308) ~ (all_65_0_39 = 0)
% 34.73/9.57 | (515) ? [v0] : (( ~ (v0 = 0) & ssList(all_8_2_9) = v0) | ( ~ (v0 = 0) & ssItem(all_36_2_17) = v0))
% 34.73/9.57 |
% 34.73/9.57 | Instantiating (515) with all_506_0_103 yields:
% 34.73/9.57 | (516) ( ~ (all_506_0_103 = 0) & ssList(all_8_2_9) = all_506_0_103) | ( ~ (all_506_0_103 = 0) & ssItem(all_36_2_17) = all_506_0_103)
% 34.73/9.57 |
% 34.73/9.57 +-Applying beta-rule and splitting (516), into two cases.
% 34.73/9.57 |-Branch one:
% 34.73/9.57 | (517) ~ (all_506_0_103 = 0) & ssList(all_8_2_9) = all_506_0_103
% 34.73/9.57 |
% 34.73/9.57 | Applying alpha-rule on (517) yields:
% 34.73/9.57 | (518) ~ (all_506_0_103 = 0)
% 34.73/9.57 | (519) ssList(all_8_2_9) = all_506_0_103
% 34.73/9.57 |
% 34.73/9.57 | Instantiating formula (130) with all_8_2_9, all_506_0_103, 0 and discharging atoms ssList(all_8_2_9) = all_506_0_103, ssList(all_8_2_9) = 0, yields:
% 34.73/9.57 | (520) all_506_0_103 = 0
% 34.73/9.57 |
% 34.73/9.57 | Equations (520) can reduce 518 to:
% 34.73/9.57 | (169) $false
% 34.73/9.57 |
% 34.73/9.57 |-The branch is then unsatisfiable
% 34.73/9.57 |-Branch two:
% 34.73/9.57 | (522) ~ (all_506_0_103 = 0) & ssItem(all_36_2_17) = all_506_0_103
% 34.73/9.57 |
% 34.73/9.57 | Applying alpha-rule on (522) yields:
% 34.73/9.57 | (518) ~ (all_506_0_103 = 0)
% 34.73/9.57 | (524) ssItem(all_36_2_17) = all_506_0_103
% 34.73/9.57 |
% 34.73/9.57 | Instantiating formula (79) with all_36_2_17, all_506_0_103, 0 and discharging atoms ssItem(all_36_2_17) = all_506_0_103, ssItem(all_36_2_17) = 0, yields:
% 34.73/9.57 | (520) all_506_0_103 = 0
% 34.73/9.57 |
% 34.73/9.57 | Instantiating formula (79) with all_36_2_17, all_480_1_86, all_506_0_103 and discharging atoms ssItem(all_36_2_17) = all_506_0_103, ssItem(all_36_2_17) = all_480_1_86, yields:
% 34.73/9.57 | (526) all_506_0_103 = all_480_1_86
% 34.73/9.57 |
% 34.73/9.57 | Combining equations (520,526) yields a new equation:
% 34.73/9.57 | (527) all_480_1_86 = 0
% 34.73/9.57 |
% 34.73/9.57 | Combining equations (527,526) yields a new equation:
% 34.73/9.57 | (520) all_506_0_103 = 0
% 34.73/9.57 |
% 34.73/9.57 | Equations (520) can reduce 518 to:
% 34.73/9.57 | (169) $false
% 34.73/9.57 |
% 34.73/9.57 |-The branch is then unsatisfiable
% 34.73/9.57 |-Branch two:
% 34.73/9.57 | (530) memberP(all_0_5_5, all_36_2_17) = all_65_0_39
% 34.73/9.57 | (531) ? [v0] : ? [v1] : (memberP(nil, all_36_2_17) = v1 & ssList(nil) = v0 & ( ~ (v0 = 0) | all_65_0_39 = 0))
% 34.73/9.57 |
% 34.73/9.57 | Instantiating (531) with all_187_0_108, all_187_1_109 yields:
% 34.73/9.57 | (532) memberP(nil, all_36_2_17) = all_187_0_108 & ssList(nil) = all_187_1_109 & ( ~ (all_187_1_109 = 0) | all_65_0_39 = 0)
% 34.73/9.57 |
% 34.73/9.57 | Applying alpha-rule on (532) yields:
% 34.73/9.57 | (533) memberP(nil, all_36_2_17) = all_187_0_108
% 34.73/9.57 | (534) ssList(nil) = all_187_1_109
% 34.73/9.57 | (535) ~ (all_187_1_109 = 0) | all_65_0_39 = 0
% 34.73/9.57 |
% 34.73/9.57 +-Applying beta-rule and splitting (535), into two cases.
% 34.73/9.57 |-Branch one:
% 34.73/9.57 | (536) ~ (all_187_1_109 = 0)
% 34.73/9.57 |
% 34.73/9.57 | Instantiating formula (130) with nil, all_187_1_109, 0 and discharging atoms ssList(nil) = all_187_1_109, ssList(nil) = 0, yields:
% 34.73/9.57 | (537) all_187_1_109 = 0
% 34.73/9.57 |
% 34.73/9.57 | Equations (537) can reduce 536 to:
% 34.73/9.57 | (169) $false
% 34.73/9.57 |
% 34.73/9.57 |-The branch is then unsatisfiable
% 34.73/9.57 |-Branch two:
% 34.73/9.57 | (537) all_187_1_109 = 0
% 34.73/9.57 | (491) all_65_0_39 = 0
% 34.73/9.57 |
% 34.73/9.57 | Equations (491) can reduce 308 to:
% 34.73/9.57 | (169) $false
% 34.73/9.57 |
% 34.73/9.57 |-The branch is then unsatisfiable
% 34.73/9.57 |-Branch two:
% 34.73/9.57 | (491) all_65_0_39 = 0
% 34.73/9.57 | (543) ~ (all_65_1_40 = 0)
% 34.73/9.57 |
% 34.73/9.57 | Equations (300) can reduce 543 to:
% 34.73/9.57 | (169) $false
% 34.73/9.57 |
% 34.73/9.57 |-The branch is then unsatisfiable
% 34.73/9.57 |-Branch two:
% 34.73/9.57 | (545) cons(all_36_2_17, nil) = nil
% 34.73/9.57 | (546) ? [v0] : ( ~ (v0 = 0) & ssItem(all_36_2_17) = v0)
% 34.73/9.57 |
% 34.73/9.57 | Instantiating (546) with all_85_0_116 yields:
% 34.73/9.57 | (547) ~ (all_85_0_116 = 0) & ssItem(all_36_2_17) = all_85_0_116
% 34.73/9.57 |
% 34.73/9.57 | Applying alpha-rule on (547) yields:
% 34.73/9.57 | (548) ~ (all_85_0_116 = 0)
% 34.73/9.57 | (549) ssItem(all_36_2_17) = all_85_0_116
% 34.73/9.57 |
% 34.73/9.57 +-Applying beta-rule and splitting (197), into two cases.
% 34.73/9.57 |-Branch one:
% 34.73/9.57 | (307) ~ (cons(all_36_2_17, nil) = nil)
% 34.73/9.57 |
% 34.73/9.57 | Using (545) and (307) yields:
% 34.73/9.57 | (187) $false
% 34.73/9.57 |
% 34.73/9.57 |-The branch is then unsatisfiable
% 34.73/9.57 |-Branch two:
% 34.73/9.57 | (545) cons(all_36_2_17, nil) = nil
% 34.73/9.57 | (553) ? [v0] : ? [v1] : (hd(nil) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v0 = 0) | v1 = all_36_2_17))
% 34.73/9.57 |
% 34.73/9.57 | Instantiating (553) with all_94_0_117, all_94_1_118 yields:
% 34.73/9.57 | (554) hd(nil) = all_94_0_117 & ssItem(all_36_2_17) = all_94_1_118 & ( ~ (all_94_1_118 = 0) | all_94_0_117 = all_36_2_17)
% 34.73/9.57 |
% 34.73/9.57 | Applying alpha-rule on (554) yields:
% 34.73/9.57 | (555) hd(nil) = all_94_0_117
% 34.73/9.57 | (556) ssItem(all_36_2_17) = all_94_1_118
% 34.73/9.57 | (557) ~ (all_94_1_118 = 0) | all_94_0_117 = all_36_2_17
% 34.73/9.57 |
% 34.73/9.57 +-Applying beta-rule and splitting (196), into two cases.
% 34.73/9.57 |-Branch one:
% 34.73/9.57 | (307) ~ (cons(all_36_2_17, nil) = nil)
% 34.73/9.57 |
% 34.73/9.57 | Using (545) and (307) yields:
% 34.73/9.57 | (187) $false
% 34.73/9.57 |
% 34.73/9.57 |-The branch is then unsatisfiable
% 34.73/9.57 |-Branch two:
% 34.73/9.57 | (545) cons(all_36_2_17, nil) = nil
% 34.73/9.57 | (561) ? [v0] : ? [v1] : (tl(nil) = v1 & ssItem(all_36_2_17) = v0 & ( ~ (v0 = 0) | v1 = nil))
% 34.73/9.57 |
% 34.73/9.57 | Instantiating (561) with all_103_0_119, all_103_1_120 yields:
% 34.73/9.57 | (562) tl(nil) = all_103_0_119 & ssItem(all_36_2_17) = all_103_1_120 & ( ~ (all_103_1_120 = 0) | all_103_0_119 = nil)
% 34.73/9.57 |
% 34.73/9.57 | Applying alpha-rule on (562) yields:
% 34.73/9.57 | (563) tl(nil) = all_103_0_119
% 34.73/9.57 | (564) ssItem(all_36_2_17) = all_103_1_120
% 34.73/9.57 | (565) ~ (all_103_1_120 = 0) | all_103_0_119 = nil
% 34.73/9.57 |
% 34.73/9.57 | Instantiating formula (79) with all_36_2_17, all_94_1_118, 0 and discharging atoms ssItem(all_36_2_17) = all_94_1_118, ssItem(all_36_2_17) = 0, yields:
% 34.73/9.57 | (566) all_94_1_118 = 0
% 34.73/9.57 |
% 34.73/9.57 | Instantiating formula (79) with all_36_2_17, all_94_1_118, all_103_1_120 and discharging atoms ssItem(all_36_2_17) = all_103_1_120, ssItem(all_36_2_17) = all_94_1_118, yields:
% 34.73/9.57 | (567) all_103_1_120 = all_94_1_118
% 34.73/9.57 |
% 34.73/9.57 | Instantiating formula (79) with all_36_2_17, all_85_0_116, all_103_1_120 and discharging atoms ssItem(all_36_2_17) = all_103_1_120, ssItem(all_36_2_17) = all_85_0_116, yields:
% 34.73/9.57 | (568) all_103_1_120 = all_85_0_116
% 34.73/9.57 |
% 34.73/9.57 | Combining equations (567,568) yields a new equation:
% 34.73/9.57 | (569) all_94_1_118 = all_85_0_116
% 34.73/9.57 |
% 34.73/9.57 | Simplifying 569 yields:
% 34.73/9.57 | (570) all_94_1_118 = all_85_0_116
% 34.73/9.57 |
% 34.73/9.57 | Combining equations (566,570) yields a new equation:
% 34.73/9.57 | (571) all_85_0_116 = 0
% 34.73/9.57 |
% 34.73/9.57 | Equations (571) can reduce 548 to:
% 34.73/9.57 | (169) $false
% 34.73/9.57 |
% 34.73/9.57 |-The branch is then unsatisfiable
% 34.73/9.57 |-Branch two:
% 34.73/9.57 | (573) ~ (all_36_2_17 = 0) & ssList(all_0_5_5) = all_36_2_17
% 34.73/9.57 |
% 34.73/9.57 | Applying alpha-rule on (573) yields:
% 34.73/9.57 | (574) ~ (all_36_2_17 = 0)
% 34.73/9.57 | (575) ssList(all_0_5_5) = all_36_2_17
% 34.73/9.57 |
% 34.73/9.57 | Instantiating formula (130) with all_0_5_5, all_36_2_17, 0 and discharging atoms ssList(all_0_5_5) = all_36_2_17, ssList(all_0_5_5) = 0, yields:
% 34.73/9.58 | (576) all_36_2_17 = 0
% 34.73/9.58 |
% 34.73/9.58 | Equations (576) can reduce 574 to:
% 34.73/9.58 | (169) $false
% 34.73/9.58 |
% 34.73/9.58 |-The branch is then unsatisfiable
% 34.73/9.58 |-Branch two:
% 34.73/9.58 | (181) ~ (all_0_2_2 = 0)
% 34.73/9.58 | (579) ? [v0] : ( ~ (v0 = 0) & ssList(nil) = v0)
% 34.73/9.58 |
% 34.73/9.58 | Instantiating (579) with all_28_0_123 yields:
% 34.73/9.58 | (580) ~ (all_28_0_123 = 0) & ssList(nil) = all_28_0_123
% 34.73/9.58 |
% 34.73/9.58 | Applying alpha-rule on (580) yields:
% 34.73/9.58 | (581) ~ (all_28_0_123 = 0)
% 34.73/9.58 | (582) ssList(nil) = all_28_0_123
% 34.73/9.58 |
% 34.73/9.58 | Instantiating formula (130) with nil, all_28_0_123, 0 and discharging atoms ssList(nil) = all_28_0_123, ssList(nil) = 0, yields:
% 34.73/9.58 | (583) all_28_0_123 = 0
% 34.73/9.58 |
% 34.73/9.58 | Equations (583) can reduce 581 to:
% 34.73/9.58 | (169) $false
% 34.73/9.58 |
% 34.73/9.58 |-The branch is then unsatisfiable
% 34.73/9.58 |-Branch two:
% 34.73/9.58 | (585) ~ (all_8_5_12 = 0) & ssList(all_0_5_5) = all_8_5_12
% 34.73/9.58 |
% 34.73/9.58 | Applying alpha-rule on (585) yields:
% 34.73/9.58 | (586) ~ (all_8_5_12 = 0)
% 34.73/9.58 | (587) ssList(all_0_5_5) = all_8_5_12
% 34.73/9.58 |
% 34.73/9.58 | Instantiating formula (130) with all_0_5_5, all_8_5_12, 0 and discharging atoms ssList(all_0_5_5) = all_8_5_12, ssList(all_0_5_5) = 0, yields:
% 34.73/9.58 | (588) all_8_5_12 = 0
% 34.73/9.58 |
% 34.73/9.58 | Equations (588) can reduce 586 to:
% 34.73/9.58 | (169) $false
% 34.73/9.58 |
% 34.73/9.58 |-The branch is then unsatisfiable
% 34.73/9.58 |-Branch two:
% 34.73/9.58 | (168) all_0_4_4 = nil
% 34.73/9.58 | (335) ~ (all_0_5_5 = nil)
% 34.73/9.58 |
% 34.73/9.58 | From (168) and (145) follows:
% 34.73/9.58 | (592) segmentP(nil, all_0_5_5) = 0
% 34.73/9.58 |
% 34.73/9.58 +-Applying beta-rule and splitting (151), into two cases.
% 34.73/9.58 |-Branch one:
% 34.73/9.58 | (593) ~ (segmentP(nil, all_0_5_5) = 0)
% 34.73/9.58 |
% 34.73/9.58 | Using (592) and (593) yields:
% 34.73/9.58 | (187) $false
% 34.73/9.58 |
% 34.73/9.58 |-The branch is then unsatisfiable
% 34.73/9.58 |-Branch two:
% 34.73/9.58 | (592) segmentP(nil, all_0_5_5) = 0
% 34.73/9.58 | (596) all_0_5_5 = nil | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_5_5) = v0)
% 34.73/9.58 |
% 34.73/9.58 +-Applying beta-rule and splitting (153), into two cases.
% 34.73/9.58 |-Branch one:
% 34.73/9.58 | (463) all_0_4_4 = all_0_5_5
% 34.73/9.58 |
% 34.73/9.58 | Combining equations (463,168) yields a new equation:
% 34.73/9.58 | (598) all_0_5_5 = nil
% 34.73/9.58 |
% 34.73/9.58 | Simplifying 598 yields:
% 34.73/9.58 | (337) all_0_5_5 = nil
% 34.73/9.58 |
% 34.73/9.58 | Equations (337) can reduce 335 to:
% 34.73/9.58 | (169) $false
% 34.73/9.58 |
% 34.73/9.58 |-The branch is then unsatisfiable
% 34.73/9.58 |-Branch two:
% 34.73/9.58 | (412) ~ (all_0_4_4 = all_0_5_5)
% 34.73/9.58 | (466) ? [v0] : ? [v1] : (segmentP(all_0_5_5, all_0_4_4) = v1 & ssList(all_0_5_5) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 34.73/9.58 |
% 34.73/9.58 | Instantiating (466) with all_26_0_135, all_26_1_136 yields:
% 34.73/9.58 | (603) segmentP(all_0_5_5, all_0_4_4) = all_26_0_135 & ssList(all_0_5_5) = all_26_1_136 & ( ~ (all_26_0_135 = 0) | ~ (all_26_1_136 = 0))
% 34.73/9.58 |
% 34.73/9.58 | Applying alpha-rule on (603) yields:
% 34.73/9.58 | (604) segmentP(all_0_5_5, all_0_4_4) = all_26_0_135
% 34.73/9.58 | (605) ssList(all_0_5_5) = all_26_1_136
% 34.73/9.58 | (606) ~ (all_26_0_135 = 0) | ~ (all_26_1_136 = 0)
% 34.73/9.58 |
% 34.73/9.58 | Equations (168) can reduce 412 to:
% 34.73/9.58 | (607) ~ (all_0_5_5 = nil)
% 34.73/9.58 |
% 34.73/9.58 | Simplifying 607 yields:
% 34.73/9.58 | (335) ~ (all_0_5_5 = nil)
% 34.73/9.58 |
% 34.73/9.58 +-Applying beta-rule and splitting (156), into two cases.
% 34.73/9.58 |-Branch one:
% 34.73/9.58 | (337) all_0_5_5 = nil
% 34.73/9.58 |
% 34.73/9.58 | Equations (337) can reduce 335 to:
% 34.73/9.58 | (169) $false
% 34.73/9.58 |
% 34.73/9.58 |-The branch is then unsatisfiable
% 34.73/9.58 |-Branch two:
% 34.73/9.58 | (335) ~ (all_0_5_5 = nil)
% 34.73/9.58 | (340) ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_5_5 & ssItem(v1) = 0)
% 34.73/9.58 |
% 34.73/9.58 +-Applying beta-rule and splitting (596), into two cases.
% 34.73/9.58 |-Branch one:
% 34.73/9.58 | (337) all_0_5_5 = nil
% 34.73/9.58 |
% 34.73/9.58 | Equations (337) can reduce 335 to:
% 34.73/9.58 | (169) $false
% 34.73/9.58 |
% 34.73/9.58 |-The branch is then unsatisfiable
% 34.73/9.58 |-Branch two:
% 34.73/9.58 | (335) ~ (all_0_5_5 = nil)
% 34.73/9.58 | (616) ? [v0] : ( ~ (v0 = 0) & ssList(all_0_5_5) = v0)
% 34.73/9.58 |
% 34.73/9.58 | Instantiating (616) with all_40_0_139 yields:
% 34.73/9.58 | (617) ~ (all_40_0_139 = 0) & ssList(all_0_5_5) = all_40_0_139
% 34.73/9.58 |
% 34.73/9.58 | Applying alpha-rule on (617) yields:
% 34.73/9.58 | (618) ~ (all_40_0_139 = 0)
% 34.73/9.58 | (619) ssList(all_0_5_5) = all_40_0_139
% 34.73/9.58 |
% 34.73/9.58 | Instantiating formula (130) with all_0_5_5, all_40_0_139, 0 and discharging atoms ssList(all_0_5_5) = all_40_0_139, ssList(all_0_5_5) = 0, yields:
% 34.73/9.58 | (620) all_40_0_139 = 0
% 34.73/9.58 |
% 34.73/9.58 | Instantiating formula (130) with all_0_5_5, all_26_1_136, all_40_0_139 and discharging atoms ssList(all_0_5_5) = all_40_0_139, ssList(all_0_5_5) = all_26_1_136, yields:
% 34.73/9.58 | (621) all_40_0_139 = all_26_1_136
% 34.73/9.58 |
% 34.73/9.58 | Combining equations (620,621) yields a new equation:
% 34.73/9.58 | (622) all_26_1_136 = 0
% 34.73/9.58 |
% 34.73/9.58 | Combining equations (622,621) yields a new equation:
% 34.73/9.58 | (620) all_40_0_139 = 0
% 34.73/9.58 |
% 34.73/9.58 | Equations (620) can reduce 618 to:
% 34.73/9.58 | (169) $false
% 34.73/9.58 |
% 34.73/9.58 |-The branch is then unsatisfiable
% 34.73/9.58 % SZS output end Proof for theBenchmark
% 34.73/9.58
% 34.73/9.58 8978ms
%------------------------------------------------------------------------------