TSTP Solution File: SWC057+1 by ePrincess---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : ePrincess---1.0
% Problem : SWC057+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : ePrincess-casc -timeout=%d %s
% Computer : n009.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 20:15:58 EDT 2022
% Result : Theorem 25.01s 7.37s
% Output : Proof 121.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC057+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : ePrincess-casc -timeout=%d %s
% 0.12/0.33 % Computer : n009.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 12 13:13:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.49/0.57 ____ _
% 0.49/0.57 ___ / __ \_____(_)___ ________ __________
% 0.49/0.57 / _ \/ /_/ / ___/ / __ \/ ___/ _ \/ ___/ ___/
% 0.49/0.57 / __/ ____/ / / / / / / /__/ __(__ |__ )
% 0.49/0.57 \___/_/ /_/ /_/_/ /_/\___/\___/____/____/
% 0.49/0.57
% 0.49/0.57 A Theorem Prover for First-Order Logic
% 0.49/0.57 (ePrincess v.1.0)
% 0.49/0.57
% 0.49/0.57 (c) Philipp Rümmer, 2009-2015
% 0.49/0.57 (c) Peter Backeman, 2014-2015
% 0.49/0.57 (contributions by Angelo Brillout, Peter Baumgartner)
% 0.49/0.57 Free software under GNU Lesser General Public License (LGPL).
% 0.49/0.57 Bug reports to peter@backeman.se
% 0.49/0.57
% 0.49/0.57 For more information, visit http://user.uu.se/~petba168/breu/
% 0.49/0.57
% 0.49/0.57 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.49/0.62 Prover 0: Options: -triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -resolutionMethod=nonUnifying +ignoreQuantifiers -generateTriggers=all
% 2.39/1.08 Prover 0: Preprocessing ...
% 4.73/1.67 Prover 0: Constructing countermodel ...
% 18.71/5.92 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -resolutionMethod=normal +ignoreQuantifiers -generateTriggers=all
% 19.72/6.07 Prover 1: Preprocessing ...
% 20.76/6.31 Prover 1: Constructing countermodel ...
% 25.01/7.37 Prover 1: proved (1452ms)
% 25.01/7.37 Prover 0: stopped
% 25.01/7.37
% 25.01/7.37 No countermodel exists, formula is valid
% 25.01/7.37 % SZS status Theorem for theBenchmark
% 25.01/7.37
% 25.01/7.37 Generating proof ... found it (size 488)
% 120.28/83.52
% 120.28/83.52 % SZS output start Proof for theBenchmark
% 120.28/83.52 Assumed formulas after preprocessing and simplification:
% 120.28/83.52 | (0) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ( ~ (v7 = v6) & ~ (v0 = 0) & equalelemsP(nil) = 0 & duplicatefreeP(nil) = 0 & strictorderedP(nil) = 0 & totalorderedP(nil) = 0 & strictorderP(nil) = 0 & totalorderP(nil) = 0 & cyclefreeP(nil) = 0 & frontsegP(v2, v1) = v5 & singletonP(nil) = v0 & ssList(v2) = 0 & ssList(v1) = 0 & ssList(nil) = 0 & neq(v2, nil) = v3 & neq(v1, nil) = v4 & ssItem(v7) = 0 & ssItem(v6) = 0 & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v11 = 0 | ~ (strictorderedP(v8) = 0) | ~ (lt(v9, v10) = v11) | ~ (ssList(v12) = 0) | ~ (cons(v10, v16) = v17) | ~ (cons(v9, v13) = v14) | ~ (app(v15, v17) = v8) | ~ (app(v12, v14) = v15) | ~ (ssItem(v9) = 0) | ? [v18] : (( ~ (v18 = 0) & ssList(v16) = v18) | ( ~ (v18 = 0) & ssList(v13) = v18) | ( ~ (v18 = 0) & ssList(v8) = v18) | ( ~ (v18 = 0) & ssItem(v10) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ! [v16] : ! [v17] : (v11 = 0 | ~ (totalorderedP(v8) = 0) | ~ (leq(v9, v10) = v11) | ~ (ssList(v12) = 0) | ~ (cons(v10, v16) = v17) | ~ (cons(v9, v13) = v14) | ~ (app(v15, v17) = v8) | ~ (app(v12, v14) = v15) | ~ (ssItem(v9) = 0) | ? [v18] : (( ~ (v18 = 0) & ssList(v16) = v18) | ( ~ (v18 = 0) & ssList(v13) = v18) | ( ~ (v18 = 0) & ssList(v8) = v18) | ( ~ (v18 = 0) & ssItem(v10) = v18))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ! [v15] : ( ~ (duplicatefreeP(v8) = 0) | ~ (ssList(v10) = 0) | ~ (cons(v9, v14) = v15) | ~ (cons(v9, v11) = v12) | ~ (app(v13, v15) = v8) | ~ (app(v10, v12) = v13) | ~ (ssItem(v9) = 0) | ? [v16] : (( ~ (v16 = 0) & ssList(v14) = v16) | ( ~ (v16 = 0) & ssList(v11) = v16) | ( ~ (v16 = 0) & ssList(v8) = v16))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v14 = 0 | ~ (segmentP(v13, v9) = v14) | ~ (segmentP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ~ (app(v11, v12) = v13) | ~ (app(v10, v8) = v11) | ? [v15] : (( ~ (v15 = 0) & ssList(v12) = v15) | ( ~ (v15 = 0) & ssList(v10) = v15) | ( ~ (v15 = 0) & ssList(v9) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : (v10 = v9 | ~ (equalelemsP(v8) = 0) | ~ (ssList(v11) = 0) | ~ (cons(v10, v12) = v13) | ~ (cons(v9, v13) = v14) | ~ (app(v11, v14) = v8) | ~ (ssItem(v10) = 0) | ~ (ssItem(v9) = 0) | ? [v15] : (( ~ (v15 = 0) & ssList(v12) = v15) | ( ~ (v15 = 0) & ssList(v8) = v15))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ! [v14] : ( ~ (frontsegP(v11, v13) = v14) | ~ (cons(v9, v12) = v13) | ~ (cons(v8, v10) = v11) | ~ (ssItem(v9) = 0) | ~ (ssItem(v8) = 0) | ? [v15] : ? [v16] : (( ~ (v15 = 0) & ssList(v10) = v15) | (frontsegP(v10, v12) = v16 & ssList(v12) = v15 & ( ~ (v15 = 0) | (( ~ (v16 = 0) | ~ (v9 = v8) | v14 = 0) & ( ~ (v14 = 0) | (v16 = 0 & v9 = v8))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = 0 | ~ (segmentP(v8, v9) = v10) | ~ (ssList(v8) = 0) | ~ (app(v12, v13) = v8) | ~ (app(v11, v9) = v12) | ? [v14] : (( ~ (v14 = 0) & ssList(v13) = v14) | ( ~ (v14 = 0) & ssList(v11) = v14) | ( ~ (v14 = 0) & ssList(v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : (v10 = 0 | ~ (memberP(v8, v9) = v10) | ~ (ssList(v11) = 0) | ~ (ssList(v8) = 0) | ~ (cons(v9, v12) = v13) | ~ (app(v11, v13) = v8) | ? [v14] : (( ~ (v14 = 0) & ssList(v12) = v14) | ( ~ (v14 = 0) & ssItem(v9) = v14))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (memberP(v12, v8) = v13) | ~ (memberP(v9, v8) = v10) | ~ (app(v9, v11) = v12) | ~ (ssItem(v8) = 0) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssList(v9) = v14) | (memberP(v11, v8) = v15 & ssList(v11) = v14 & ( ~ (v14 = 0) | (( ~ (v13 = 0) | v15 = 0 | v10 = 0) & (v13 = 0 | ( ~ (v15 = 0) & ~ (v10 = 0)))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ! [v13] : ( ~ (ssList(v8) = 0) | ~ (cons(v11, v9) = v12) | ~ (app(v12, v8) = v13) | ~ (app(v9, v8) = v10) | ? [v14] : ? [v15] : (( ~ (v14 = 0) & ssList(v9) = v14) | (cons(v11, v10) = v15 & ssItem(v11) = v14 & ( ~ (v14 = 0) | v15 = v13)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = v10 | ~ (ssList(v9) = 0) | ~ (ssList(v8) = 0) | ~ (cons(v12, v9) = v11) | ~ (cons(v10, v8) = v11) | ? [v13] : (( ~ (v13 = 0) & ssItem(v12) = v13) | ( ~ (v13 = 0) & ssItem(v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (rearsegP(v11, v9) = v12) | ~ (rearsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ~ (app(v10, v8) = v11) | ? [v13] : (( ~ (v13 = 0) & ssList(v10) = v13) | ( ~ (v13 = 0) & ssList(v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v12 = 0 | ~ (frontsegP(v11, v9) = v12) | ~ (frontsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ~ (app(v8, v10) = v11) | ? [v13] : (( ~ (v13 = 0) & ssList(v10) = v13) | ( ~ (v13 = 0) & ssList(v9) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : (v9 = v8 | ~ (ssList(v9) = 0) | ~ (ssList(v8) = 0) | ~ (cons(v12, v9) = v11) | ~ (cons(v10, v8) = v11) | ? [v13] : (( ~ (v13 = 0) & ssItem(v12) = v13) | ( ~ (v13 = 0) & ssItem(v10) = v13))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (memberP(v11, v8) = v12) | ~ (cons(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ~ (ssItem(v8) = 0) | ? [v13] : ? [v14] : (memberP(v10, v8) = v14 & ssList(v10) = v13 & ( ~ (v13 = 0) | (( ~ (v12 = 0) | v14 = 0 | v9 = v8) & (v12 = 0 | ( ~ (v14 = 0) & ~ (v9 = v8))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ! [v12] : ( ~ (ssList(v8) = 0) | ~ (app(v10, v11) = v12) | ~ (app(v8, v9) = v10) | ? [v13] : ? [v14] : ? [v15] : (( ~ (v13 = 0) & ssList(v9) = v13) | (ssList(v11) = v13 & app(v9, v11) = v14 & app(v8, v14) = v15 & ( ~ (v13 = 0) | v15 = v12)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | v8 = nil | ~ (tl(v8) = v10) | ~ (hd(v8) = v9) | ~ (cons(v9, v10) = v11) | ? [v12] : ( ~ (v12 = 0) & ssList(v8) = v12)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (ssList(v8) = 0) | ~ (app(v11, v9) = v10) | ~ (app(v8, v9) = v10) | ? [v12] : (( ~ (v12 = 0) & ssList(v11) = v12) | ( ~ (v12 = 0) & ssList(v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = v8 | ~ (ssList(v8) = 0) | ~ (app(v9, v11) = v10) | ~ (app(v9, v8) = v10) | ? [v12] : (( ~ (v12 = 0) & ssList(v11) = v12) | ( ~ (v12 = 0) & ssList(v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (gt(v8, v10) = v11) | ~ (gt(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssItem(v9) = v12) | (gt(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (geq(v8, v10) = v11) | ~ (geq(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssItem(v9) = v12) | (geq(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (lt(v8, v10) = v11) | ~ (lt(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssItem(v9) = v12) | (lt(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (lt(v8, v10) = v11) | ~ (leq(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssItem(v9) = v12) | (lt(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (leq(v8, v10) = v11) | ~ (leq(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssItem(v9) = v12) | (leq(v9, v10) = v13 & ssItem(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (segmentP(v8, v10) = v11) | ~ (segmentP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v9) = v12) | (segmentP(v9, v10) = v13 & ssList(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (rearsegP(v8, v10) = v11) | ~ (rearsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v9) = v12) | (rearsegP(v9, v10) = v13 & ssList(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v11 = 0 | ~ (frontsegP(v8, v10) = v11) | ~ (frontsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v9) = v12) | (frontsegP(v9, v10) = v13 & ssList(v10) = v12 & ( ~ (v13 = 0) | ~ (v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (rearsegP(v8, v9) = v10) | ~ (ssList(v8) = 0) | ~ (app(v11, v9) = v8) | ? [v12] : (( ~ (v12 = 0) & ssList(v11) = v12) | ( ~ (v12 = 0) & ssList(v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v10 = 0 | ~ (frontsegP(v8, v9) = v10) | ~ (ssList(v8) = 0) | ~ (app(v9, v11) = v8) | ? [v12] : (( ~ (v12 = 0) & ssList(v11) = v12) | ( ~ (v12 = 0) & ssList(v9) = v12))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (gt(v11, v10) = v9) | ~ (gt(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (geq(v11, v10) = v9) | ~ (geq(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (lt(v11, v10) = v9) | ~ (lt(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (leq(v11, v10) = v9) | ~ (leq(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (segmentP(v11, v10) = v9) | ~ (segmentP(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (rearsegP(v11, v10) = v9) | ~ (rearsegP(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (frontsegP(v11, v10) = v9) | ~ (frontsegP(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (memberP(v11, v10) = v9) | ~ (memberP(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (cons(v11, v10) = v9) | ~ (cons(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (app(v11, v10) = v9) | ~ (app(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v9 = v8 | ~ (neq(v11, v10) = v9) | ~ (neq(v11, v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = nil | ~ (tl(v8) = v9) | ~ (app(v9, v10) = v11) | ? [v12] : ? [v13] : ? [v14] : (( ~ (v12 = 0) & ssList(v8) = v12) | (tl(v13) = v14 & ssList(v10) = v12 & app(v8, v10) = v13 & ( ~ (v12 = 0) | v14 = v11)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v8 = nil | ~ (hd(v8) = v9) | ~ (app(v8, v10) = v11) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v8) = v12) | (hd(v11) = v13 & ssList(v10) = v12 & ( ~ (v12 = 0) | v13 = v9)))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (hd(v9) = v10) | ~ (lt(v8, v10) = v11) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (strictorderedP(v13) = v14 & strictorderedP(v9) = v15 & ssList(v9) = v12 & cons(v8, v9) = v13 & ( ~ (v12 = 0) | (( ~ (v14 = 0) | v9 = nil | (v15 = 0 & v11 = 0)) & (v14 = 0 | ( ~ (v9 = nil) & ( ~ (v15 = 0) | ~ (v11 = 0)))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (hd(v9) = v10) | ~ (leq(v8, v10) = v11) | ~ (ssItem(v8) = 0) | ? [v12] : ? [v13] : ? [v14] : ? [v15] : (totalorderedP(v13) = v14 & totalorderedP(v9) = v15 & ssList(v9) = v12 & cons(v8, v9) = v13 & ( ~ (v12 = 0) | (( ~ (v14 = 0) | v9 = nil | (v15 = 0 & v11 = 0)) & (v14 = 0 | ( ~ (v9 = nil) & ( ~ (v15 = 0) | ~ (v11 = 0)))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (strictorderP(v8) = 0) | ~ (lt(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v8) = v12) | (lt(v10, v9) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v13 = 0 | v11 = 0 | ~ (ssList(v14) = 0) | ~ (cons(v10, v18) = v19) | ~ (cons(v9, v15) = v16) | ~ (app(v17, v19) = v8) | ~ (app(v14, v16) = v17) | ? [v20] : (( ~ (v20 = 0) & ssList(v18) = v20) | ( ~ (v20 = 0) & ssList(v15) = v20))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (totalorderP(v8) = 0) | ~ (leq(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v8) = v12) | (leq(v10, v9) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : (v13 = 0 | v11 = 0 | ~ (ssList(v14) = 0) | ~ (cons(v10, v18) = v19) | ~ (cons(v9, v15) = v16) | ~ (app(v17, v19) = v8) | ~ (app(v14, v16) = v17) | ? [v20] : (( ~ (v20 = 0) & ssList(v18) = v20) | ( ~ (v20 = 0) & ssList(v15) = v20))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (cyclefreeP(v8) = 0) | ~ (leq(v9, v10) = v11) | ~ (ssItem(v9) = 0) | ? [v12] : ? [v13] : (( ~ (v12 = 0) & ssList(v8) = v12) | (leq(v10, v9) = v13 & ssItem(v10) = v12 & ( ~ (v12 = 0) | ! [v14] : ! [v15] : ! [v16] : ! [v17] : ! [v18] : ! [v19] : ( ~ (v13 = 0) | ~ (v11 = 0) | ~ (ssList(v14) = 0) | ~ (cons(v10, v18) = v19) | ~ (cons(v9, v15) = v16) | ~ (app(v17, v19) = v8) | ~ (app(v14, v16) = v17) | ? [v20] : (( ~ (v20 = 0) & ssList(v18) = v20) | ( ~ (v20 = 0) & ssList(v15) = v20))))))) & ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, nil) = v10) | ~ (app(v10, v8) = v11) | ? [v12] : ? [v13] : (cons(v9, v8) = v13 & ssItem(v9) = v12 & ( ~ (v12 = 0) | v13 = v11))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = v8 | ~ (lt(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (leq(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v12 = 0) | ~ (v11 = 0)))) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = v8 | ~ (ssList(v8) = 0) | ~ (neq(v8, v9) = v10) | ? [v11] : ( ~ (v11 = 0) & ssList(v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v10 = 0 | v9 = v8 | ~ (neq(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ( ~ (v11 = 0) & ssItem(v9) = v11)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (tl(v10) = v9) | ~ (tl(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (hd(v10) = v9) | ~ (hd(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (equalelemsP(v10) = v9) | ~ (equalelemsP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (duplicatefreeP(v10) = v9) | ~ (duplicatefreeP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (strictorderedP(v10) = v9) | ~ (strictorderedP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (totalorderedP(v10) = v9) | ~ (totalorderedP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (strictorderP(v10) = v9) | ~ (strictorderP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (totalorderP(v10) = v9) | ~ (totalorderP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (cyclefreeP(v10) = v9) | ~ (cyclefreeP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (singletonP(v10) = v9) | ~ (singletonP(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (ssList(v10) = v9) | ~ (ssList(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = v8 | ~ (ssItem(v10) = v9) | ~ (ssItem(v10) = v8)) & ! [v8] : ! [v9] : ! [v10] : (v9 = 0 | ~ (singletonP(v8) = v9) | ~ (cons(v10, nil) = v8) | ? [v11] : (( ~ (v11 = 0) & ssList(v8) = v11) | ( ~ (v11 = 0) & ssItem(v10) = v11))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (gt(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (lt(v9, v8) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | (( ~ (v12 = 0) | v10 = 0) & ( ~ (v10 = 0) | v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (geq(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (leq(v9, v8) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | (( ~ (v12 = 0) | v10 = 0) & ( ~ (v10 = 0) | v12 = 0))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (lt(v8, v9) = v10) | ~ (ssItem(v8) = 0) | ? [v11] : ? [v12] : (leq(v8, v9) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | (( ~ (v12 = 0) | v10 = 0 | v9 = v8) & ( ~ (v10 = 0) | (v12 = 0 & ~ (v9 = v8))))))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, v8) = v10) | ? [v11] : ? [v12] : (tl(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = v8))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, v8) = v10) | ? [v11] : ? [v12] : (hd(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = v9))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, v8) = v10) | ? [v11] : ? [v12] : (ssList(v10) = v12 & ssItem(v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v8] : ! [v9] : ! [v10] : ( ~ (ssList(v8) = 0) | ~ (app(v8, v9) = v10) | ? [v11] : ? [v12] : (ssList(v10) = v12 & ssList(v9) = v11 & ( ~ (v11 = 0) | v12 = 0))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (geq(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v10] : ? [v11] : (geq(v9, v8) = v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (leq(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v10] : ? [v11] : (leq(v9, v8) = v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (segmentP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : (segmentP(v9, v8) = v11 & ssList(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (rearsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : (rearsegP(v9, v8) = v11 & ssList(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (frontsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : (frontsegP(v9, v8) = v11 & ssList(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : (v9 = v8 | ~ (app(v8, nil) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = v8 | ~ (app(nil, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = nil | ~ (ssList(v8) = 0) | ~ (app(v8, v9) = nil) | ? [v10] : ( ~ (v10 = 0) & ssList(v9) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (geq(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssItem(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (equalelemsP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ((v20 = v8 & v17 = 0 & v15 = 0 & v13 = 0 & v11 = 0 & ~ (v12 = v10) & ssList(v16) = 0 & ssList(v14) = 0 & cons(v12, v16) = v18 & cons(v10, v18) = v19 & app(v14, v19) = v8 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (duplicatefreeP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ((v23 = v8 & v21 = 0 & v17 = 0 & v15 = 0 & v13 = 0 & v12 = v10 & v11 = 0 & ssList(v20) = 0 & ssList(v16) = 0 & ssList(v14) = 0 & cons(v10, v20) = v22 & cons(v10, v16) = v18 & app(v19, v22) = v8 & app(v14, v18) = v19 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (strictorderedP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v24 = v8 & v22 = 0 & v18 = 0 & v16 = 0 & v13 = 0 & v11 = 0 & ~ (v14 = 0) & lt(v10, v12) = v14 & ssList(v21) = 0 & ssList(v17) = 0 & ssList(v15) = 0 & cons(v12, v21) = v23 & cons(v10, v17) = v19 & app(v20, v23) = v8 & app(v15, v19) = v20 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (totalorderedP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ((v24 = v8 & v22 = 0 & v18 = 0 & v16 = 0 & v13 = 0 & v11 = 0 & ~ (v14 = 0) & leq(v10, v12) = v14 & ssList(v21) = 0 & ssList(v17) = 0 & ssList(v15) = 0 & cons(v12, v21) = v23 & cons(v10, v17) = v19 & app(v20, v23) = v8 & app(v15, v19) = v20 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (strictorderP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = v8 & v23 = 0 & v19 = 0 & v17 = 0 & v13 = 0 & v11 = 0 & ~ (v15 = 0) & ~ (v14 = 0) & lt(v12, v10) = v15 & lt(v10, v12) = v14 & ssList(v22) = 0 & ssList(v18) = 0 & ssList(v16) = 0 & cons(v12, v22) = v24 & cons(v10, v18) = v20 & app(v21, v24) = v8 & app(v16, v20) = v21 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (totalorderP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = v8 & v23 = 0 & v19 = 0 & v17 = 0 & v13 = 0 & v11 = 0 & ~ (v15 = 0) & ~ (v14 = 0) & leq(v12, v10) = v15 & leq(v10, v12) = v14 & ssList(v22) = 0 & ssList(v18) = 0 & ssList(v16) = 0 & cons(v12, v22) = v24 & cons(v10, v18) = v20 & app(v21, v24) = v8 & app(v16, v20) = v21 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (cyclefreeP(v8) = v9) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ? [v18] : ? [v19] : ? [v20] : ? [v21] : ? [v22] : ? [v23] : ? [v24] : ? [v25] : ((v25 = v8 & v23 = 0 & v19 = 0 & v17 = 0 & v15 = 0 & v14 = 0 & v13 = 0 & v11 = 0 & leq(v12, v10) = 0 & leq(v10, v12) = 0 & ssList(v22) = 0 & ssList(v18) = 0 & ssList(v16) = 0 & cons(v12, v22) = v24 & cons(v10, v18) = v20 & app(v21, v24) = v8 & app(v16, v20) = v21 & ssItem(v12) = 0 & ssItem(v10) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v9 = 0 | ~ (leq(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssItem(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (segmentP(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (segmentP(v8, nil) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (rearsegP(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (rearsegP(v8, nil) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (frontsegP(v8, v8) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v9 = 0 | ~ (frontsegP(v8, nil) = v9) | ? [v10] : ( ~ (v10 = 0) & ssList(v8) = v10)) & ! [v8] : ! [v9] : (v8 = nil | ~ (tl(v8) = v9) | ? [v10] : ? [v11] : (ssList(v9) = v11 & ssList(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : (v8 = nil | ~ (tl(v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = v9 & ssList(v9) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v8 = nil | ~ (hd(v8) = v9) | ? [v10] : ? [v11] : (ssList(v8) = v10 & ssItem(v9) = v11 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : (v8 = nil | ~ (hd(v8) = v9) | ? [v10] : ? [v11] : ((v11 = 0 & v10 = v9 & ssItem(v9) = 0) | ( ~ (v10 = 0) & ssList(v8) = v10))) & ! [v8] : ! [v9] : (v8 = nil | ~ (ssList(v8) = 0) | ~ (app(v8, v9) = nil) | ? [v10] : ( ~ (v10 = 0) & ssList(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (gt(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v10] : ? [v11] : (gt(v9, v8) = v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : ( ~ (tl(v8) = v9) | ? [v10] : ? [v11] : (hd(v8) = v11 & ssList(v8) = v10 & ( ~ (v10 = 0) | ! [v12] : (v12 = v8 | v12 = nil | v8 = nil | ~ (tl(v12) = v9) | ? [v13] : ? [v14] : (hd(v12) = v14 & ssList(v12) = v13 & ( ~ (v14 = v11) | ~ (v13 = 0))))))) & ! [v8] : ! [v9] : ( ~ (lt(v8, v9) = 0) | ~ (ssItem(v8) = 0) | ? [v10] : ? [v11] : (lt(v9, v8) = v11 & ssItem(v9) = v10 & ( ~ (v11 = 0) | ~ (v10 = 0)))) & ! [v8] : ! [v9] : ( ~ (segmentP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v15 = v8 & v14 = 0 & v11 = 0 & ssList(v13) = 0 & ssList(v10) = 0 & app(v12, v13) = v8 & app(v10, v9) = v12) | ( ~ (v10 = 0) & ssList(v9) = v10))) & ! [v8] : ! [v9] : ( ~ (rearsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v8 & v11 = 0 & ssList(v10) = 0 & app(v10, v9) = v8) | ( ~ (v10 = 0) & ssList(v9) = v10))) & ! [v8] : ! [v9] : ( ~ (frontsegP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ((v12 = v8 & v11 = 0 & ssList(v10) = 0 & app(v9, v10) = v8) | ( ~ (v10 = 0) & ssList(v9) = v10))) & ! [v8] : ! [v9] : ( ~ (memberP(v8, v9) = 0) | ~ (ssList(v8) = 0) | ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v15 = v8 & v13 = 0 & v11 = 0 & ssList(v12) = 0 & ssList(v10) = 0 & cons(v9, v12) = v14 & app(v10, v14) = v8) | ( ~ (v10 = 0) & ssItem(v9) = v10))) & ! [v8] : ! [v9] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, v8) = v8) | ? [v10] : ( ~ (v10 = 0) & ssItem(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (ssList(v8) = 0) | ~ (cons(v9, v8) = nil) | ? [v10] : ( ~ (v10 = 0) & ssItem(v9) = v10)) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (equalelemsP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (duplicatefreeP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (strictorderedP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (totalorderedP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (strictorderP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (totalorderP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : ! [v9] : ( ~ (cons(v8, nil) = v9) | ? [v10] : ? [v11] : (cyclefreeP(v9) = v11 & ssItem(v8) = v10 & ( ~ (v10 = 0) | v11 = 0))) & ! [v8] : (v8 = nil | ~ (segmentP(nil, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & ssList(v8) = v9)) & ! [v8] : (v8 = nil | ~ (rearsegP(nil, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & ssList(v8) = v9)) & ! [v8] : (v8 = nil | ~ (frontsegP(nil, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & ssList(v8) = v9)) & ! [v8] : (v8 = nil | ~ (ssList(v8) = 0) | ? [v9] : ? [v10] : (ssList(v9) = 0 & cons(v10, v9) = v8 & ssItem(v10) = 0)) & ! [v8] : (v8 = nil | ~ (app(nil, nil) = v8)) & ! [v8] : (v8 = 0 | ~ (segmentP(nil, nil) = v8)) & ! [v8] : (v8 = 0 | ~ (rearsegP(nil, nil) = v8)) & ! [v8] : (v8 = 0 | ~ (frontsegP(nil, nil) = v8)) & ! [v8] : ( ~ (lt(v8, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & ssItem(v8) = v9)) & ! [v8] : ( ~ (singletonP(v8) = 0) | ? [v9] : ? [v10] : ? [v11] : ((v11 = v8 & v10 = 0 & cons(v9, nil) = v8 & ssItem(v9) = 0) | ( ~ (v9 = 0) & ssList(v8) = v9))) & ! [v8] : ( ~ (memberP(nil, v8) = 0) | ? [v9] : ( ~ (v9 = 0) & ssItem(v8) = v9)) & ! [v8] : ( ~ (ssList(v8) = 0) | ~ (neq(v8, v8) = 0)) & ! [v8] : ( ~ (neq(v8, v8) = 0) | ~ (ssItem(v8) = 0)) & ((v5 = 0 & v4 = 0) | (v2 = nil & v1 = nil)) & ((v3 = 0 & ! [v8] : ( ~ (neq(v8, nil) = 0) | ? [v9] : ? [v10] : ? [v11] : (segmentP(v2, v8) = v10 & segmentP(v1, v8) = v11 & ssList(v8) = v9 & ( ~ (v11 = 0) | ~ (v10 = 0) | ~ (v9 = 0))))) | (v2 = nil & ~ (v1 = nil))))
% 120.64/83.63 | Instantiating (0) with all_0_0_0, all_0_1_1, all_0_2_2, all_0_3_3, all_0_4_4, all_0_5_5, all_0_6_6, all_0_7_7 yields:
% 120.64/83.63 | (1) ~ (all_0_0_0 = all_0_1_1) & ~ (all_0_7_7 = 0) & equalelemsP(nil) = 0 & duplicatefreeP(nil) = 0 & strictorderedP(nil) = 0 & totalorderedP(nil) = 0 & strictorderP(nil) = 0 & totalorderP(nil) = 0 & cyclefreeP(nil) = 0 & frontsegP(all_0_5_5, all_0_6_6) = all_0_2_2 & singletonP(nil) = all_0_7_7 & ssList(all_0_5_5) = 0 & ssList(all_0_6_6) = 0 & ssList(nil) = 0 & neq(all_0_5_5, nil) = all_0_4_4 & neq(all_0_6_6, nil) = all_0_3_3 & ssItem(all_0_0_0) = 0 & ssItem(all_0_1_1) = 0 & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v3 = 0 | ~ (strictorderedP(v0) = 0) | ~ (lt(v1, v2) = v3) | ~ (ssList(v4) = 0) | ~ (cons(v2, v8) = v9) | ~ (cons(v1, v5) = v6) | ~ (app(v7, v9) = v0) | ~ (app(v4, v6) = v7) | ~ (ssItem(v1) = 0) | ? [v10] : (( ~ (v10 = 0) & ssList(v8) = v10) | ( ~ (v10 = 0) & ssList(v5) = v10) | ( ~ (v10 = 0) & ssList(v0) = v10) | ( ~ (v10 = 0) & ssItem(v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ! [v8] : ! [v9] : (v3 = 0 | ~ (totalorderedP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssList(v4) = 0) | ~ (cons(v2, v8) = v9) | ~ (cons(v1, v5) = v6) | ~ (app(v7, v9) = v0) | ~ (app(v4, v6) = v7) | ~ (ssItem(v1) = 0) | ? [v10] : (( ~ (v10 = 0) & ssList(v8) = v10) | ( ~ (v10 = 0) & ssList(v5) = v10) | ( ~ (v10 = 0) & ssList(v0) = v10) | ( ~ (v10 = 0) & ssItem(v2) = v10))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ! [v7] : ( ~ (duplicatefreeP(v0) = 0) | ~ (ssList(v2) = 0) | ~ (cons(v1, v6) = v7) | ~ (cons(v1, v3) = v4) | ~ (app(v5, v7) = v0) | ~ (app(v2, v4) = v5) | ~ (ssItem(v1) = 0) | ? [v8] : (( ~ (v8 = 0) & ssList(v6) = v8) | ( ~ (v8 = 0) & ssList(v3) = v8) | ( ~ (v8 = 0) & ssList(v0) = v8))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v6 = 0 | ~ (segmentP(v5, v1) = v6) | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v3, v4) = v5) | ~ (app(v2, v0) = v3) | ? [v7] : (( ~ (v7 = 0) & ssList(v4) = v7) | ( ~ (v7 = 0) & ssList(v2) = v7) | ( ~ (v7 = 0) & ssList(v1) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : (v2 = v1 | ~ (equalelemsP(v0) = 0) | ~ (ssList(v3) = 0) | ~ (cons(v2, v4) = v5) | ~ (cons(v1, v5) = v6) | ~ (app(v3, v6) = v0) | ~ (ssItem(v2) = 0) | ~ (ssItem(v1) = 0) | ? [v7] : (( ~ (v7 = 0) & ssList(v4) = v7) | ( ~ (v7 = 0) & ssList(v0) = v7))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ! [v6] : ( ~ (frontsegP(v3, v5) = v6) | ~ (cons(v1, v4) = v5) | ~ (cons(v0, v2) = v3) | ~ (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ? [v7] : ? [v8] : (( ~ (v7 = 0) & ssList(v2) = v7) | (frontsegP(v2, v4) = v8 & ssList(v4) = v7 & ( ~ (v7 = 0) | (( ~ (v8 = 0) | ~ (v1 = v0) | v6 = 0) & ( ~ (v6 = 0) | (v8 = 0 & v1 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = 0 | ~ (segmentP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v4, v5) = v0) | ~ (app(v3, v1) = v4) | ? [v6] : (( ~ (v6 = 0) & ssList(v5) = v6) | ( ~ (v6 = 0) & ssList(v3) = v6) | ( ~ (v6 = 0) & ssList(v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : (v2 = 0 | ~ (memberP(v0, v1) = v2) | ~ (ssList(v3) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v1, v4) = v5) | ~ (app(v3, v5) = v0) | ? [v6] : (( ~ (v6 = 0) & ssList(v4) = v6) | ( ~ (v6 = 0) & ssItem(v1) = v6))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (memberP(v4, v0) = v5) | ~ (memberP(v1, v0) = v2) | ~ (app(v1, v3) = v4) | ~ (ssItem(v0) = 0) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & ssList(v1) = v6) | (memberP(v3, v0) = v7 & ssList(v3) = v6 & ( ~ (v6 = 0) | (( ~ (v5 = 0) | v7 = 0 | v2 = 0) & (v5 = 0 | ( ~ (v7 = 0) & ~ (v2 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ! [v5] : ( ~ (ssList(v0) = 0) | ~ (cons(v3, v1) = v4) | ~ (app(v4, v0) = v5) | ~ (app(v1, v0) = v2) | ? [v6] : ? [v7] : (( ~ (v6 = 0) & ssList(v1) = v6) | (cons(v3, v2) = v7 & ssItem(v3) = v6 & ( ~ (v6 = 0) | v7 = v5)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = v2 | ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssItem(v4) = v5) | ( ~ (v5 = 0) & ssItem(v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (rearsegP(v3, v1) = v4) | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssList(v2) = v5) | ( ~ (v5 = 0) & ssList(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v4 = 0 | ~ (frontsegP(v3, v1) = v4) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ~ (app(v0, v2) = v3) | ? [v5] : (( ~ (v5 = 0) & ssList(v2) = v5) | ( ~ (v5 = 0) & ssList(v1) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : (v1 = v0 | ~ (ssList(v1) = 0) | ~ (ssList(v0) = 0) | ~ (cons(v4, v1) = v3) | ~ (cons(v2, v0) = v3) | ? [v5] : (( ~ (v5 = 0) & ssItem(v4) = v5) | ( ~ (v5 = 0) & ssItem(v2) = v5))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (memberP(v3, v0) = v4) | ~ (cons(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ~ (ssItem(v0) = 0) | ? [v5] : ? [v6] : (memberP(v2, v0) = v6 & ssList(v2) = v5 & ( ~ (v5 = 0) | (( ~ (v4 = 0) | v6 = 0 | v1 = v0) & (v4 = 0 | ( ~ (v6 = 0) & ~ (v1 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ! [v4] : ( ~ (ssList(v0) = 0) | ~ (app(v2, v3) = v4) | ~ (app(v0, v1) = v2) | ? [v5] : ? [v6] : ? [v7] : (( ~ (v5 = 0) & ssList(v1) = v5) | (ssList(v3) = v5 & app(v1, v3) = v6 & app(v0, v6) = v7 & ( ~ (v5 = 0) | v7 = v4)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & ssList(v0) = v4)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ssList(v0) = 0) | ~ (app(v3, v1) = v2) | ~ (app(v0, v1) = v2) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v2) | ~ (app(v1, v0) = v2) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (gt(v0, v2) = v3) | ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (gt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (geq(v0, v2) = v3) | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (geq(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lt(v0, v2) = v3) | ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (lt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (lt(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (lt(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (leq(v0, v2) = v3) | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssItem(v1) = v4) | (leq(v1, v2) = v5 & ssItem(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (segmentP(v0, v2) = v3) | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (segmentP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (rearsegP(v0, v2) = v3) | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (rearsegP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = 0 | ~ (frontsegP(v0, v2) = v3) | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v1) = v4) | (frontsegP(v1, v2) = v5 & ssList(v2) = v4 & ( ~ (v5 = 0) | ~ (v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (rearsegP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v3, v1) = v0) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v2 = 0 | ~ (frontsegP(v0, v1) = v2) | ~ (ssList(v0) = 0) | ~ (app(v1, v3) = v0) | ? [v4] : (( ~ (v4 = 0) & ssList(v3) = v4) | ( ~ (v4 = 0) & ssList(v1) = v4))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (tl(v0) = v1) | ~ (app(v1, v2) = v3) | ? [v4] : ? [v5] : ? [v6] : (( ~ (v4 = 0) & ssList(v0) = v4) | (tl(v5) = v6 & ssList(v2) = v4 & app(v0, v2) = v5 & ( ~ (v4 = 0) | v6 = v3)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v0 = nil | ~ (hd(v0) = v1) | ~ (app(v0, v2) = v3) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (hd(v3) = v5 & ssList(v2) = v4 & ( ~ (v4 = 0) | v5 = v1)))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (hd(v1) = v2) | ~ (lt(v0, v2) = v3) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (strictorderedP(v5) = v6 & strictorderedP(v1) = v7 & ssList(v1) = v4 & cons(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v1 = nil | (v7 = 0 & v3 = 0)) & (v6 = 0 | ( ~ (v1 = nil) & ( ~ (v7 = 0) | ~ (v3 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (hd(v1) = v2) | ~ (leq(v0, v2) = v3) | ~ (ssItem(v0) = 0) | ? [v4] : ? [v5] : ? [v6] : ? [v7] : (totalorderedP(v5) = v6 & totalorderedP(v1) = v7 & ssList(v1) = v4 & cons(v0, v1) = v5 & ( ~ (v4 = 0) | (( ~ (v6 = 0) | v1 = nil | (v7 = 0 & v3 = 0)) & (v6 = 0 | ( ~ (v1 = nil) & ( ~ (v7 = 0) | ~ (v3 = 0)))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (strictorderP(v0) = 0) | ~ (lt(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (lt(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v5 = 0 | v3 = 0 | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (totalorderP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (leq(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : (v5 = 0 | v3 = 0 | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (cyclefreeP(v0) = 0) | ~ (leq(v1, v2) = v3) | ~ (ssItem(v1) = 0) | ? [v4] : ? [v5] : (( ~ (v4 = 0) & ssList(v0) = v4) | (leq(v2, v1) = v5 & ssItem(v2) = v4 & ( ~ (v4 = 0) | ! [v6] : ! [v7] : ! [v8] : ! [v9] : ! [v10] : ! [v11] : ( ~ (v5 = 0) | ~ (v3 = 0) | ~ (ssList(v6) = 0) | ~ (cons(v2, v10) = v11) | ~ (cons(v1, v7) = v8) | ~ (app(v9, v11) = v0) | ~ (app(v6, v8) = v9) | ? [v12] : (( ~ (v12 = 0) & ssList(v10) = v12) | ( ~ (v12 = 0) & ssList(v7) = v12))))))) & ! [v0] : ! [v1] : ! [v2] : ! [v3] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, nil) = v2) | ~ (app(v2, v0) = v3) | ? [v4] : ? [v5] : (cons(v1, v0) = v5 & ssItem(v1) = v4 & ( ~ (v4 = 0) | v5 = v3))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (lt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v0, v1) = v4 & ssItem(v1) = v3 & ( ~ (v4 = 0) | ~ (v3 = 0)))) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (ssList(v0) = 0) | ~ (neq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & ssList(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (neq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & ssItem(v1) = v3)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | ~ (equalelemsP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | ~ (duplicatefreeP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderP(v2) = v1) | ~ (strictorderP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ (totalorderP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ (cyclefreeP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0)) & ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (singletonP(v0) = v1) | ~ (cons(v2, nil) = v0) | ? [v3] : (( ~ (v3 = 0) & ssList(v0) = v3) | ( ~ (v3 = 0) & ssItem(v2) = v3))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (gt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (lt(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (geq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v1, v0) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0) & ( ~ (v2 = 0) | v4 = 0))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (lt(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ? [v4] : (leq(v0, v1) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | (( ~ (v4 = 0) | v2 = 0 | v1 = v0) & ( ~ (v2 = 0) | (v4 = 0 & ~ (v1 = v0))))))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (tl(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v1))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (app(v0, v1) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (geq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (leq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (frontsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (equalelemsP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ((v12 = v0 & v9 = 0 & v7 = 0 & v5 = 0 & v3 = 0 & ~ (v4 = v2) & ssList(v8) = 0 & ssList(v6) = 0 & cons(v4, v8) = v10 & cons(v2, v10) = v11 & app(v6, v11) = v0 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (duplicatefreeP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ((v15 = v0 & v13 = 0 & v9 = 0 & v7 = 0 & v5 = 0 & v4 = v2 & v3 = 0 & ssList(v12) = 0 & ssList(v8) = 0 & ssList(v6) = 0 & cons(v2, v12) = v14 & cons(v2, v8) = v10 & app(v11, v14) = v0 & app(v6, v10) = v11 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (strictorderedP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v0 & v14 = 0 & v10 = 0 & v8 = 0 & v5 = 0 & v3 = 0 & ~ (v6 = 0) & lt(v2, v4) = v6 & ssList(v13) = 0 & ssList(v9) = 0 & ssList(v7) = 0 & cons(v4, v13) = v15 & cons(v2, v9) = v11 & app(v12, v15) = v0 & app(v7, v11) = v12 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (totalorderedP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ((v16 = v0 & v14 = 0 & v10 = 0 & v8 = 0 & v5 = 0 & v3 = 0 & ~ (v6 = 0) & leq(v2, v4) = v6 & ssList(v13) = 0 & ssList(v9) = 0 & ssList(v7) = 0 & cons(v4, v13) = v15 & cons(v2, v9) = v11 & app(v12, v15) = v0 & app(v7, v11) = v12 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (strictorderP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v5 = 0 & v3 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & lt(v4, v2) = v7 & lt(v2, v4) = v6 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (totalorderP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v5 = 0 & v3 = 0 & ~ (v7 = 0) & ~ (v6 = 0) & leq(v4, v2) = v7 & leq(v2, v4) = v6 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (cyclefreeP(v0) = v1) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ? [v8] : ? [v9] : ? [v10] : ? [v11] : ? [v12] : ? [v13] : ? [v14] : ? [v15] : ? [v16] : ? [v17] : ((v17 = v0 & v15 = 0 & v11 = 0 & v9 = 0 & v7 = 0 & v6 = 0 & v5 = 0 & v3 = 0 & leq(v4, v2) = 0 & leq(v2, v4) = 0 & ssList(v14) = 0 & ssList(v10) = 0 & ssList(v8) = 0 & cons(v4, v14) = v16 & cons(v2, v10) = v12 & app(v13, v16) = v0 & app(v8, v12) = v13 & ssItem(v4) = 0 & ssItem(v2) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2)) & ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (ssList(v1) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssList(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : (ssList(v0) = v2 & ssItem(v1) = v3 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssItem(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2))) & ! [v0] : ! [v1] : (v0 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (gt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (hd(v0) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | ! [v4] : (v4 = v0 | v4 = nil | v0 = nil | ~ (tl(v4) = v1) | ? [v5] : ? [v6] : (hd(v4) = v6 & ssList(v4) = v5 & ( ~ (v6 = v3) | ~ (v5 = 0))))))) & ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (lt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0)))) & ! [v0] : ! [v1] : ( ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v0 & v6 = 0 & v3 = 0 & ssList(v5) = 0 & ssList(v2) = 0 & app(v4, v5) = v0 & app(v2, v1) = v4) | ( ~ (v2 = 0) & ssList(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & v3 = 0 & ssList(v2) = 0 & app(v2, v1) = v0) | ( ~ (v2 = 0) & ssList(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ((v4 = v0 & v3 = 0 & ssList(v2) = 0 & app(v1, v2) = v0) | ( ~ (v2 = 0) & ssList(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (memberP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : ? [v4] : ? [v5] : ? [v6] : ? [v7] : ((v7 = v0 & v5 = 0 & v3 = 0 & ssList(v4) = 0 & ssList(v2) = 0 & cons(v1, v4) = v6 & app(v2, v6) = v0) | ( ~ (v2 = 0) & ssItem(v1) = v2))) & ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v0) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = nil) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2)) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0))) & ! [v0] : (v0 = nil | ~ (segmentP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1)) & ! [v0] : (v0 = nil | ~ (rearsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1)) & ! [v0] : (v0 = nil | ~ (frontsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1)) & ! [v0] : (v0 = nil | ~ (ssList(v0) = 0) | ? [v1] : ? [v2] : (ssList(v1) = 0 & cons(v2, v1) = v0 & ssItem(v2) = 0)) & ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0)) & ! [v0] : (v0 = 0 | ~ (segmentP(nil, nil) = v0)) & ! [v0] : (v0 = 0 | ~ (rearsegP(nil, nil) = v0)) & ! [v0] : (v0 = 0 | ~ (frontsegP(nil, nil) = v0)) & ! [v0] : ( ~ (lt(v0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1)) & ! [v0] : ( ~ (singletonP(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v0 & v2 = 0 & cons(v1, nil) = v0 & ssItem(v1) = 0) | ( ~ (v1 = 0) & ssList(v0) = v1))) & ! [v0] : ( ~ (memberP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1)) & ! [v0] : ( ~ (ssList(v0) = 0) | ~ (neq(v0, v0) = 0)) & ! [v0] : ( ~ (neq(v0, v0) = 0) | ~ (ssItem(v0) = 0)) & ((all_0_2_2 = 0 & all_0_3_3 = 0) | (all_0_5_5 = nil & all_0_6_6 = nil)) & ((all_0_4_4 = 0 & ! [v0] : ( ~ (neq(v0, nil) = 0) | ? [v1] : ? [v2] : ? [v3] : (segmentP(all_0_5_5, v0) = v2 & segmentP(all_0_6_6, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))) | (all_0_5_5 = nil & ~ (all_0_6_6 = nil)))
% 121.01/83.67 |
% 121.01/83.67 | Applying alpha-rule on (1) yields:
% 121.01/83.67 | (2) ! [v0] : (v0 = nil | ~ (rearsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 121.01/83.67 | (3) ssList(all_0_6_6) = 0
% 121.01/83.67 | (4) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssItem(v2) = v1) | ~ (ssItem(v2) = v0))
% 121.01/83.67 | (5) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 121.01/83.67 | (6) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : (ssList(v0) = v2 & ssItem(v1) = v3 & ( ~ (v2 = 0) | v3 = 0)))
% 121.01/83.67 | (7) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 121.01/83.67 | (8) ! [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))))
% 121.01/83.67 | (9) ! [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)))
% 121.01/83.68 | (10) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 121.01/83.68 | (11) ! [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)))
% 121.01/83.68 | (12) ! [v0] : (v0 = nil | ~ (segmentP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 121.01/83.68 | (13) ! [v0] : ! [v1] : (v1 = v0 | ~ (geq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (geq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 121.01/83.68 | (14) ! [v0] : ( ~ (ssList(v0) = 0) | ~ (neq(v0, v0) = 0))
% 121.01/83.68 | (15) ! [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)))))
% 121.01/83.68 | (16) ! [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)))
% 121.01/83.68 | (17) ! [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)))
% 121.01/83.68 | (18) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderedP(v2) = v1) | ~ (strictorderedP(v2) = v0))
% 121.01/83.68 | (19) frontsegP(all_0_5_5, all_0_6_6) = all_0_2_2
% 121.01/83.68 | (20) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (cyclefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 121.01/83.68 | (21) ! [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)))))
% 121.01/83.68 | (22) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (tl(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v0)))
% 121.01/83.68 | (23) ! [v0] : ! [v1] : ( ~ (lt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (lt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 121.01/83.68 | (24) ! [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))))
% 121.01/83.68 | (25) ! [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)))))))
% 121.01/83.68 | (26) ! [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)))
% 121.01/83.68 | (27) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (cons(v3, v2) = v1) | ~ (cons(v3, v2) = v0))
% 121.01/83.68 | (28) ! [v0] : ! [v1] : (v0 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 121.01/83.68 | (29) ! [v0] : ! [v1] : (v1 = v0 | ~ (rearsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (rearsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 121.01/83.69 | (30) (all_0_4_4 = 0 & ! [v0] : ( ~ (neq(v0, nil) = 0) | ? [v1] : ? [v2] : ? [v3] : (segmentP(all_0_5_5, v0) = v2 & segmentP(all_0_6_6, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))) | (all_0_5_5 = nil & ~ (all_0_6_6 = nil))
% 121.01/83.69 | (31) cyclefreeP(nil) = 0
% 121.01/83.69 | (32) ! [v0] : ! [v1] : (v1 = 0 | ~ (leq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 121.01/83.69 | (33) ! [v0] : ! [v1] : ! [v2] : (v1 = 0 | ~ (singletonP(v0) = v1) | ~ (cons(v2, nil) = v0) | ? [v3] : (( ~ (v3 = 0) & ssList(v0) = v3) | ( ~ (v3 = 0) & ssItem(v2) = v3)))
% 121.01/83.69 | (34) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssList(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 121.01/83.69 | (35) ! [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)))))))
% 121.01/83.69 | (36) ! [v0] : ( ~ (lt(v0, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 121.01/83.69 | (37) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (leq(v3, v2) = v1) | ~ (leq(v3, v2) = v0))
% 121.01/83.69 | (38) ! [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)))))
% 121.01/83.69 | (39) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (frontsegP(v3, v2) = v1) | ~ (frontsegP(v3, v2) = v0))
% 121.01/83.69 | (40) ! [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)))))
% 121.01/83.69 | (41) ! [v0] : ( ~ (singletonP(v0) = 0) | ? [v1] : ? [v2] : ? [v3] : ((v3 = v0 & v2 = 0 & cons(v1, nil) = v0 & ssItem(v1) = 0) | ( ~ (v1 = 0) & ssList(v0) = v1)))
% 121.01/83.69 | (42) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (totalorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 121.01/83.69 | (43) ! [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)))
% 121.01/83.69 | (44) ! [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)))
% 121.01/83.69 | (45) ! [v0] : ( ~ (memberP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssItem(v0) = v1))
% 121.01/83.69 | (46) ! [v0] : ! [v1] : (v0 = nil | ~ (tl(v0) = v1) | ? [v2] : ? [v3] : (ssList(v1) = v3 & ssList(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 121.01/83.69 | (47) ! [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)))
% 121.01/83.69 | (48) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v0) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 121.01/83.69 | (49) ! [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))))
% 121.01/83.69 | (50) totalorderedP(nil) = 0
% 121.01/83.69 | (51) ! [v0] : ! [v1] : (v1 = 0 | ~ (geq(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssItem(v0) = v2))
% 121.01/83.69 | (52) ! [v0] : (v0 = nil | ~ (ssList(v0) = 0) | ? [v1] : ? [v2] : (ssList(v1) = 0 & cons(v2, v1) = v0 & ssItem(v2) = 0))
% 121.01/83.69 | (53) ! [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)))
% 121.01/83.69 | (54) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (geq(v3, v2) = v1) | ~ (geq(v3, v2) = v0))
% 121.01/83.69 | (55) ! [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)))
% 121.01/83.69 | (56) ! [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)))
% 121.01/83.69 | (57) neq(all_0_6_6, nil) = all_0_3_3
% 121.01/83.69 | (58) ! [v0] : ! [v1] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = nil) | ? [v2] : ( ~ (v2 = 0) & ssItem(v1) = v2))
% 121.01/83.69 | (59) strictorderedP(nil) = 0
% 121.01/83.69 | (60) ! [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))))))))
% 121.01/83.70 | (61) ! [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)))
% 121.01/83.70 | (62) singletonP(nil) = all_0_7_7
% 121.01/83.70 | (63) ! [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)))
% 121.01/83.70 | (64) ! [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)))))))
% 121.01/83.70 | (65) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (equalelemsP(v2) = v1) | ~ (equalelemsP(v2) = v0))
% 121.01/83.70 | (66) ! [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)))
% 121.01/83.70 | (67) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 121.01/83.70 | (68) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 121.01/83.70 | (69) ! [v0] : (v0 = nil | ~ (app(nil, nil) = v0))
% 121.01/83.70 | (70) ! [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)))))
% 121.01/83.70 | (71) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (neq(v0, v1) = v2) | ~ (ssItem(v0) = 0) | ? [v3] : ( ~ (v3 = 0) & ssItem(v1) = v3))
% 121.01/83.70 | (72) ! [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)))
% 121.01/83.70 | (73) ! [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)))
% 121.01/83.70 | (74) ssList(all_0_5_5) = 0
% 121.01/83.70 | (75) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (rearsegP(v3, v2) = v1) | ~ (rearsegP(v3, v2) = v0))
% 121.01/83.70 | (76) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (ssList(v2) = v1) | ~ (ssList(v2) = v0))
% 121.01/83.70 | (77) ! [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))))))))
% 121.01/83.70 | (78) equalelemsP(nil) = 0
% 121.01/83.70 | (79) ! [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))))
% 121.01/83.70 | (80) ! [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)))
% 121.01/83.70 | (81) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (singletonP(v2) = v1) | ~ (singletonP(v2) = v0))
% 121.01/83.70 | (82) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderedP(v2) = v1) | ~ (totalorderedP(v2) = v0))
% 121.01/83.70 | (83) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = v1)))
% 121.01/83.70 | (84) ! [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)))))))
% 121.01/83.70 | (85) ssItem(all_0_1_1) = 0
% 121.01/83.70 | (86) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (memberP(v3, v2) = v1) | ~ (memberP(v3, v2) = v0))
% 121.01/83.70 | (87) ! [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)))
% 121.01/83.70 | (88) ! [v0] : (v0 = 0 | ~ (segmentP(nil, nil) = v0))
% 121.01/83.70 | (89) ! [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)))
% 121.01/83.70 | (90) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v3 = v0 | v0 = nil | ~ (tl(v0) = v2) | ~ (hd(v0) = v1) | ~ (cons(v1, v2) = v3) | ? [v4] : ( ~ (v4 = 0) & ssList(v0) = v4))
% 121.01/83.70 | (91) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (app(v0, v1) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssList(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 121.01/83.70 | (92) ! [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)))))
% 121.01/83.70 | (93) totalorderP(nil) = 0
% 121.01/83.70 | (94) ssList(nil) = 0
% 121.01/83.70 | (95) (all_0_2_2 = 0 & all_0_3_3 = 0) | (all_0_5_5 = nil & all_0_6_6 = nil)
% 121.01/83.71 | (96) ! [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)))))
% 121.01/83.71 | (97) ~ (all_0_7_7 = 0)
% 121.01/83.71 | (98) ! [v0] : ! [v1] : (v1 = 0 | ~ (rearsegP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 121.01/83.71 | (99) ! [v0] : (v0 = nil | ~ (frontsegP(nil, v0) = 0) | ? [v1] : ( ~ (v1 = 0) & ssList(v0) = v1))
% 121.01/83.71 | (100) ! [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)))
% 121.01/83.71 | (101) ssItem(all_0_0_0) = 0
% 121.01/83.71 | (102) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (duplicatefreeP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 121.01/83.71 | (103) strictorderP(nil) = 0
% 121.01/83.71 | (104) ! [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)))
% 121.01/83.71 | (105) ! [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)))))))
% 121.01/83.71 | (106) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(nil, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 121.01/83.71 | (107) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (equalelemsP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 121.01/83.71 | (108) ! [v0] : (v0 = 0 | ~ (rearsegP(nil, nil) = v0))
% 121.01/83.71 | (109) ! [v0] : ! [v1] : ( ~ (cons(v0, nil) = v1) | ? [v2] : ? [v3] : (strictorderedP(v1) = v3 & ssItem(v0) = v2 & ( ~ (v2 = 0) | v3 = 0)))
% 121.01/83.71 | (110) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (cyclefreeP(v2) = v1) | ~ (cyclefreeP(v2) = v0))
% 121.01/83.71 | (111) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (duplicatefreeP(v2) = v1) | ~ (duplicatefreeP(v2) = v0))
% 121.01/83.71 | (112) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (neq(v3, v2) = v1) | ~ (neq(v3, v2) = v0))
% 121.01/83.71 | (113) ! [v0] : ! [v1] : ( ~ (gt(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (gt(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 121.01/83.71 | (114) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (app(v3, v2) = v1) | ~ (app(v3, v2) = v0))
% 121.01/83.71 | (115) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (lt(v3, v2) = v1) | ~ (lt(v3, v2) = v0))
% 121.01/83.71 | (116) ! [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))))
% 121.01/83.71 | (117) ! [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)))))
% 121.01/83.71 | (118) ! [v0] : ! [v1] : (v0 = nil | ~ (hd(v0) = v1) | ? [v2] : ? [v3] : ((v3 = 0 & v2 = v1 & ssItem(v1) = 0) | ( ~ (v2 = 0) & ssList(v0) = v2)))
% 121.01/83.71 | (119) ! [v0] : ! [v1] : ! [v2] : ( ~ (ssList(v0) = 0) | ~ (cons(v1, v0) = v2) | ? [v3] : ? [v4] : (ssList(v2) = v4 & ssItem(v1) = v3 & ( ~ (v3 = 0) | v4 = 0)))
% 121.01/83.71 | (120) ! [v0] : ( ~ (neq(v0, v0) = 0) | ~ (ssItem(v0) = 0))
% 121.01/83.71 | (121) ! [v0] : ! [v1] : (v1 = nil | ~ (ssList(v0) = 0) | ~ (app(v0, v1) = nil) | ? [v2] : ( ~ (v2 = 0) & ssList(v1) = v2))
% 121.01/83.71 | (122) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (hd(v2) = v1) | ~ (hd(v2) = v0))
% 121.01/83.71 | (123) ! [v0] : ! [v1] : (v1 = v0 | ~ (frontsegP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (frontsegP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 121.01/83.71 | (124) ! [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)))))))
% 121.01/83.71 | (125) ! [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))))))))
% 121.01/83.71 | (126) ! [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)))
% 121.01/83.71 | (127) duplicatefreeP(nil) = 0
% 121.01/83.71 | (128) ! [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)))
% 121.01/83.71 | (129) ! [v0] : (v0 = 0 | ~ (frontsegP(nil, nil) = v0))
% 121.01/83.71 | (130) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (totalorderP(v2) = v1) | ~ (totalorderP(v2) = v0))
% 121.01/83.71 | (131) ! [v0] : ! [v1] : (v1 = v0 | ~ (app(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 121.01/83.71 | (132) ~ (all_0_0_0 = all_0_1_1)
% 121.01/83.71 | (133) ! [v0] : ! [v1] : ! [v2] : (v2 = 0 | v1 = v0 | ~ (ssList(v0) = 0) | ~ (neq(v0, v1) = v2) | ? [v3] : ( ~ (v3 = 0) & ssList(v1) = v3))
% 121.01/83.71 | (134) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (gt(v3, v2) = v1) | ~ (gt(v3, v2) = v0))
% 121.01/83.71 | (135) neq(all_0_5_5, nil) = all_0_4_4
% 121.01/83.71 | (136) ! [v0] : ! [v1] : (v1 = v0 | ~ (leq(v0, v1) = 0) | ~ (ssItem(v0) = 0) | ? [v2] : ? [v3] : (leq(v1, v0) = v3 & ssItem(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 121.01/83.71 | (137) ! [v0] : ! [v1] : ! [v2] : ! [v3] : (v1 = v0 | ~ (segmentP(v3, v2) = v1) | ~ (segmentP(v3, v2) = v0))
% 121.01/83.71 | (138) ! [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)))))
% 121.01/83.71 | (139) ! [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)))))))
% 121.01/83.71 | (140) ! [v0] : ! [v1] : (v1 = 0 | ~ (segmentP(v0, nil) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 121.01/83.71 | (141) ! [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)))
% 121.01/83.72 | (142) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (strictorderP(v2) = v1) | ~ (strictorderP(v2) = v0))
% 121.01/83.72 | (143) ! [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)))))
% 121.01/83.72 | (144) ! [v0] : ! [v1] : ! [v2] : (v1 = v0 | ~ (tl(v2) = v1) | ~ (tl(v2) = v0))
% 121.01/83.72 | (145) ! [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)))
% 121.01/83.72 | (146) ! [v0] : ! [v1] : (v1 = 0 | ~ (frontsegP(v0, v0) = v1) | ? [v2] : ( ~ (v2 = 0) & ssList(v0) = v2))
% 121.01/83.72 | (147) ! [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)))
% 121.01/83.72 | (148) ! [v0] : ! [v1] : (v1 = v0 | ~ (segmentP(v0, v1) = 0) | ~ (ssList(v0) = 0) | ? [v2] : ? [v3] : (segmentP(v1, v0) = v3 & ssList(v1) = v2 & ( ~ (v3 = 0) | ~ (v2 = 0))))
% 121.01/83.72 | (149) ! [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)))
% 121.01/83.72 |
% 121.01/83.72 | Instantiating formula (112) with all_0_6_6, nil, all_0_3_3, all_0_4_4 and discharging atoms neq(all_0_6_6, nil) = all_0_3_3, yields:
% 121.01/83.72 | (150) all_0_3_3 = all_0_4_4 | ~ (neq(all_0_6_6, nil) = all_0_4_4)
% 121.01/83.72 |
% 121.01/83.72 | Instantiating formula (52) with all_0_5_5 and discharging atoms ssList(all_0_5_5) = 0, yields:
% 121.01/83.72 | (151) all_0_5_5 = nil | ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_5_5 & ssItem(v1) = 0)
% 121.01/83.72 |
% 121.01/83.72 | Instantiating formula (52) with all_0_6_6 and discharging atoms ssList(all_0_6_6) = 0, yields:
% 121.01/83.72 | (152) all_0_6_6 = nil | ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_6_6 & ssItem(v1) = 0)
% 121.01/83.72 |
% 121.01/83.72 +-Applying beta-rule and splitting (30), into two cases.
% 121.01/83.72 |-Branch one:
% 121.01/83.72 | (153) all_0_4_4 = 0 & ! [v0] : ( ~ (neq(v0, nil) = 0) | ? [v1] : ? [v2] : ? [v3] : (segmentP(all_0_5_5, v0) = v2 & segmentP(all_0_6_6, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))
% 121.01/83.72 |
% 121.01/83.72 | Applying alpha-rule on (153) yields:
% 121.01/83.72 | (154) all_0_4_4 = 0
% 121.01/83.72 | (155) ! [v0] : ( ~ (neq(v0, nil) = 0) | ? [v1] : ? [v2] : ? [v3] : (segmentP(all_0_5_5, v0) = v2 & segmentP(all_0_6_6, v0) = v3 & ssList(v0) = v1 & ( ~ (v3 = 0) | ~ (v2 = 0) | ~ (v1 = 0))))
% 121.01/83.72 |
% 121.01/83.72 | Instantiating formula (155) with all_0_5_5 yields:
% 121.01/83.72 | (156) ~ (neq(all_0_5_5, nil) = 0) | ? [v0] : ? [v1] : ? [v2] : (segmentP(all_0_5_5, all_0_5_5) = v1 & segmentP(all_0_6_6, all_0_5_5) = v2 & ssList(all_0_5_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 121.01/83.72 |
% 121.01/83.72 | Instantiating formula (155) with all_0_6_6 yields:
% 121.01/83.72 | (157) ~ (neq(all_0_6_6, nil) = 0) | ? [v0] : ? [v1] : ? [v2] : (segmentP(all_0_5_5, all_0_6_6) = v1 & segmentP(all_0_6_6, all_0_6_6) = v2 & ssList(all_0_6_6) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 121.01/83.72 |
% 121.01/83.72 | From (154) and (135) follows:
% 121.01/83.72 | (158) neq(all_0_5_5, nil) = 0
% 121.01/83.72 |
% 121.01/83.72 +-Applying beta-rule and splitting (156), into two cases.
% 121.01/83.72 |-Branch one:
% 121.01/83.72 | (159) ~ (neq(all_0_5_5, nil) = 0)
% 121.01/83.72 |
% 121.01/83.72 | Using (158) and (159) yields:
% 121.01/83.72 | (160) $false
% 121.01/83.72 |
% 121.01/83.72 |-The branch is then unsatisfiable
% 121.01/83.72 |-Branch two:
% 121.01/83.72 | (158) neq(all_0_5_5, nil) = 0
% 121.01/83.72 | (162) ? [v0] : ? [v1] : ? [v2] : (segmentP(all_0_5_5, all_0_5_5) = v1 & segmentP(all_0_6_6, all_0_5_5) = v2 & ssList(all_0_5_5) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 121.01/83.72 |
% 121.01/83.72 | Instantiating (162) with all_15_0_8, all_15_1_9, all_15_2_10 yields:
% 121.01/83.72 | (163) segmentP(all_0_5_5, all_0_5_5) = all_15_1_9 & segmentP(all_0_6_6, all_0_5_5) = all_15_0_8 & ssList(all_0_5_5) = all_15_2_10 & ( ~ (all_15_0_8 = 0) | ~ (all_15_1_9 = 0) | ~ (all_15_2_10 = 0))
% 121.01/83.72 |
% 121.01/83.72 | Applying alpha-rule on (163) yields:
% 121.01/83.72 | (164) segmentP(all_0_5_5, all_0_5_5) = all_15_1_9
% 121.01/83.72 | (165) segmentP(all_0_6_6, all_0_5_5) = all_15_0_8
% 121.01/83.72 | (166) ssList(all_0_5_5) = all_15_2_10
% 121.01/83.72 | (167) ~ (all_15_0_8 = 0) | ~ (all_15_1_9 = 0) | ~ (all_15_2_10 = 0)
% 121.01/83.72 |
% 121.01/83.72 | Instantiating formula (76) with all_0_5_5, all_15_2_10, 0 and discharging atoms ssList(all_0_5_5) = all_15_2_10, ssList(all_0_5_5) = 0, yields:
% 121.01/83.72 | (168) all_15_2_10 = 0
% 121.01/83.72 |
% 121.01/83.72 | Instantiating formula (76) with all_0_6_6, all_15_2_10, 0 and discharging atoms ssList(all_0_6_6) = 0, yields:
% 121.01/83.72 | (169) all_15_2_10 = 0 | ~ (ssList(all_0_6_6) = all_15_2_10)
% 121.01/83.72 |
% 121.01/83.72 | Instantiating formula (76) with nil, all_15_2_10, 0 and discharging atoms ssList(nil) = 0, yields:
% 121.01/83.72 | (170) all_15_2_10 = 0 | ~ (ssList(nil) = all_15_2_10)
% 121.01/83.72 |
% 121.01/83.72 | From (168) and (166) follows:
% 121.01/83.72 | (74) ssList(all_0_5_5) = 0
% 121.01/83.72 |
% 121.01/83.72 | Instantiating formula (5) with all_15_1_9, all_0_5_5 and discharging atoms segmentP(all_0_5_5, all_0_5_5) = all_15_1_9, yields:
% 121.01/83.72 | (172) all_15_1_9 = 0 | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_5_5) = v0)
% 121.01/83.72 |
% 121.01/83.72 | Instantiating formula (5) with all_15_0_8, all_0_6_6 yields:
% 121.01/83.72 | (173) all_15_0_8 = 0 | ~ (segmentP(all_0_6_6, all_0_6_6) = all_15_0_8) | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 121.01/83.72 |
% 121.01/83.72 | Instantiating formula (140) with all_15_0_8, all_0_6_6 yields:
% 121.01/83.72 | (174) all_15_0_8 = 0 | ~ (segmentP(all_0_6_6, nil) = all_15_0_8) | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 121.01/83.72 |
% 121.01/83.72 +-Applying beta-rule and splitting (95), into two cases.
% 121.01/83.72 |-Branch one:
% 121.01/83.72 | (175) all_0_2_2 = 0 & all_0_3_3 = 0
% 121.01/83.72 |
% 121.01/83.72 | Applying alpha-rule on (175) yields:
% 121.01/83.72 | (176) all_0_2_2 = 0
% 121.01/83.72 | (177) all_0_3_3 = 0
% 121.01/83.72 |
% 121.01/83.72 | From (176) and (19) follows:
% 121.01/83.72 | (178) frontsegP(all_0_5_5, all_0_6_6) = 0
% 121.01/83.72 |
% 121.01/83.72 | From (177) and (57) follows:
% 121.01/83.72 | (179) neq(all_0_6_6, nil) = 0
% 121.01/83.72 |
% 121.01/83.72 +-Applying beta-rule and splitting (172), into two cases.
% 121.01/83.72 |-Branch one:
% 121.01/83.72 | (180) all_15_1_9 = 0
% 121.01/83.72 |
% 121.01/83.72 | From (180) and (164) follows:
% 121.01/83.72 | (181) segmentP(all_0_5_5, all_0_5_5) = 0
% 121.01/83.72 |
% 121.01/83.72 +-Applying beta-rule and splitting (157), into two cases.
% 121.01/83.72 |-Branch one:
% 121.01/83.72 | (182) ~ (neq(all_0_6_6, nil) = 0)
% 121.01/83.72 |
% 121.01/83.72 | Using (179) and (182) yields:
% 121.01/83.72 | (160) $false
% 121.01/83.73 |
% 121.01/83.73 |-The branch is then unsatisfiable
% 121.01/83.73 |-Branch two:
% 121.01/83.73 | (179) neq(all_0_6_6, nil) = 0
% 121.01/83.73 | (185) ? [v0] : ? [v1] : ? [v2] : (segmentP(all_0_5_5, all_0_6_6) = v1 & segmentP(all_0_6_6, all_0_6_6) = v2 & ssList(all_0_6_6) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 121.01/83.73 |
% 121.01/83.73 | Instantiating (185) with all_35_0_11, all_35_1_12, all_35_2_13 yields:
% 121.01/83.73 | (186) segmentP(all_0_5_5, all_0_6_6) = all_35_1_12 & segmentP(all_0_6_6, all_0_6_6) = all_35_0_11 & ssList(all_0_6_6) = all_35_2_13 & ( ~ (all_35_0_11 = 0) | ~ (all_35_1_12 = 0) | ~ (all_35_2_13 = 0))
% 121.01/83.73 |
% 121.01/83.73 | Applying alpha-rule on (186) yields:
% 121.01/83.73 | (187) segmentP(all_0_5_5, all_0_6_6) = all_35_1_12
% 121.01/83.73 | (188) segmentP(all_0_6_6, all_0_6_6) = all_35_0_11
% 121.01/83.73 | (189) ssList(all_0_6_6) = all_35_2_13
% 121.01/83.73 | (190) ~ (all_35_0_11 = 0) | ~ (all_35_1_12 = 0) | ~ (all_35_2_13 = 0)
% 121.01/83.73 |
% 121.01/83.73 +-Applying beta-rule and splitting (167), into two cases.
% 121.01/83.73 |-Branch one:
% 121.01/83.73 | (191) ~ (all_15_0_8 = 0)
% 121.01/83.73 |
% 121.01/83.73 | Instantiating formula (76) with all_0_6_6, all_35_2_13, 0 and discharging atoms ssList(all_0_6_6) = all_35_2_13, ssList(all_0_6_6) = 0, yields:
% 121.01/83.73 | (192) all_35_2_13 = 0
% 121.01/83.73 |
% 121.01/83.73 | Instantiating formula (76) with nil, all_35_2_13, 0 and discharging atoms ssList(nil) = 0, yields:
% 121.01/83.73 | (193) all_35_2_13 = 0 | ~ (ssList(nil) = all_35_2_13)
% 121.01/83.73 |
% 121.01/83.73 | From (192) and (189) follows:
% 121.01/83.73 | (3) ssList(all_0_6_6) = 0
% 121.01/83.73 |
% 121.01/83.73 +-Applying beta-rule and splitting (174), into two cases.
% 121.01/83.73 |-Branch one:
% 121.01/83.73 | (195) ~ (segmentP(all_0_6_6, nil) = all_15_0_8)
% 121.01/83.73 |
% 121.01/83.73 +-Applying beta-rule and splitting (173), into two cases.
% 121.01/83.73 |-Branch one:
% 121.01/83.73 | (196) ~ (segmentP(all_0_6_6, all_0_6_6) = all_15_0_8)
% 121.01/83.73 |
% 121.01/83.73 | Using (165) and (196) yields:
% 121.01/83.73 | (197) ~ (all_0_5_5 = all_0_6_6)
% 121.01/83.73 |
% 121.01/83.73 | Using (165) and (195) yields:
% 121.01/83.73 | (198) ~ (all_0_5_5 = nil)
% 121.01/83.73 |
% 121.01/83.73 +-Applying beta-rule and splitting (151), into two cases.
% 121.01/83.73 |-Branch one:
% 121.01/83.73 | (199) all_0_5_5 = nil
% 121.01/83.73 |
% 121.01/83.73 | Equations (199) can reduce 198 to:
% 121.01/83.73 | (200) $false
% 121.01/83.73 |
% 121.01/83.73 |-The branch is then unsatisfiable
% 121.01/83.73 |-Branch two:
% 121.01/83.73 | (198) ~ (all_0_5_5 = nil)
% 121.01/83.73 | (202) ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_5_5 & ssItem(v1) = 0)
% 121.01/83.73 |
% 121.01/83.73 | Instantiating (202) with all_61_0_14, all_61_1_15 yields:
% 121.01/83.73 | (203) ssList(all_61_1_15) = 0 & cons(all_61_0_14, all_61_1_15) = all_0_5_5 & ssItem(all_61_0_14) = 0
% 121.01/83.73 |
% 121.01/83.73 | Applying alpha-rule on (203) yields:
% 121.01/83.73 | (204) ssList(all_61_1_15) = 0
% 121.01/83.73 | (205) cons(all_61_0_14, all_61_1_15) = all_0_5_5
% 121.01/83.73 | (206) ssItem(all_61_0_14) = 0
% 121.01/83.73 |
% 121.01/83.73 | Instantiating formula (104) with all_0_5_5, all_0_5_5 and discharging atoms segmentP(all_0_5_5, all_0_5_5) = 0, ssList(all_0_5_5) = 0, yields:
% 121.01/83.73 | (207) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = all_0_5_5 & v4 = 0 & v1 = 0 & ssList(v3) = 0 & ssList(v0) = 0 & app(v2, v3) = all_0_5_5 & app(v0, all_0_5_5) = v2) | ( ~ (v0 = 0) & ssList(all_0_5_5) = v0))
% 121.01/83.73 |
% 121.01/83.73 | Instantiating formula (140) with all_35_1_12, all_0_5_5 yields:
% 121.01/83.73 | (208) all_35_1_12 = 0 | ~ (segmentP(all_0_5_5, nil) = all_35_1_12) | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_5_5) = v0)
% 121.01/83.73 |
% 121.01/83.73 | Instantiating formula (5) with all_35_0_11, all_0_6_6 and discharging atoms segmentP(all_0_6_6, all_0_6_6) = all_35_0_11, yields:
% 121.01/83.73 | (209) all_35_0_11 = 0 | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 121.01/83.73 |
% 121.01/83.73 | Instantiating formula (123) with all_0_6_6, all_0_5_5 and discharging atoms frontsegP(all_0_5_5, all_0_6_6) = 0, ssList(all_0_5_5) = 0, yields:
% 121.01/83.73 | (210) all_0_5_5 = all_0_6_6 | ? [v0] : ? [v1] : (frontsegP(all_0_6_6, all_0_5_5) = v1 & ssList(all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 121.01/83.73 |
% 121.01/83.73 | Instantiating formula (149) with all_0_6_6, all_0_5_5 and discharging atoms frontsegP(all_0_5_5, all_0_6_6) = 0, ssList(all_0_5_5) = 0, yields:
% 121.01/83.73 | (211) ? [v0] : ? [v1] : ? [v2] : ((v2 = all_0_5_5 & v1 = 0 & ssList(v0) = 0 & app(all_0_6_6, v0) = all_0_5_5) | ( ~ (v0 = 0) & ssList(all_0_6_6) = v0))
% 121.01/83.73 |
% 121.01/83.73 | Instantiating formula (22) with all_0_5_5, all_61_0_14, all_61_1_15 and discharging atoms ssList(all_61_1_15) = 0, cons(all_61_0_14, all_61_1_15) = all_0_5_5, yields:
% 121.01/83.73 | (212) ? [v0] : ? [v1] : (tl(all_0_5_5) = v1 & ssItem(all_61_0_14) = v0 & ( ~ (v0 = 0) | v1 = all_61_1_15))
% 121.01/83.73 |
% 121.01/83.73 | Instantiating formula (83) with all_0_5_5, all_61_0_14, all_61_1_15 and discharging atoms ssList(all_61_1_15) = 0, cons(all_61_0_14, all_61_1_15) = all_0_5_5, yields:
% 121.01/83.73 | (213) ? [v0] : ? [v1] : (hd(all_0_5_5) = v1 & ssItem(all_61_0_14) = v0 & ( ~ (v0 = 0) | v1 = all_61_0_14))
% 121.01/83.73 |
% 121.01/83.73 | Instantiating (213) with all_68_0_16, all_68_1_17 yields:
% 121.01/83.73 | (214) hd(all_0_5_5) = all_68_0_16 & ssItem(all_61_0_14) = all_68_1_17 & ( ~ (all_68_1_17 = 0) | all_68_0_16 = all_61_0_14)
% 121.01/83.73 |
% 121.01/83.73 | Applying alpha-rule on (214) yields:
% 121.01/83.73 | (215) hd(all_0_5_5) = all_68_0_16
% 121.01/83.73 | (216) ssItem(all_61_0_14) = all_68_1_17
% 121.01/83.73 | (217) ~ (all_68_1_17 = 0) | all_68_0_16 = all_61_0_14
% 121.01/83.73 |
% 121.01/83.73 | Instantiating (212) with all_70_0_18, all_70_1_19 yields:
% 121.01/83.73 | (218) tl(all_0_5_5) = all_70_0_18 & ssItem(all_61_0_14) = all_70_1_19 & ( ~ (all_70_1_19 = 0) | all_70_0_18 = all_61_1_15)
% 121.01/83.73 |
% 121.01/83.73 | Applying alpha-rule on (218) yields:
% 121.01/83.73 | (219) tl(all_0_5_5) = all_70_0_18
% 121.01/83.73 | (220) ssItem(all_61_0_14) = all_70_1_19
% 121.01/83.73 | (221) ~ (all_70_1_19 = 0) | all_70_0_18 = all_61_1_15
% 121.01/83.73 |
% 121.01/83.73 | Instantiating (211) with all_72_0_20, all_72_1_21, all_72_2_22 yields:
% 121.01/83.73 | (222) (all_72_0_20 = all_0_5_5 & all_72_1_21 = 0 & ssList(all_72_2_22) = 0 & app(all_0_6_6, all_72_2_22) = all_0_5_5) | ( ~ (all_72_2_22 = 0) & ssList(all_0_6_6) = all_72_2_22)
% 121.01/83.73 |
% 121.01/83.73 | Instantiating (207) with all_73_0_23, all_73_1_24, all_73_2_25, all_73_3_26, all_73_4_27, all_73_5_28 yields:
% 121.01/83.73 | (223) (all_73_0_23 = all_0_5_5 & all_73_1_24 = 0 & all_73_4_27 = 0 & ssList(all_73_2_25) = 0 & ssList(all_73_5_28) = 0 & app(all_73_3_26, all_73_2_25) = all_0_5_5 & app(all_73_5_28, all_0_5_5) = all_73_3_26) | ( ~ (all_73_5_28 = 0) & ssList(all_0_5_5) = all_73_5_28)
% 121.01/83.73 |
% 121.01/83.73 +-Applying beta-rule and splitting (222), into two cases.
% 121.01/83.73 |-Branch one:
% 121.01/83.73 | (224) all_72_0_20 = all_0_5_5 & all_72_1_21 = 0 & ssList(all_72_2_22) = 0 & app(all_0_6_6, all_72_2_22) = all_0_5_5
% 121.01/83.73 |
% 121.01/83.73 | Applying alpha-rule on (224) yields:
% 121.01/83.73 | (225) all_72_0_20 = all_0_5_5
% 121.01/83.73 | (226) all_72_1_21 = 0
% 121.01/83.73 | (227) ssList(all_72_2_22) = 0
% 121.01/83.73 | (228) app(all_0_6_6, all_72_2_22) = all_0_5_5
% 121.01/83.73 |
% 121.01/83.73 +-Applying beta-rule and splitting (210), into two cases.
% 121.01/83.73 |-Branch one:
% 121.01/83.73 | (229) all_0_5_5 = all_0_6_6
% 121.01/83.73 |
% 121.01/83.73 | Equations (229) can reduce 197 to:
% 121.01/83.73 | (200) $false
% 121.01/83.73 |
% 121.01/83.73 |-The branch is then unsatisfiable
% 121.01/83.73 |-Branch two:
% 121.01/83.73 | (197) ~ (all_0_5_5 = all_0_6_6)
% 121.01/83.73 | (232) ? [v0] : ? [v1] : (frontsegP(all_0_6_6, all_0_5_5) = v1 & ssList(all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 121.01/83.73 |
% 121.01/83.73 | Instantiating (232) with all_81_0_29, all_81_1_30 yields:
% 121.01/83.73 | (233) frontsegP(all_0_6_6, all_0_5_5) = all_81_0_29 & ssList(all_0_6_6) = all_81_1_30 & ( ~ (all_81_0_29 = 0) | ~ (all_81_1_30 = 0))
% 121.01/83.73 |
% 121.01/83.73 | Applying alpha-rule on (233) yields:
% 121.01/83.73 | (234) frontsegP(all_0_6_6, all_0_5_5) = all_81_0_29
% 121.01/83.73 | (235) ssList(all_0_6_6) = all_81_1_30
% 121.01/83.73 | (236) ~ (all_81_0_29 = 0) | ~ (all_81_1_30 = 0)
% 121.01/83.73 |
% 121.01/83.73 +-Applying beta-rule and splitting (223), into two cases.
% 121.01/83.73 |-Branch one:
% 121.01/83.73 | (237) all_73_0_23 = all_0_5_5 & all_73_1_24 = 0 & all_73_4_27 = 0 & ssList(all_73_2_25) = 0 & ssList(all_73_5_28) = 0 & app(all_73_3_26, all_73_2_25) = all_0_5_5 & app(all_73_5_28, all_0_5_5) = all_73_3_26
% 121.01/83.73 |
% 121.01/83.73 | Applying alpha-rule on (237) yields:
% 121.01/83.73 | (238) all_73_4_27 = 0
% 121.01/83.73 | (239) all_73_0_23 = all_0_5_5
% 121.01/83.73 | (240) app(all_73_5_28, all_0_5_5) = all_73_3_26
% 121.01/83.73 | (241) all_73_1_24 = 0
% 121.01/83.73 | (242) ssList(all_73_2_25) = 0
% 121.01/83.73 | (243) ssList(all_73_5_28) = 0
% 121.01/83.73 | (244) app(all_73_3_26, all_73_2_25) = all_0_5_5
% 121.01/83.73 |
% 121.01/83.73 | Instantiating formula (76) with all_0_6_6, all_81_1_30, 0 and discharging atoms ssList(all_0_6_6) = all_81_1_30, ssList(all_0_6_6) = 0, yields:
% 121.01/83.73 | (245) all_81_1_30 = 0
% 121.01/83.73 |
% 121.01/83.73 | Instantiating formula (76) with nil, all_81_1_30, 0 and discharging atoms ssList(nil) = 0, yields:
% 121.01/83.73 | (246) all_81_1_30 = 0 | ~ (ssList(nil) = all_81_1_30)
% 121.01/83.73 |
% 121.01/83.73 | Instantiating formula (4) with all_61_0_14, all_70_1_19, 0 and discharging atoms ssItem(all_61_0_14) = all_70_1_19, ssItem(all_61_0_14) = 0, yields:
% 121.01/83.73 | (247) all_70_1_19 = 0
% 121.01/83.73 |
% 121.01/83.73 | Instantiating formula (4) with all_61_0_14, all_68_1_17, all_70_1_19 and discharging atoms ssItem(all_61_0_14) = all_70_1_19, ssItem(all_61_0_14) = all_68_1_17, yields:
% 121.01/83.73 | (248) all_70_1_19 = all_68_1_17
% 121.01/83.73 |
% 121.01/83.74 | Combining equations (247,248) yields a new equation:
% 121.01/83.74 | (249) all_68_1_17 = 0
% 121.01/83.74 |
% 121.01/83.74 | Combining equations (249,248) yields a new equation:
% 121.01/83.74 | (247) all_70_1_19 = 0
% 121.01/83.74 |
% 121.01/83.74 | From (245) and (235) follows:
% 121.01/83.74 | (3) ssList(all_0_6_6) = 0
% 121.01/83.74 |
% 121.01/83.74 | From (249) and (216) follows:
% 121.01/83.74 | (206) ssItem(all_61_0_14) = 0
% 121.01/83.74 |
% 121.01/83.74 +-Applying beta-rule and splitting (209), into two cases.
% 121.01/83.74 |-Branch one:
% 121.01/83.74 | (253) all_35_0_11 = 0
% 121.01/83.74 |
% 121.01/83.74 | From (253) and (188) follows:
% 121.01/83.74 | (254) segmentP(all_0_6_6, all_0_6_6) = 0
% 121.01/83.74 |
% 121.01/83.74 +-Applying beta-rule and splitting (190), into two cases.
% 121.01/83.74 |-Branch one:
% 121.01/83.74 | (255) ~ (all_35_0_11 = 0)
% 121.01/83.74 |
% 121.01/83.74 | Equations (253) can reduce 255 to:
% 121.01/83.74 | (200) $false
% 121.01/83.74 |
% 121.01/83.74 |-The branch is then unsatisfiable
% 121.01/83.74 |-Branch two:
% 121.01/83.74 | (253) all_35_0_11 = 0
% 121.01/83.74 | (258) ~ (all_35_1_12 = 0) | ~ (all_35_2_13 = 0)
% 121.01/83.74 |
% 121.01/83.74 +-Applying beta-rule and splitting (258), into two cases.
% 121.01/83.74 |-Branch one:
% 121.01/83.74 | (259) ~ (all_35_1_12 = 0)
% 121.01/83.74 |
% 121.01/83.74 +-Applying beta-rule and splitting (208), into two cases.
% 121.01/83.74 |-Branch one:
% 121.01/83.74 | (260) ~ (segmentP(all_0_5_5, nil) = all_35_1_12)
% 121.01/83.74 |
% 121.01/83.74 +-Applying beta-rule and splitting (221), into two cases.
% 121.01/83.74 |-Branch one:
% 121.01/83.74 | (261) ~ (all_70_1_19 = 0)
% 121.01/83.74 |
% 121.01/83.74 | Equations (247) can reduce 261 to:
% 121.01/83.74 | (200) $false
% 121.01/83.74 |
% 121.01/83.74 |-The branch is then unsatisfiable
% 121.01/83.74 |-Branch two:
% 121.01/83.74 | (247) all_70_1_19 = 0
% 121.01/83.74 | (264) all_70_0_18 = all_61_1_15
% 121.01/83.74 |
% 121.01/83.74 | From (264) and (219) follows:
% 121.01/83.74 | (265) tl(all_0_5_5) = all_61_1_15
% 121.01/83.74 |
% 121.01/83.74 | Using (187) and (260) yields:
% 121.01/83.74 | (266) ~ (all_0_6_6 = nil)
% 121.01/83.74 |
% 121.01/83.74 +-Applying beta-rule and splitting (152), into two cases.
% 121.01/83.74 |-Branch one:
% 121.01/83.74 | (267) all_0_6_6 = nil
% 121.01/83.74 |
% 121.01/83.74 | Equations (267) can reduce 266 to:
% 121.01/83.74 | (200) $false
% 121.01/83.74 |
% 121.01/83.74 |-The branch is then unsatisfiable
% 121.01/83.74 |-Branch two:
% 121.01/83.74 | (266) ~ (all_0_6_6 = nil)
% 121.01/83.74 | (270) ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_6_6 & ssItem(v1) = 0)
% 121.01/83.74 |
% 121.01/83.74 | Instantiating (270) with all_127_0_31, all_127_1_32 yields:
% 121.01/83.74 | (271) ssList(all_127_1_32) = 0 & cons(all_127_0_31, all_127_1_32) = all_0_6_6 & ssItem(all_127_0_31) = 0
% 121.01/83.74 |
% 121.01/83.74 | Applying alpha-rule on (271) yields:
% 121.01/83.74 | (272) ssList(all_127_1_32) = 0
% 121.01/83.74 | (273) cons(all_127_0_31, all_127_1_32) = all_0_6_6
% 121.01/83.74 | (274) ssItem(all_127_0_31) = 0
% 121.01/83.74 |
% 121.01/83.74 | Instantiating formula (105) with all_61_1_15, all_0_5_5 and discharging atoms tl(all_0_5_5) = all_61_1_15, yields:
% 121.01/83.74 | (275) ? [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) = all_61_1_15) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssList(v2) = v3 & ( ~ (v4 = v1) | ~ (v3 = 0))))))
% 121.01/83.74 |
% 121.01/83.74 | Instantiating formula (104) with all_0_6_6, all_0_6_6 and discharging atoms segmentP(all_0_6_6, all_0_6_6) = 0, ssList(all_0_6_6) = 0, yields:
% 121.01/83.74 | (276) ? [v0] : ? [v1] : ? [v2] : ? [v3] : ? [v4] : ? [v5] : ((v5 = all_0_6_6 & v4 = 0 & v1 = 0 & ssList(v3) = 0 & ssList(v0) = 0 & app(v2, v3) = all_0_6_6 & app(v0, all_0_6_6) = v2) | ( ~ (v0 = 0) & ssList(all_0_6_6) = v0))
% 121.01/83.74 |
% 121.01/83.74 | Instantiating formula (35) with all_81_0_29, all_0_5_5, all_61_1_15, all_0_6_6, all_127_1_32, all_61_0_14, all_61_0_14 and discharging atoms frontsegP(all_0_6_6, all_0_5_5) = all_81_0_29, cons(all_61_0_14, all_61_1_15) = all_0_5_5, ssItem(all_61_0_14) = 0, yields:
% 121.01/83.74 | (277) ~ (cons(all_61_0_14, all_127_1_32) = all_0_6_6) | ? [v0] : ? [v1] : (( ~ (v0 = 0) & ssList(all_127_1_32) = v0) | (frontsegP(all_127_1_32, all_61_1_15) = v1 & ssList(all_61_1_15) = v0 & ( ~ (v0 = 0) | (( ~ (v1 = 0) | all_81_0_29 = 0) & ( ~ (all_81_0_29 = 0) | v1 = 0)))))
% 121.01/83.74 |
% 121.01/83.74 | Instantiating formula (22) with all_0_6_6, all_127_0_31, all_127_1_32 and discharging atoms ssList(all_127_1_32) = 0, cons(all_127_0_31, all_127_1_32) = all_0_6_6, yields:
% 121.01/83.74 | (278) ? [v0] : ? [v1] : (tl(all_0_6_6) = v1 & ssItem(all_127_0_31) = v0 & ( ~ (v0 = 0) | v1 = all_127_1_32))
% 121.01/83.74 |
% 121.01/83.74 | Instantiating formula (83) with all_0_6_6, all_127_0_31, all_127_1_32 and discharging atoms ssList(all_127_1_32) = 0, cons(all_127_0_31, all_127_1_32) = all_0_6_6, yields:
% 121.01/83.74 | (279) ? [v0] : ? [v1] : (hd(all_0_6_6) = v1 & ssItem(all_127_0_31) = v0 & ( ~ (v0 = 0) | v1 = all_127_0_31))
% 121.01/83.74 |
% 121.01/83.74 | Instantiating formula (8) with all_0_5_5, all_73_2_25, all_73_3_26, all_0_5_5, all_73_5_28 and discharging atoms ssList(all_73_5_28) = 0, app(all_73_3_26, all_73_2_25) = all_0_5_5, app(all_73_5_28, all_0_5_5) = all_73_3_26, yields:
% 121.01/83.74 | (280) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & ssList(all_0_5_5) = v0) | (ssList(all_73_2_25) = v0 & app(all_73_5_28, v1) = v2 & app(all_0_5_5, all_73_2_25) = v1 & ( ~ (v0 = 0) | v2 = all_0_5_5)))
% 121.01/83.74 |
% 121.01/83.74 | Instantiating formula (91) with all_73_3_26, all_0_5_5, all_73_5_28 and discharging atoms ssList(all_73_5_28) = 0, app(all_73_5_28, all_0_5_5) = all_73_3_26, yields:
% 121.01/83.74 | (281) ? [v0] : ? [v1] : (ssList(all_73_3_26) = v1 & ssList(all_0_5_5) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 121.01/83.74 |
% 121.01/83.74 | Instantiating formula (35) with 0, all_0_6_6, all_127_1_32, all_0_5_5, all_61_1_15, all_127_0_31, all_61_0_14 and discharging atoms frontsegP(all_0_5_5, all_0_6_6) = 0, cons(all_127_0_31, all_127_1_32) = all_0_6_6, cons(all_61_0_14, all_61_1_15) = all_0_5_5, ssItem(all_127_0_31) = 0, ssItem(all_61_0_14) = 0, yields:
% 121.01/83.74 | (282) ? [v0] : ? [v1] : (( ~ (v0 = 0) & ssList(all_61_1_15) = v0) | (frontsegP(all_61_1_15, all_127_1_32) = v1 & ssList(all_127_1_32) = v0 & ( ~ (v0 = 0) | (v1 = 0 & all_127_0_31 = all_61_0_14))))
% 121.01/83.74 |
% 121.01/83.74 | Instantiating formula (35) with all_81_0_29, all_0_5_5, all_61_1_15, all_0_6_6, all_127_1_32, all_61_0_14, all_127_0_31 and discharging atoms frontsegP(all_0_6_6, all_0_5_5) = all_81_0_29, cons(all_127_0_31, all_127_1_32) = all_0_6_6, cons(all_61_0_14, all_61_1_15) = all_0_5_5, ssItem(all_127_0_31) = 0, ssItem(all_61_0_14) = 0, yields:
% 121.01/83.74 | (283) ? [v0] : ? [v1] : (( ~ (v0 = 0) & ssList(all_127_1_32) = v0) | (frontsegP(all_127_1_32, all_61_1_15) = v1 & ssList(all_61_1_15) = v0 & ( ~ (v0 = 0) | (( ~ (v1 = 0) | ~ (all_127_0_31 = all_61_0_14) | all_81_0_29 = 0) & ( ~ (all_81_0_29 = 0) | (v1 = 0 & all_127_0_31 = all_61_0_14))))))
% 121.01/83.74 |
% 121.01/83.74 | Instantiating (283) with all_134_0_33, all_134_1_34 yields:
% 121.01/83.74 | (284) ( ~ (all_134_1_34 = 0) & ssList(all_127_1_32) = all_134_1_34) | (frontsegP(all_127_1_32, all_61_1_15) = all_134_0_33 & ssList(all_61_1_15) = all_134_1_34 & ( ~ (all_134_1_34 = 0) | (( ~ (all_134_0_33 = 0) | ~ (all_127_0_31 = all_61_0_14) | all_81_0_29 = 0) & ( ~ (all_81_0_29 = 0) | (all_134_0_33 = 0 & all_127_0_31 = all_61_0_14)))))
% 121.01/83.74 |
% 121.01/83.74 | Instantiating (281) with all_135_0_35, all_135_1_36 yields:
% 121.01/83.74 | (285) ssList(all_73_3_26) = all_135_0_35 & ssList(all_0_5_5) = all_135_1_36 & ( ~ (all_135_1_36 = 0) | all_135_0_35 = 0)
% 121.01/83.74 |
% 121.01/83.74 | Applying alpha-rule on (285) yields:
% 121.01/83.74 | (286) ssList(all_73_3_26) = all_135_0_35
% 121.01/83.74 | (287) ssList(all_0_5_5) = all_135_1_36
% 121.01/83.74 | (288) ~ (all_135_1_36 = 0) | all_135_0_35 = 0
% 121.01/83.74 |
% 121.01/83.74 | Instantiating (280) with all_137_0_37, all_137_1_38, all_137_2_39 yields:
% 121.01/83.74 | (289) ( ~ (all_137_2_39 = 0) & ssList(all_0_5_5) = all_137_2_39) | (ssList(all_73_2_25) = all_137_2_39 & app(all_73_5_28, all_137_1_38) = all_137_0_37 & app(all_0_5_5, all_73_2_25) = all_137_1_38 & ( ~ (all_137_2_39 = 0) | all_137_0_37 = all_0_5_5))
% 121.01/83.74 |
% 121.01/83.74 | Instantiating (282) with all_138_0_40, all_138_1_41 yields:
% 121.01/83.74 | (290) ( ~ (all_138_1_41 = 0) & ssList(all_61_1_15) = all_138_1_41) | (frontsegP(all_61_1_15, all_127_1_32) = all_138_0_40 & ssList(all_127_1_32) = all_138_1_41 & ( ~ (all_138_1_41 = 0) | (all_138_0_40 = 0 & all_127_0_31 = all_61_0_14)))
% 121.01/83.74 |
% 121.01/83.74 | Instantiating (279) with all_139_0_42, all_139_1_43 yields:
% 121.01/83.74 | (291) hd(all_0_6_6) = all_139_0_42 & ssItem(all_127_0_31) = all_139_1_43 & ( ~ (all_139_1_43 = 0) | all_139_0_42 = all_127_0_31)
% 121.01/83.74 |
% 121.01/83.74 | Applying alpha-rule on (291) yields:
% 121.01/83.74 | (292) hd(all_0_6_6) = all_139_0_42
% 121.01/83.74 | (293) ssItem(all_127_0_31) = all_139_1_43
% 121.01/83.74 | (294) ~ (all_139_1_43 = 0) | all_139_0_42 = all_127_0_31
% 121.01/83.74 |
% 121.01/83.74 | Instantiating (278) with all_141_0_44, all_141_1_45 yields:
% 121.01/83.74 | (295) tl(all_0_6_6) = all_141_0_44 & ssItem(all_127_0_31) = all_141_1_45 & ( ~ (all_141_1_45 = 0) | all_141_0_44 = all_127_1_32)
% 121.01/83.74 |
% 121.01/83.74 | Applying alpha-rule on (295) yields:
% 121.01/83.74 | (296) tl(all_0_6_6) = all_141_0_44
% 121.01/83.74 | (297) ssItem(all_127_0_31) = all_141_1_45
% 121.01/83.74 | (298) ~ (all_141_1_45 = 0) | all_141_0_44 = all_127_1_32
% 121.01/83.74 |
% 121.01/83.74 | Instantiating (276) with all_143_0_46, all_143_1_47, all_143_2_48, all_143_3_49, all_143_4_50, all_143_5_51 yields:
% 121.01/83.74 | (299) (all_143_0_46 = all_0_6_6 & all_143_1_47 = 0 & all_143_4_50 = 0 & ssList(all_143_2_48) = 0 & ssList(all_143_5_51) = 0 & app(all_143_3_49, all_143_2_48) = all_0_6_6 & app(all_143_5_51, all_0_6_6) = all_143_3_49) | ( ~ (all_143_5_51 = 0) & ssList(all_0_6_6) = all_143_5_51)
% 121.01/83.74 |
% 121.01/83.74 | Instantiating (275) with all_144_0_52, all_144_1_53 yields:
% 121.01/83.74 | (300) hd(all_0_5_5) = all_144_0_52 & ssList(all_0_5_5) = all_144_1_53 & ( ~ (all_144_1_53 = 0) | ! [v0] : (v0 = all_0_5_5 | v0 = nil | all_0_5_5 = nil | ~ (tl(v0) = all_61_1_15) | ? [v1] : ? [v2] : (hd(v0) = v2 & ssList(v0) = v1 & ( ~ (v2 = all_144_0_52) | ~ (v1 = 0)))))
% 121.01/83.75 |
% 121.01/83.75 | Applying alpha-rule on (300) yields:
% 121.01/83.75 | (301) hd(all_0_5_5) = all_144_0_52
% 121.01/83.75 | (302) ssList(all_0_5_5) = all_144_1_53
% 121.01/83.75 | (303) ~ (all_144_1_53 = 0) | ! [v0] : (v0 = all_0_5_5 | v0 = nil | all_0_5_5 = nil | ~ (tl(v0) = all_61_1_15) | ? [v1] : ? [v2] : (hd(v0) = v2 & ssList(v0) = v1 & ( ~ (v2 = all_144_0_52) | ~ (v1 = 0))))
% 121.01/83.75 |
% 121.01/83.75 +-Applying beta-rule and splitting (284), into two cases.
% 121.01/83.75 |-Branch one:
% 121.01/83.75 | (304) ~ (all_134_1_34 = 0) & ssList(all_127_1_32) = all_134_1_34
% 121.01/83.75 |
% 121.01/83.75 | Applying alpha-rule on (304) yields:
% 121.01/83.75 | (305) ~ (all_134_1_34 = 0)
% 121.01/83.75 | (306) ssList(all_127_1_32) = all_134_1_34
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_127_1_32, all_134_1_34, 0 and discharging atoms ssList(all_127_1_32) = all_134_1_34, ssList(all_127_1_32) = 0, yields:
% 121.01/83.75 | (307) all_134_1_34 = 0
% 121.01/83.75 |
% 121.01/83.75 | Equations (307) can reduce 305 to:
% 121.01/83.75 | (200) $false
% 121.01/83.75 |
% 121.01/83.75 |-The branch is then unsatisfiable
% 121.01/83.75 |-Branch two:
% 121.01/83.75 | (309) frontsegP(all_127_1_32, all_61_1_15) = all_134_0_33 & ssList(all_61_1_15) = all_134_1_34 & ( ~ (all_134_1_34 = 0) | (( ~ (all_134_0_33 = 0) | ~ (all_127_0_31 = all_61_0_14) | all_81_0_29 = 0) & ( ~ (all_81_0_29 = 0) | (all_134_0_33 = 0 & all_127_0_31 = all_61_0_14))))
% 121.01/83.75 |
% 121.01/83.75 | Applying alpha-rule on (309) yields:
% 121.01/83.75 | (310) frontsegP(all_127_1_32, all_61_1_15) = all_134_0_33
% 121.01/83.75 | (311) ssList(all_61_1_15) = all_134_1_34
% 121.01/83.75 | (312) ~ (all_134_1_34 = 0) | (( ~ (all_134_0_33 = 0) | ~ (all_127_0_31 = all_61_0_14) | all_81_0_29 = 0) & ( ~ (all_81_0_29 = 0) | (all_134_0_33 = 0 & all_127_0_31 = all_61_0_14)))
% 121.01/83.75 |
% 121.01/83.75 +-Applying beta-rule and splitting (299), into two cases.
% 121.01/83.75 |-Branch one:
% 121.01/83.75 | (313) all_143_0_46 = all_0_6_6 & all_143_1_47 = 0 & all_143_4_50 = 0 & ssList(all_143_2_48) = 0 & ssList(all_143_5_51) = 0 & app(all_143_3_49, all_143_2_48) = all_0_6_6 & app(all_143_5_51, all_0_6_6) = all_143_3_49
% 121.01/83.75 |
% 121.01/83.75 | Applying alpha-rule on (313) yields:
% 121.01/83.75 | (314) app(all_143_5_51, all_0_6_6) = all_143_3_49
% 121.01/83.75 | (315) all_143_0_46 = all_0_6_6
% 121.01/83.75 | (316) ssList(all_143_2_48) = 0
% 121.01/83.75 | (317) ssList(all_143_5_51) = 0
% 121.01/83.75 | (318) app(all_143_3_49, all_143_2_48) = all_0_6_6
% 121.01/83.75 | (319) all_143_1_47 = 0
% 121.01/83.75 | (320) all_143_4_50 = 0
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_73_3_26, all_135_0_35, 0 and discharging atoms ssList(all_73_3_26) = all_135_0_35, yields:
% 121.01/83.75 | (321) all_135_0_35 = 0 | ~ (ssList(all_73_3_26) = 0)
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_72_2_22, all_135_0_35, 0 and discharging atoms ssList(all_72_2_22) = 0, yields:
% 121.01/83.75 | (322) all_135_0_35 = 0 | ~ (ssList(all_72_2_22) = all_135_0_35)
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_61_1_15, all_135_0_35, 0 and discharging atoms ssList(all_61_1_15) = 0, yields:
% 121.01/83.75 | (323) all_135_0_35 = 0 | ~ (ssList(all_61_1_15) = all_135_0_35)
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_0_5_5, all_135_0_35, 0 and discharging atoms ssList(all_0_5_5) = 0, yields:
% 121.01/83.75 | (324) all_135_0_35 = 0 | ~ (ssList(all_0_5_5) = all_135_0_35)
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_0_6_6, all_135_0_35, 0 and discharging atoms ssList(all_0_6_6) = 0, yields:
% 121.01/83.75 | (325) all_135_0_35 = 0 | ~ (ssList(all_0_6_6) = all_135_0_35)
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with nil, all_135_0_35, 0 and discharging atoms ssList(nil) = 0, yields:
% 121.01/83.75 | (326) all_135_0_35 = 0 | ~ (ssList(nil) = all_135_0_35)
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_61_1_15, all_134_1_34, 0 and discharging atoms ssList(all_61_1_15) = all_134_1_34, ssList(all_61_1_15) = 0, yields:
% 121.01/83.75 | (307) all_134_1_34 = 0
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_0_5_5, all_134_1_34, 0 and discharging atoms ssList(all_0_5_5) = 0, yields:
% 121.01/83.75 | (328) all_134_1_34 = 0 | ~ (ssList(all_0_5_5) = all_134_1_34)
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_0_6_6, all_134_1_34, 0 and discharging atoms ssList(all_0_6_6) = 0, yields:
% 121.01/83.75 | (329) all_134_1_34 = 0 | ~ (ssList(all_0_6_6) = all_134_1_34)
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with nil, all_134_1_34, 0 and discharging atoms ssList(nil) = 0, yields:
% 121.01/83.75 | (330) all_134_1_34 = 0 | ~ (ssList(nil) = all_134_1_34)
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_61_1_15, all_134_1_34, all_135_0_35 and discharging atoms ssList(all_61_1_15) = all_134_1_34, yields:
% 121.01/83.75 | (331) all_135_0_35 = all_134_1_34 | ~ (ssList(all_61_1_15) = all_135_0_35)
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_0_5_5, all_144_1_53, 0 and discharging atoms ssList(all_0_5_5) = all_144_1_53, ssList(all_0_5_5) = 0, yields:
% 121.01/83.75 | (332) all_144_1_53 = 0
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_0_5_5, all_144_1_53, all_135_0_35 and discharging atoms ssList(all_0_5_5) = all_144_1_53, yields:
% 121.01/83.75 | (333) all_144_1_53 = all_135_0_35 | ~ (ssList(all_0_5_5) = all_135_0_35)
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_0_5_5, all_144_1_53, all_134_1_34 and discharging atoms ssList(all_0_5_5) = all_144_1_53, yields:
% 121.01/83.75 | (334) all_144_1_53 = all_134_1_34 | ~ (ssList(all_0_5_5) = all_134_1_34)
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_0_5_5, all_135_1_36, all_135_0_35 and discharging atoms ssList(all_0_5_5) = all_135_1_36, yields:
% 121.01/83.75 | (335) all_135_0_35 = all_135_1_36 | ~ (ssList(all_0_5_5) = all_135_0_35)
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_0_5_5, all_135_1_36, all_134_1_34 and discharging atoms ssList(all_0_5_5) = all_135_1_36, yields:
% 121.01/83.75 | (336) all_135_1_36 = all_134_1_34 | ~ (ssList(all_0_5_5) = all_134_1_34)
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_0_5_5, all_135_1_36, all_144_1_53 and discharging atoms ssList(all_0_5_5) = all_144_1_53, ssList(all_0_5_5) = all_135_1_36, yields:
% 121.01/83.75 | (337) all_144_1_53 = all_135_1_36
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (4) with all_127_0_31, all_141_1_45, 0 and discharging atoms ssItem(all_127_0_31) = all_141_1_45, ssItem(all_127_0_31) = 0, yields:
% 121.01/83.75 | (338) all_141_1_45 = 0
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (4) with all_127_0_31, all_139_1_43, all_141_1_45 and discharging atoms ssItem(all_127_0_31) = all_141_1_45, ssItem(all_127_0_31) = all_139_1_43, yields:
% 121.01/83.75 | (339) all_141_1_45 = all_139_1_43
% 121.01/83.75 |
% 121.01/83.75 | Combining equations (332,337) yields a new equation:
% 121.01/83.75 | (340) all_135_1_36 = 0
% 121.01/83.75 |
% 121.01/83.75 | Combining equations (338,339) yields a new equation:
% 121.01/83.75 | (341) all_139_1_43 = 0
% 121.01/83.75 |
% 121.01/83.75 | Combining equations (341,339) yields a new equation:
% 121.01/83.75 | (338) all_141_1_45 = 0
% 121.01/83.75 |
% 121.01/83.75 | Combining equations (340,337) yields a new equation:
% 121.01/83.75 | (332) all_144_1_53 = 0
% 121.01/83.75 |
% 121.01/83.75 | From (307) and (311) follows:
% 121.01/83.75 | (204) ssList(all_61_1_15) = 0
% 121.01/83.75 |
% 121.01/83.75 | From (340) and (287) follows:
% 121.01/83.75 | (74) ssList(all_0_5_5) = 0
% 121.01/83.75 |
% 121.01/83.75 +-Applying beta-rule and splitting (298), into two cases.
% 121.01/83.75 |-Branch one:
% 121.01/83.75 | (346) ~ (all_141_1_45 = 0)
% 121.01/83.75 |
% 121.01/83.75 | Equations (338) can reduce 346 to:
% 121.01/83.75 | (200) $false
% 121.01/83.75 |
% 121.01/83.75 |-The branch is then unsatisfiable
% 121.01/83.75 |-Branch two:
% 121.01/83.75 | (338) all_141_1_45 = 0
% 121.01/83.75 | (349) all_141_0_44 = all_127_1_32
% 121.01/83.75 |
% 121.01/83.75 | From (349) and (296) follows:
% 121.01/83.75 | (350) tl(all_0_6_6) = all_127_1_32
% 121.01/83.75 |
% 121.01/83.75 +-Applying beta-rule and splitting (289), into two cases.
% 121.01/83.75 |-Branch one:
% 121.01/83.75 | (351) ~ (all_137_2_39 = 0) & ssList(all_0_5_5) = all_137_2_39
% 121.01/83.75 |
% 121.01/83.75 | Applying alpha-rule on (351) yields:
% 121.01/83.75 | (352) ~ (all_137_2_39 = 0)
% 121.01/83.75 | (353) ssList(all_0_5_5) = all_137_2_39
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_0_5_5, all_137_2_39, 0 and discharging atoms ssList(all_0_5_5) = all_137_2_39, ssList(all_0_5_5) = 0, yields:
% 121.01/83.75 | (354) all_137_2_39 = 0
% 121.01/83.75 |
% 121.01/83.75 | Equations (354) can reduce 352 to:
% 121.01/83.75 | (200) $false
% 121.01/83.75 |
% 121.01/83.75 |-The branch is then unsatisfiable
% 121.01/83.75 |-Branch two:
% 121.01/83.75 | (356) ssList(all_73_2_25) = all_137_2_39 & app(all_73_5_28, all_137_1_38) = all_137_0_37 & app(all_0_5_5, all_73_2_25) = all_137_1_38 & ( ~ (all_137_2_39 = 0) | all_137_0_37 = all_0_5_5)
% 121.01/83.75 |
% 121.01/83.75 | Applying alpha-rule on (356) yields:
% 121.01/83.75 | (357) ssList(all_73_2_25) = all_137_2_39
% 121.01/83.75 | (358) app(all_73_5_28, all_137_1_38) = all_137_0_37
% 121.01/83.75 | (359) app(all_0_5_5, all_73_2_25) = all_137_1_38
% 121.01/83.75 | (360) ~ (all_137_2_39 = 0) | all_137_0_37 = all_0_5_5
% 121.01/83.75 |
% 121.01/83.75 +-Applying beta-rule and splitting (288), into two cases.
% 121.01/83.75 |-Branch one:
% 121.01/83.75 | (361) ~ (all_135_1_36 = 0)
% 121.01/83.75 |
% 121.01/83.75 | Equations (340) can reduce 361 to:
% 121.01/83.75 | (200) $false
% 121.01/83.75 |
% 121.01/83.75 |-The branch is then unsatisfiable
% 121.01/83.75 |-Branch two:
% 121.01/83.75 | (340) all_135_1_36 = 0
% 121.01/83.75 | (364) all_135_0_35 = 0
% 121.01/83.75 |
% 121.01/83.75 | From (364) and (286) follows:
% 121.01/83.75 | (365) ssList(all_73_3_26) = 0
% 121.01/83.75 |
% 121.01/83.75 +-Applying beta-rule and splitting (290), into two cases.
% 121.01/83.75 |-Branch one:
% 121.01/83.75 | (366) ~ (all_138_1_41 = 0) & ssList(all_61_1_15) = all_138_1_41
% 121.01/83.75 |
% 121.01/83.75 | Applying alpha-rule on (366) yields:
% 121.01/83.75 | (367) ~ (all_138_1_41 = 0)
% 121.01/83.75 | (368) ssList(all_61_1_15) = all_138_1_41
% 121.01/83.75 |
% 121.01/83.75 | Instantiating formula (76) with all_61_1_15, all_138_1_41, 0 and discharging atoms ssList(all_61_1_15) = all_138_1_41, ssList(all_61_1_15) = 0, yields:
% 121.01/83.76 | (369) all_138_1_41 = 0
% 121.01/83.76 |
% 121.01/83.76 | Equations (369) can reduce 367 to:
% 121.01/83.76 | (200) $false
% 121.01/83.76 |
% 121.01/83.76 |-The branch is then unsatisfiable
% 121.01/83.76 |-Branch two:
% 121.01/83.76 | (371) frontsegP(all_61_1_15, all_127_1_32) = all_138_0_40 & ssList(all_127_1_32) = all_138_1_41 & ( ~ (all_138_1_41 = 0) | (all_138_0_40 = 0 & all_127_0_31 = all_61_0_14))
% 121.01/83.76 |
% 121.01/83.76 | Applying alpha-rule on (371) yields:
% 121.01/83.76 | (372) frontsegP(all_61_1_15, all_127_1_32) = all_138_0_40
% 121.01/83.76 | (373) ssList(all_127_1_32) = all_138_1_41
% 121.01/83.76 | (374) ~ (all_138_1_41 = 0) | (all_138_0_40 = 0 & all_127_0_31 = all_61_0_14)
% 121.01/83.76 |
% 121.01/83.76 +-Applying beta-rule and splitting (303), into two cases.
% 121.01/83.76 |-Branch one:
% 121.01/83.76 | (375) ~ (all_144_1_53 = 0)
% 121.01/83.76 |
% 121.01/83.76 | Equations (332) can reduce 375 to:
% 121.01/83.76 | (200) $false
% 121.01/83.76 |
% 121.01/83.76 |-The branch is then unsatisfiable
% 121.01/83.76 |-Branch two:
% 121.01/83.76 | (332) all_144_1_53 = 0
% 121.01/83.76 | (378) ! [v0] : (v0 = all_0_5_5 | v0 = nil | all_0_5_5 = nil | ~ (tl(v0) = all_61_1_15) | ? [v1] : ? [v2] : (hd(v0) = v2 & ssList(v0) = v1 & ( ~ (v2 = all_144_0_52) | ~ (v1 = 0))))
% 121.01/83.76 |
% 121.01/83.76 | Instantiating formula (76) with all_127_1_32, all_138_1_41, 0 and discharging atoms ssList(all_127_1_32) = all_138_1_41, ssList(all_127_1_32) = 0, yields:
% 121.01/83.76 | (369) all_138_1_41 = 0
% 121.01/83.76 |
% 121.01/83.76 | Instantiating formula (76) with all_73_2_25, all_137_2_39, 0 and discharging atoms ssList(all_73_2_25) = all_137_2_39, ssList(all_73_2_25) = 0, yields:
% 121.01/83.76 | (354) all_137_2_39 = 0
% 121.01/83.76 |
% 121.01/83.76 | From (369) and (373) follows:
% 121.01/83.76 | (272) ssList(all_127_1_32) = 0
% 121.01/83.76 |
% 121.01/83.76 +-Applying beta-rule and splitting (374), into two cases.
% 121.01/83.76 |-Branch one:
% 121.01/83.76 | (367) ~ (all_138_1_41 = 0)
% 121.01/83.76 |
% 121.01/83.76 | Equations (369) can reduce 367 to:
% 121.01/83.76 | (200) $false
% 121.01/83.76 |
% 121.01/83.76 |-The branch is then unsatisfiable
% 121.01/83.76 |-Branch two:
% 121.01/83.76 | (369) all_138_1_41 = 0
% 121.01/83.76 | (385) all_138_0_40 = 0 & all_127_0_31 = all_61_0_14
% 121.01/83.76 |
% 121.01/83.76 | Applying alpha-rule on (385) yields:
% 121.01/83.76 | (386) all_138_0_40 = 0
% 121.01/83.76 | (387) all_127_0_31 = all_61_0_14
% 121.01/83.76 |
% 121.01/83.76 | From (387) and (273) follows:
% 121.01/83.76 | (388) cons(all_61_0_14, all_127_1_32) = all_0_6_6
% 121.01/83.76 |
% 121.01/83.76 +-Applying beta-rule and splitting (312), into two cases.
% 121.01/83.76 |-Branch one:
% 121.01/83.76 | (305) ~ (all_134_1_34 = 0)
% 121.01/83.76 |
% 121.01/83.76 | Equations (307) can reduce 305 to:
% 121.01/83.76 | (200) $false
% 121.01/83.76 |
% 121.01/83.76 |-The branch is then unsatisfiable
% 121.01/83.76 |-Branch two:
% 121.01/83.76 | (307) all_134_1_34 = 0
% 121.01/83.76 | (392) ( ~ (all_134_0_33 = 0) | ~ (all_127_0_31 = all_61_0_14) | all_81_0_29 = 0) & ( ~ (all_81_0_29 = 0) | (all_134_0_33 = 0 & all_127_0_31 = all_61_0_14))
% 121.01/83.76 |
% 121.01/83.76 +-Applying beta-rule and splitting (360), into two cases.
% 121.01/83.76 |-Branch one:
% 121.01/83.76 | (352) ~ (all_137_2_39 = 0)
% 121.01/83.76 |
% 121.01/83.76 | Equations (354) can reduce 352 to:
% 121.01/83.76 | (200) $false
% 121.01/83.76 |
% 121.01/83.76 |-The branch is then unsatisfiable
% 121.01/83.76 |-Branch two:
% 121.01/83.76 | (354) all_137_2_39 = 0
% 121.01/83.76 | (396) all_137_0_37 = all_0_5_5
% 121.01/83.76 |
% 121.01/83.76 | From (396) and (358) follows:
% 121.01/83.76 | (397) app(all_73_5_28, all_137_1_38) = all_0_5_5
% 121.01/83.76 |
% 121.01/83.76 +-Applying beta-rule and splitting (277), into two cases.
% 121.01/83.76 |-Branch one:
% 121.01/83.76 | (398) ~ (cons(all_61_0_14, all_127_1_32) = all_0_6_6)
% 121.01/83.76 |
% 121.01/83.76 | Using (388) and (398) yields:
% 121.01/83.76 | (160) $false
% 121.01/83.76 |
% 121.01/83.76 |-The branch is then unsatisfiable
% 121.01/83.76 |-Branch two:
% 121.01/83.76 | (388) cons(all_61_0_14, all_127_1_32) = all_0_6_6
% 121.01/83.76 | (401) ? [v0] : ? [v1] : (( ~ (v0 = 0) & ssList(all_127_1_32) = v0) | (frontsegP(all_127_1_32, all_61_1_15) = v1 & ssList(all_61_1_15) = v0 & ( ~ (v0 = 0) | (( ~ (v1 = 0) | all_81_0_29 = 0) & ( ~ (all_81_0_29 = 0) | v1 = 0)))))
% 121.01/83.76 |
% 121.01/83.76 | Instantiating (401) with all_216_0_56, all_216_1_57 yields:
% 121.01/83.76 | (402) ( ~ (all_216_1_57 = 0) & ssList(all_127_1_32) = all_216_1_57) | (frontsegP(all_127_1_32, all_61_1_15) = all_216_0_56 & ssList(all_61_1_15) = all_216_1_57 & ( ~ (all_216_1_57 = 0) | (( ~ (all_216_0_56 = 0) | all_81_0_29 = 0) & ( ~ (all_81_0_29 = 0) | all_216_0_56 = 0))))
% 121.01/83.76 |
% 121.01/83.76 +-Applying beta-rule and splitting (402), into two cases.
% 121.01/83.76 |-Branch one:
% 121.01/83.76 | (403) ~ (all_216_1_57 = 0) & ssList(all_127_1_32) = all_216_1_57
% 121.01/83.76 |
% 121.01/83.76 | Applying alpha-rule on (403) yields:
% 121.01/83.76 | (404) ~ (all_216_1_57 = 0)
% 121.01/83.76 | (405) ssList(all_127_1_32) = all_216_1_57
% 121.01/83.76 |
% 121.01/83.76 | Instantiating formula (76) with all_127_1_32, all_216_1_57, 0 and discharging atoms ssList(all_127_1_32) = all_216_1_57, ssList(all_127_1_32) = 0, yields:
% 121.01/83.76 | (406) all_216_1_57 = 0
% 121.01/83.76 |
% 121.01/83.76 | Equations (406) can reduce 404 to:
% 121.01/83.76 | (200) $false
% 121.01/83.76 |
% 121.01/83.76 |-The branch is then unsatisfiable
% 121.01/83.76 |-Branch two:
% 121.01/83.76 | (408) frontsegP(all_127_1_32, all_61_1_15) = all_216_0_56 & ssList(all_61_1_15) = all_216_1_57 & ( ~ (all_216_1_57 = 0) | (( ~ (all_216_0_56 = 0) | all_81_0_29 = 0) & ( ~ (all_81_0_29 = 0) | all_216_0_56 = 0)))
% 121.01/83.76 |
% 121.01/83.76 | Applying alpha-rule on (408) yields:
% 121.01/83.76 | (409) frontsegP(all_127_1_32, all_61_1_15) = all_216_0_56
% 121.01/83.76 | (410) ssList(all_61_1_15) = all_216_1_57
% 121.01/83.76 | (411) ~ (all_216_1_57 = 0) | (( ~ (all_216_0_56 = 0) | all_81_0_29 = 0) & ( ~ (all_81_0_29 = 0) | all_216_0_56 = 0))
% 121.01/83.76 |
% 121.01/83.76 | Instantiating formula (76) with all_61_1_15, all_216_1_57, 0 and discharging atoms ssList(all_61_1_15) = all_216_1_57, ssList(all_61_1_15) = 0, yields:
% 121.01/83.76 | (406) all_216_1_57 = 0
% 121.01/83.76 |
% 121.01/83.76 | From (406) and (410) follows:
% 121.01/83.76 | (204) ssList(all_61_1_15) = 0
% 121.01/83.76 |
% 121.01/83.76 +-Applying beta-rule and splitting (170), into two cases.
% 121.01/83.76 |-Branch one:
% 121.01/83.76 | (414) ~ (ssList(nil) = all_15_2_10)
% 121.01/83.76 |
% 121.01/83.76 | From (168) and (414) follows:
% 121.01/83.76 | (415) ~ (ssList(nil) = 0)
% 121.01/83.76 |
% 121.01/83.76 | Using (94) and (415) yields:
% 121.01/83.76 | (160) $false
% 121.01/83.76 |
% 121.01/83.76 |-The branch is then unsatisfiable
% 121.01/83.76 |-Branch two:
% 121.01/83.76 | (417) ssList(nil) = all_15_2_10
% 121.01/83.76 | (168) all_15_2_10 = 0
% 121.01/83.76 |
% 121.01/83.76 | From (168) and (417) follows:
% 121.01/83.76 | (94) ssList(nil) = 0
% 121.01/83.76 |
% 121.01/83.76 +-Applying beta-rule and splitting (169), into two cases.
% 121.01/83.76 |-Branch one:
% 121.01/83.76 | (420) ~ (ssList(all_0_6_6) = all_15_2_10)
% 121.01/83.76 |
% 121.01/83.76 | From (168) and (420) follows:
% 121.01/83.76 | (421) ~ (ssList(all_0_6_6) = 0)
% 121.01/83.76 |
% 121.01/83.76 | Using (3) and (421) yields:
% 121.01/83.76 | (160) $false
% 121.01/83.76 |
% 121.01/83.76 |-The branch is then unsatisfiable
% 121.01/83.76 |-Branch two:
% 121.01/83.76 | (423) ssList(all_0_6_6) = all_15_2_10
% 121.01/83.76 | (168) all_15_2_10 = 0
% 121.01/83.76 |
% 121.01/83.76 | From (168) and (423) follows:
% 121.01/83.76 | (3) ssList(all_0_6_6) = 0
% 121.01/83.76 |
% 121.01/83.76 | Instantiating formula (105) with all_127_1_32, all_0_6_6 and discharging atoms tl(all_0_6_6) = all_127_1_32, yields:
% 121.01/83.76 | (426) ? [v0] : ? [v1] : (hd(all_0_6_6) = v1 & ssList(all_0_6_6) = v0 & ( ~ (v0 = 0) | ! [v2] : (v2 = all_0_6_6 | v2 = nil | all_0_6_6 = nil | ~ (tl(v2) = all_127_1_32) | ? [v3] : ? [v4] : (hd(v2) = v4 & ssList(v2) = v3 & ( ~ (v4 = v1) | ~ (v3 = 0))))))
% 121.01/83.76 |
% 121.01/83.76 | Instantiating formula (8) with all_0_5_5, all_72_2_22, all_0_6_6, all_143_2_48, all_143_3_49 and discharging atoms app(all_143_3_49, all_143_2_48) = all_0_6_6, app(all_0_6_6, all_72_2_22) = all_0_5_5, yields:
% 121.01/83.76 | (427) ~ (ssList(all_143_3_49) = 0) | ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & ssList(all_143_2_48) = v0) | (ssList(all_72_2_22) = v0 & app(all_143_2_48, all_72_2_22) = v1 & app(all_143_3_49, v1) = v2 & ( ~ (v0 = 0) | v2 = all_0_5_5)))
% 121.01/83.76 |
% 121.01/83.76 | Instantiating formula (8) with all_0_6_6, all_143_2_48, all_143_3_49, all_0_6_6, all_143_5_51 and discharging atoms ssList(all_143_5_51) = 0, app(all_143_3_49, all_143_2_48) = all_0_6_6, app(all_143_5_51, all_0_6_6) = all_143_3_49, yields:
% 121.01/83.76 | (428) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & ssList(all_0_6_6) = v0) | (ssList(all_143_2_48) = v0 & app(all_143_5_51, v1) = v2 & app(all_0_6_6, all_143_2_48) = v1 & ( ~ (v0 = 0) | v2 = all_0_6_6)))
% 121.01/83.76 |
% 121.01/83.76 | Instantiating formula (91) with all_143_3_49, all_0_6_6, all_143_5_51 and discharging atoms ssList(all_143_5_51) = 0, app(all_143_5_51, all_0_6_6) = all_143_3_49, yields:
% 121.01/83.76 | (429) ? [v0] : ? [v1] : (ssList(all_143_3_49) = v1 & ssList(all_0_6_6) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 121.01/83.76 |
% 121.01/83.76 | Instantiating formula (91) with all_0_5_5, all_137_1_38, all_73_5_28 and discharging atoms ssList(all_73_5_28) = 0, app(all_73_5_28, all_137_1_38) = all_0_5_5, yields:
% 121.01/83.76 | (430) ? [v0] : ? [v1] : (ssList(all_137_1_38) = v0 & ssList(all_0_5_5) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 121.01/83.76 |
% 121.01/83.76 | Instantiating (430) with all_261_0_63, all_261_1_64 yields:
% 121.01/83.76 | (431) ssList(all_137_1_38) = all_261_1_64 & ssList(all_0_5_5) = all_261_0_63 & ( ~ (all_261_1_64 = 0) | all_261_0_63 = 0)
% 121.01/83.77 |
% 121.01/83.77 | Applying alpha-rule on (431) yields:
% 121.01/83.77 | (432) ssList(all_137_1_38) = all_261_1_64
% 121.01/83.77 | (433) ssList(all_0_5_5) = all_261_0_63
% 121.01/83.77 | (434) ~ (all_261_1_64 = 0) | all_261_0_63 = 0
% 121.01/83.77 |
% 121.01/83.77 | Instantiating (429) with all_263_0_65, all_263_1_66 yields:
% 121.01/83.77 | (435) ssList(all_143_3_49) = all_263_0_65 & ssList(all_0_6_6) = all_263_1_66 & ( ~ (all_263_1_66 = 0) | all_263_0_65 = 0)
% 121.01/83.77 |
% 121.01/83.77 | Applying alpha-rule on (435) yields:
% 121.01/83.77 | (436) ssList(all_143_3_49) = all_263_0_65
% 121.01/83.77 | (437) ssList(all_0_6_6) = all_263_1_66
% 121.01/83.77 | (438) ~ (all_263_1_66 = 0) | all_263_0_65 = 0
% 121.01/83.77 |
% 121.01/83.77 | Instantiating (428) with all_270_0_74, all_270_1_75, all_270_2_76 yields:
% 121.01/83.77 | (439) ( ~ (all_270_2_76 = 0) & ssList(all_0_6_6) = all_270_2_76) | (ssList(all_143_2_48) = all_270_2_76 & app(all_143_5_51, all_270_1_75) = all_270_0_74 & app(all_0_6_6, all_143_2_48) = all_270_1_75 & ( ~ (all_270_2_76 = 0) | all_270_0_74 = all_0_6_6))
% 121.01/83.77 |
% 121.01/83.77 | Instantiating (426) with all_272_0_80, all_272_1_81 yields:
% 121.01/83.77 | (440) hd(all_0_6_6) = all_272_0_80 & ssList(all_0_6_6) = all_272_1_81 & ( ~ (all_272_1_81 = 0) | ! [v0] : (v0 = all_0_6_6 | v0 = nil | all_0_6_6 = nil | ~ (tl(v0) = all_127_1_32) | ? [v1] : ? [v2] : (hd(v0) = v2 & ssList(v0) = v1 & ( ~ (v2 = all_272_0_80) | ~ (v1 = 0)))))
% 121.01/83.77 |
% 121.01/83.77 | Applying alpha-rule on (440) yields:
% 121.01/83.77 | (441) hd(all_0_6_6) = all_272_0_80
% 121.01/83.77 | (442) ssList(all_0_6_6) = all_272_1_81
% 121.01/83.77 | (443) ~ (all_272_1_81 = 0) | ! [v0] : (v0 = all_0_6_6 | v0 = nil | all_0_6_6 = nil | ~ (tl(v0) = all_127_1_32) | ? [v1] : ? [v2] : (hd(v0) = v2 & ssList(v0) = v1 & ( ~ (v2 = all_272_0_80) | ~ (v1 = 0))))
% 121.01/83.77 |
% 121.01/83.77 | Instantiating formula (76) with all_0_5_5, all_261_0_63, 0 and discharging atoms ssList(all_0_5_5) = all_261_0_63, ssList(all_0_5_5) = 0, yields:
% 121.01/83.77 | (444) all_261_0_63 = 0
% 121.01/83.77 |
% 121.01/83.77 | Instantiating formula (76) with all_0_6_6, all_272_1_81, 0 and discharging atoms ssList(all_0_6_6) = all_272_1_81, ssList(all_0_6_6) = 0, yields:
% 121.01/83.77 | (445) all_272_1_81 = 0
% 121.01/83.77 |
% 121.01/83.77 | Instantiating formula (76) with all_0_6_6, all_263_1_66, all_272_1_81 and discharging atoms ssList(all_0_6_6) = all_272_1_81, ssList(all_0_6_6) = all_263_1_66, yields:
% 121.01/83.77 | (446) all_272_1_81 = all_263_1_66
% 121.01/83.77 |
% 121.01/83.77 | Combining equations (445,446) yields a new equation:
% 121.01/83.77 | (447) all_263_1_66 = 0
% 121.01/83.77 |
% 121.01/83.77 | From (444) and (433) follows:
% 121.01/83.77 | (74) ssList(all_0_5_5) = 0
% 121.01/83.77 |
% 121.01/83.77 | From (447) and (437) follows:
% 121.01/83.77 | (3) ssList(all_0_6_6) = 0
% 121.01/83.77 |
% 121.01/83.77 +-Applying beta-rule and splitting (438), into two cases.
% 121.01/83.77 |-Branch one:
% 121.01/83.77 | (450) ~ (all_263_1_66 = 0)
% 121.01/83.77 |
% 121.01/83.77 | Equations (447) can reduce 450 to:
% 121.01/83.77 | (200) $false
% 121.01/83.77 |
% 121.01/83.77 |-The branch is then unsatisfiable
% 121.01/83.77 |-Branch two:
% 121.01/83.77 | (447) all_263_1_66 = 0
% 121.01/83.77 | (453) all_263_0_65 = 0
% 121.01/83.77 |
% 121.01/83.77 | From (453) and (436) follows:
% 121.01/83.77 | (454) ssList(all_143_3_49) = 0
% 121.01/83.77 |
% 121.01/83.77 +-Applying beta-rule and splitting (439), into two cases.
% 121.01/83.77 |-Branch one:
% 121.01/83.77 | (455) ~ (all_270_2_76 = 0) & ssList(all_0_6_6) = all_270_2_76
% 121.01/83.77 |
% 121.01/83.77 | Applying alpha-rule on (455) yields:
% 121.01/83.77 | (456) ~ (all_270_2_76 = 0)
% 121.01/83.77 | (457) ssList(all_0_6_6) = all_270_2_76
% 121.01/83.77 |
% 121.01/83.77 | Instantiating formula (76) with all_0_6_6, all_270_2_76, 0 and discharging atoms ssList(all_0_6_6) = all_270_2_76, ssList(all_0_6_6) = 0, yields:
% 121.01/83.77 | (458) all_270_2_76 = 0
% 121.01/83.77 |
% 121.01/83.77 | Equations (458) can reduce 456 to:
% 121.01/83.77 | (200) $false
% 121.01/83.77 |
% 121.01/83.77 |-The branch is then unsatisfiable
% 121.01/83.77 |-Branch two:
% 121.01/83.77 | (460) ssList(all_143_2_48) = all_270_2_76 & app(all_143_5_51, all_270_1_75) = all_270_0_74 & app(all_0_6_6, all_143_2_48) = all_270_1_75 & ( ~ (all_270_2_76 = 0) | all_270_0_74 = all_0_6_6)
% 121.01/83.77 |
% 121.01/83.77 | Applying alpha-rule on (460) yields:
% 121.01/83.77 | (461) ssList(all_143_2_48) = all_270_2_76
% 121.01/83.77 | (462) app(all_143_5_51, all_270_1_75) = all_270_0_74
% 121.01/83.77 | (463) app(all_0_6_6, all_143_2_48) = all_270_1_75
% 121.01/83.77 | (464) ~ (all_270_2_76 = 0) | all_270_0_74 = all_0_6_6
% 121.01/83.77 |
% 121.01/83.77 +-Applying beta-rule and splitting (427), into two cases.
% 121.01/83.77 |-Branch one:
% 121.01/83.77 | (465) ~ (ssList(all_143_3_49) = 0)
% 121.01/83.77 |
% 121.01/83.77 | Using (454) and (465) yields:
% 121.01/83.77 | (160) $false
% 121.01/83.77 |
% 121.01/83.77 |-The branch is then unsatisfiable
% 121.01/83.77 |-Branch two:
% 121.01/83.77 | (454) ssList(all_143_3_49) = 0
% 121.01/83.77 | (468) ? [v0] : ? [v1] : ? [v2] : (( ~ (v0 = 0) & ssList(all_143_2_48) = v0) | (ssList(all_72_2_22) = v0 & app(all_143_2_48, all_72_2_22) = v1 & app(all_143_3_49, v1) = v2 & ( ~ (v0 = 0) | v2 = all_0_5_5)))
% 121.01/83.77 |
% 121.01/83.77 | Instantiating (468) with all_369_0_116, all_369_1_117, all_369_2_118 yields:
% 121.01/83.77 | (469) ( ~ (all_369_2_118 = 0) & ssList(all_143_2_48) = all_369_2_118) | (ssList(all_72_2_22) = all_369_2_118 & app(all_143_2_48, all_72_2_22) = all_369_1_117 & app(all_143_3_49, all_369_1_117) = all_369_0_116 & ( ~ (all_369_2_118 = 0) | all_369_0_116 = all_0_5_5))
% 121.01/83.77 |
% 121.01/83.77 | Instantiating formula (76) with all_143_2_48, all_270_2_76, 0 and discharging atoms ssList(all_143_2_48) = all_270_2_76, ssList(all_143_2_48) = 0, yields:
% 121.46/83.77 | (458) all_270_2_76 = 0
% 121.46/83.77 |
% 121.46/83.77 | From (458) and (461) follows:
% 121.46/83.77 | (316) ssList(all_143_2_48) = 0
% 121.46/83.77 |
% 121.46/83.77 +-Applying beta-rule and splitting (464), into two cases.
% 121.46/83.77 |-Branch one:
% 121.46/83.77 | (456) ~ (all_270_2_76 = 0)
% 121.46/83.77 |
% 121.46/83.77 | Equations (458) can reduce 456 to:
% 121.46/83.77 | (200) $false
% 121.46/83.77 |
% 121.46/83.77 |-The branch is then unsatisfiable
% 121.46/83.77 |-Branch two:
% 121.46/83.77 | (458) all_270_2_76 = 0
% 121.46/83.77 | (475) all_270_0_74 = all_0_6_6
% 121.46/83.77 |
% 121.46/83.77 | From (475) and (462) follows:
% 121.46/83.77 | (476) app(all_143_5_51, all_270_1_75) = all_0_6_6
% 121.46/83.77 |
% 121.46/83.77 +-Applying beta-rule and splitting (469), into two cases.
% 121.46/83.77 |-Branch one:
% 121.46/83.77 | (477) ~ (all_369_2_118 = 0) & ssList(all_143_2_48) = all_369_2_118
% 121.46/83.77 |
% 121.46/83.77 | Applying alpha-rule on (477) yields:
% 121.46/83.77 | (478) ~ (all_369_2_118 = 0)
% 121.46/83.77 | (479) ssList(all_143_2_48) = all_369_2_118
% 121.46/83.77 |
% 121.46/83.77 | Instantiating formula (76) with all_143_2_48, all_369_2_118, 0 and discharging atoms ssList(all_143_2_48) = all_369_2_118, ssList(all_143_2_48) = 0, yields:
% 121.46/83.77 | (480) all_369_2_118 = 0
% 121.46/83.77 |
% 121.46/83.77 | Equations (480) can reduce 478 to:
% 121.46/83.77 | (200) $false
% 121.46/83.77 |
% 121.46/83.77 |-The branch is then unsatisfiable
% 121.46/83.77 |-Branch two:
% 121.46/83.77 | (482) ssList(all_72_2_22) = all_369_2_118 & app(all_143_2_48, all_72_2_22) = all_369_1_117 & app(all_143_3_49, all_369_1_117) = all_369_0_116 & ( ~ (all_369_2_118 = 0) | all_369_0_116 = all_0_5_5)
% 121.46/83.77 |
% 121.46/83.77 | Applying alpha-rule on (482) yields:
% 121.46/83.77 | (483) ssList(all_72_2_22) = all_369_2_118
% 121.46/83.77 | (484) app(all_143_2_48, all_72_2_22) = all_369_1_117
% 121.46/83.77 | (485) app(all_143_3_49, all_369_1_117) = all_369_0_116
% 121.46/83.77 | (486) ~ (all_369_2_118 = 0) | all_369_0_116 = all_0_5_5
% 121.46/83.77 |
% 121.46/83.77 | Instantiating formula (76) with all_72_2_22, all_369_2_118, 0 and discharging atoms ssList(all_72_2_22) = all_369_2_118, ssList(all_72_2_22) = 0, yields:
% 121.46/83.77 | (480) all_369_2_118 = 0
% 121.46/83.77 |
% 121.46/83.77 | From (480) and (483) follows:
% 121.46/83.77 | (227) ssList(all_72_2_22) = 0
% 121.46/83.77 |
% 121.46/83.77 +-Applying beta-rule and splitting (486), into two cases.
% 121.46/83.77 |-Branch one:
% 121.46/83.77 | (478) ~ (all_369_2_118 = 0)
% 121.46/83.77 |
% 121.46/83.77 | Equations (480) can reduce 478 to:
% 121.46/83.77 | (200) $false
% 121.46/83.77 |
% 121.46/83.77 |-The branch is then unsatisfiable
% 121.46/83.77 |-Branch two:
% 121.46/83.77 | (480) all_369_2_118 = 0
% 121.46/83.77 | (492) all_369_0_116 = all_0_5_5
% 121.46/83.77 |
% 121.46/83.77 | From (492) and (485) follows:
% 121.46/83.77 | (493) app(all_143_3_49, all_369_1_117) = all_0_5_5
% 121.46/83.77 |
% 121.46/83.77 +-Applying beta-rule and splitting (193), into two cases.
% 121.46/83.77 |-Branch one:
% 121.46/83.77 | (494) ~ (ssList(nil) = all_35_2_13)
% 121.46/83.77 |
% 121.46/83.77 | From (192) and (494) follows:
% 121.46/83.77 | (415) ~ (ssList(nil) = 0)
% 121.46/83.77 |
% 121.46/83.77 | Using (94) and (415) yields:
% 121.46/83.77 | (160) $false
% 121.46/83.77 |
% 121.46/83.77 |-The branch is then unsatisfiable
% 121.46/83.77 |-Branch two:
% 121.46/83.77 | (497) ssList(nil) = all_35_2_13
% 121.46/83.77 | (192) all_35_2_13 = 0
% 121.46/83.77 |
% 121.46/83.77 | From (192) and (497) follows:
% 121.46/83.78 | (94) ssList(nil) = 0
% 121.46/83.78 |
% 121.46/83.78 +-Applying beta-rule and splitting (246), into two cases.
% 121.46/83.78 |-Branch one:
% 121.46/83.78 | (500) ~ (ssList(nil) = all_81_1_30)
% 121.46/83.78 |
% 121.46/83.78 | From (245) and (500) follows:
% 121.46/83.78 | (415) ~ (ssList(nil) = 0)
% 121.46/83.78 |
% 121.46/83.78 | Using (94) and (415) yields:
% 121.46/83.78 | (160) $false
% 121.46/83.78 |
% 121.46/83.78 |-The branch is then unsatisfiable
% 121.46/83.78 |-Branch two:
% 121.46/83.78 | (503) ssList(nil) = all_81_1_30
% 121.46/83.78 | (245) all_81_1_30 = 0
% 121.46/83.78 |
% 121.46/83.78 | From (245) and (503) follows:
% 121.46/83.78 | (94) ssList(nil) = 0
% 121.46/83.78 |
% 121.46/83.78 +-Applying beta-rule and splitting (325), into two cases.
% 121.46/83.78 |-Branch one:
% 121.46/83.78 | (506) ~ (ssList(all_0_6_6) = all_135_0_35)
% 121.46/83.78 |
% 121.46/83.78 | From (364) and (506) follows:
% 121.46/83.78 | (421) ~ (ssList(all_0_6_6) = 0)
% 121.46/83.78 |
% 121.46/83.78 | Using (3) and (421) yields:
% 121.46/83.78 | (160) $false
% 121.46/83.78 |
% 121.46/83.78 |-The branch is then unsatisfiable
% 121.46/83.78 |-Branch two:
% 121.46/83.78 | (509) ssList(all_0_6_6) = all_135_0_35
% 121.46/83.78 | (364) all_135_0_35 = 0
% 121.46/83.78 |
% 121.46/83.78 | From (364) and (509) follows:
% 121.46/83.78 | (3) ssList(all_0_6_6) = 0
% 121.46/83.78 |
% 121.46/83.78 +-Applying beta-rule and splitting (326), into two cases.
% 121.46/83.78 |-Branch one:
% 121.46/83.78 | (512) ~ (ssList(nil) = all_135_0_35)
% 121.46/83.78 |
% 121.46/83.78 | From (364) and (512) follows:
% 121.46/83.78 | (415) ~ (ssList(nil) = 0)
% 121.46/83.78 |
% 121.46/83.78 | Using (94) and (415) yields:
% 121.46/83.78 | (160) $false
% 121.46/83.78 |
% 121.46/83.78 |-The branch is then unsatisfiable
% 121.46/83.78 |-Branch two:
% 121.46/83.78 | (515) ssList(nil) = all_135_0_35
% 121.46/83.78 | (364) all_135_0_35 = 0
% 121.46/83.78 |
% 121.46/83.78 | From (364) and (515) follows:
% 121.46/83.78 | (94) ssList(nil) = 0
% 121.46/83.78 |
% 121.46/83.78 +-Applying beta-rule and splitting (323), into two cases.
% 121.46/83.78 |-Branch one:
% 121.46/83.78 | (518) ~ (ssList(all_61_1_15) = all_135_0_35)
% 121.46/83.78 |
% 121.46/83.78 | From (364) and (518) follows:
% 121.46/83.78 | (519) ~ (ssList(all_61_1_15) = 0)
% 121.46/83.78 |
% 121.46/83.78 | Using (204) and (519) yields:
% 121.46/83.78 | (160) $false
% 121.46/83.78 |
% 121.46/83.78 |-The branch is then unsatisfiable
% 121.46/83.78 |-Branch two:
% 121.46/83.78 | (521) ssList(all_61_1_15) = all_135_0_35
% 121.46/83.78 | (364) all_135_0_35 = 0
% 121.46/83.78 |
% 121.46/83.78 | From (364) and (521) follows:
% 121.46/83.78 | (204) ssList(all_61_1_15) = 0
% 121.46/83.78 |
% 121.46/83.78 +-Applying beta-rule and splitting (333), into two cases.
% 121.46/83.78 |-Branch one:
% 121.46/83.78 | (524) ~ (ssList(all_0_5_5) = all_135_0_35)
% 121.46/83.78 |
% 121.46/83.78 | From (364) and (524) follows:
% 121.46/83.78 | (525) ~ (ssList(all_0_5_5) = 0)
% 121.46/83.78 |
% 121.46/83.78 | Using (74) and (525) yields:
% 121.46/83.78 | (160) $false
% 121.46/83.78 |
% 121.46/83.78 |-The branch is then unsatisfiable
% 121.46/83.78 |-Branch two:
% 121.46/83.78 | (527) ssList(all_0_5_5) = all_135_0_35
% 121.46/83.78 | (528) all_144_1_53 = all_135_0_35
% 121.46/83.78 |
% 121.46/83.78 | Combining equations (528,332) yields a new equation:
% 121.46/83.78 | (529) all_135_0_35 = 0
% 121.46/83.78 |
% 121.46/83.78 | Simplifying 529 yields:
% 121.46/83.78 | (364) all_135_0_35 = 0
% 121.46/83.78 |
% 121.46/83.78 | From (364) and (527) follows:
% 121.46/83.78 | (74) ssList(all_0_5_5) = 0
% 121.46/83.78 |
% 121.46/83.78 +-Applying beta-rule and splitting (324), into two cases.
% 121.46/83.78 |-Branch one:
% 121.46/83.78 | (524) ~ (ssList(all_0_5_5) = all_135_0_35)
% 121.46/83.78 |
% 121.46/83.78 | From (364) and (524) follows:
% 121.46/83.78 | (525) ~ (ssList(all_0_5_5) = 0)
% 121.46/83.78 |
% 121.46/83.78 | Using (74) and (525) yields:
% 121.46/83.78 | (160) $false
% 121.46/83.78 |
% 121.46/83.78 |-The branch is then unsatisfiable
% 121.46/83.78 |-Branch two:
% 121.46/83.78 | (527) ssList(all_0_5_5) = all_135_0_35
% 121.46/83.78 | (364) all_135_0_35 = 0
% 121.46/83.78 |
% 121.46/83.78 | From (364) and (527) follows:
% 121.46/83.78 | (74) ssList(all_0_5_5) = 0
% 121.46/83.78 |
% 121.46/83.78 +-Applying beta-rule and splitting (329), into two cases.
% 121.46/83.78 |-Branch one:
% 121.46/83.78 | (538) ~ (ssList(all_0_6_6) = all_134_1_34)
% 121.46/83.78 |
% 121.46/83.78 | From (307) and (538) follows:
% 121.46/83.78 | (421) ~ (ssList(all_0_6_6) = 0)
% 121.46/83.78 |
% 121.46/83.78 | Using (3) and (421) yields:
% 121.46/83.78 | (160) $false
% 121.46/83.78 |
% 121.46/83.78 |-The branch is then unsatisfiable
% 121.46/83.78 |-Branch two:
% 121.46/83.78 | (541) ssList(all_0_6_6) = all_134_1_34
% 121.46/83.78 | (307) all_134_1_34 = 0
% 121.46/83.78 |
% 121.46/83.78 | From (307) and (541) follows:
% 121.46/83.78 | (3) ssList(all_0_6_6) = 0
% 121.46/83.78 |
% 121.46/83.78 +-Applying beta-rule and splitting (331), into two cases.
% 121.46/83.78 |-Branch one:
% 121.46/83.78 | (518) ~ (ssList(all_61_1_15) = all_135_0_35)
% 121.46/83.78 |
% 121.46/83.78 | From (364) and (518) follows:
% 121.46/83.78 | (519) ~ (ssList(all_61_1_15) = 0)
% 121.46/83.78 |
% 121.46/83.78 | Using (204) and (519) yields:
% 121.46/83.78 | (160) $false
% 121.46/83.78 |
% 121.46/83.78 |-The branch is then unsatisfiable
% 121.46/83.78 |-Branch two:
% 121.46/83.78 | (521) ssList(all_61_1_15) = all_135_0_35
% 121.46/83.78 | (548) all_135_0_35 = all_134_1_34
% 121.46/83.78 |
% 121.46/83.78 | Combining equations (364,548) yields a new equation:
% 121.46/83.78 | (307) all_134_1_34 = 0
% 121.46/83.78 |
% 121.46/83.78 | Combining equations (307,548) yields a new equation:
% 121.46/83.78 | (364) all_135_0_35 = 0
% 121.46/83.78 |
% 121.46/83.78 +-Applying beta-rule and splitting (330), into two cases.
% 121.46/83.78 |-Branch one:
% 121.46/83.78 | (551) ~ (ssList(nil) = all_134_1_34)
% 121.46/83.78 |
% 121.46/83.78 | From (307) and (551) follows:
% 121.46/83.78 | (415) ~ (ssList(nil) = 0)
% 121.46/83.78 |
% 121.46/83.78 | Using (94) and (415) yields:
% 121.46/83.78 | (160) $false
% 121.46/83.78 |
% 121.46/83.78 |-The branch is then unsatisfiable
% 121.46/83.78 |-Branch two:
% 121.46/83.78 | (554) ssList(nil) = all_134_1_34
% 121.46/83.78 | (307) all_134_1_34 = 0
% 121.46/83.78 |
% 121.46/83.78 +-Applying beta-rule and splitting (336), into two cases.
% 121.46/83.78 |-Branch one:
% 121.46/83.78 | (556) ~ (ssList(all_0_5_5) = all_134_1_34)
% 121.46/83.78 |
% 121.46/83.78 | From (307) and (556) follows:
% 121.46/83.78 | (525) ~ (ssList(all_0_5_5) = 0)
% 121.46/83.78 |
% 121.46/83.78 | Using (74) and (525) yields:
% 121.46/83.78 | (160) $false
% 121.46/83.78 |
% 121.46/83.78 |-The branch is then unsatisfiable
% 121.46/83.78 |-Branch two:
% 121.46/83.78 | (559) ssList(all_0_5_5) = all_134_1_34
% 121.46/83.78 | (560) all_135_1_36 = all_134_1_34
% 121.46/83.78 |
% 121.46/83.78 | Combining equations (560,340) yields a new equation:
% 121.46/83.78 | (561) all_134_1_34 = 0
% 121.46/83.78 |
% 121.46/83.78 | Simplifying 561 yields:
% 121.46/83.78 | (307) all_134_1_34 = 0
% 121.46/83.78 |
% 121.46/83.78 | From (307) and (559) follows:
% 121.46/83.78 | (74) ssList(all_0_5_5) = 0
% 121.46/83.78 |
% 121.46/83.78 +-Applying beta-rule and splitting (322), into two cases.
% 121.46/83.78 |-Branch one:
% 121.46/83.78 | (564) ~ (ssList(all_72_2_22) = all_135_0_35)
% 121.46/83.78 |
% 121.46/83.78 | From (364) and (564) follows:
% 121.46/83.78 | (565) ~ (ssList(all_72_2_22) = 0)
% 121.46/83.78 |
% 121.46/83.78 | Using (227) and (565) yields:
% 121.46/83.78 | (160) $false
% 121.46/83.78 |
% 121.46/83.78 |-The branch is then unsatisfiable
% 121.46/83.78 |-Branch two:
% 121.46/83.78 | (567) ssList(all_72_2_22) = all_135_0_35
% 121.46/83.78 | (364) all_135_0_35 = 0
% 121.46/83.78 |
% 121.46/83.78 | From (364) and (567) follows:
% 121.46/83.78 | (227) ssList(all_72_2_22) = 0
% 121.46/83.78 |
% 121.46/83.78 +-Applying beta-rule and splitting (321), into two cases.
% 121.46/83.78 |-Branch one:
% 121.46/83.78 | (570) ~ (ssList(all_73_3_26) = 0)
% 121.46/83.78 |
% 121.46/83.78 | Using (365) and (570) yields:
% 121.46/83.78 | (160) $false
% 121.46/83.78 |
% 121.46/83.78 |-The branch is then unsatisfiable
% 121.46/83.78 |-Branch two:
% 121.46/83.78 | (365) ssList(all_73_3_26) = 0
% 121.46/83.78 | (364) all_135_0_35 = 0
% 121.46/83.78 |
% 121.46/83.78 +-Applying beta-rule and splitting (335), into two cases.
% 121.46/83.78 |-Branch one:
% 121.46/83.78 | (524) ~ (ssList(all_0_5_5) = all_135_0_35)
% 121.46/83.78 |
% 121.46/83.78 | From (364) and (524) follows:
% 121.46/83.78 | (525) ~ (ssList(all_0_5_5) = 0)
% 121.46/83.78 |
% 121.46/83.78 | Using (74) and (525) yields:
% 121.46/83.78 | (160) $false
% 121.46/83.78 |
% 121.46/83.78 |-The branch is then unsatisfiable
% 121.46/83.78 |-Branch two:
% 121.46/83.78 | (527) ssList(all_0_5_5) = all_135_0_35
% 121.46/83.78 | (578) all_135_0_35 = all_135_1_36
% 121.46/83.78 |
% 121.46/83.79 | Combining equations (364,578) yields a new equation:
% 121.46/83.79 | (340) all_135_1_36 = 0
% 121.46/83.79 |
% 121.46/83.79 | Combining equations (340,578) yields a new equation:
% 121.46/83.79 | (364) all_135_0_35 = 0
% 121.46/83.79 |
% 121.46/83.79 | From (364) and (527) follows:
% 121.46/83.79 | (74) ssList(all_0_5_5) = 0
% 121.46/83.79 |
% 121.46/83.79 +-Applying beta-rule and splitting (334), into two cases.
% 121.46/83.79 |-Branch one:
% 121.46/83.79 | (556) ~ (ssList(all_0_5_5) = all_134_1_34)
% 121.46/83.79 |
% 121.46/83.79 | From (307) and (556) follows:
% 121.46/83.79 | (525) ~ (ssList(all_0_5_5) = 0)
% 121.46/83.79 |
% 121.46/83.79 | Using (74) and (525) yields:
% 121.46/83.79 | (160) $false
% 121.46/83.79 |
% 121.46/83.79 |-The branch is then unsatisfiable
% 121.46/83.79 |-Branch two:
% 121.46/83.79 | (559) ssList(all_0_5_5) = all_134_1_34
% 121.46/83.79 | (586) all_144_1_53 = all_134_1_34
% 121.46/83.79 |
% 121.46/83.79 | Combining equations (332,586) yields a new equation:
% 121.46/83.79 | (307) all_134_1_34 = 0
% 121.46/83.79 |
% 121.46/83.79 | From (307) and (559) follows:
% 121.46/83.79 | (74) ssList(all_0_5_5) = 0
% 121.46/83.79 |
% 121.46/83.79 +-Applying beta-rule and splitting (328), into two cases.
% 121.46/83.79 |-Branch one:
% 121.46/83.79 | (556) ~ (ssList(all_0_5_5) = all_134_1_34)
% 121.46/83.79 |
% 121.46/83.79 | From (307) and (556) follows:
% 121.46/83.79 | (525) ~ (ssList(all_0_5_5) = 0)
% 121.46/83.79 |
% 121.46/83.79 | Using (74) and (525) yields:
% 121.46/83.79 | (160) $false
% 121.46/83.79 |
% 121.46/83.79 |-The branch is then unsatisfiable
% 121.46/83.79 |-Branch two:
% 121.46/83.79 | (559) ssList(all_0_5_5) = all_134_1_34
% 121.46/83.79 | (307) all_134_1_34 = 0
% 121.46/83.79 |
% 121.46/83.79 | From (307) and (559) follows:
% 121.46/83.79 | (74) ssList(all_0_5_5) = 0
% 121.46/83.79 |
% 121.46/83.79 | Instantiating formula (91) with all_369_1_117, all_72_2_22, all_143_2_48 and discharging atoms ssList(all_143_2_48) = 0, app(all_143_2_48, all_72_2_22) = all_369_1_117, yields:
% 121.46/83.79 | (595) ? [v0] : ? [v1] : (ssList(all_369_1_117) = v1 & ssList(all_72_2_22) = v0 & ( ~ (v0 = 0) | v1 = 0))
% 121.46/83.79 |
% 121.46/83.79 | Instantiating formula (80) with all_369_1_117, all_143_3_49, all_143_5_51, all_35_1_12, all_0_6_6, all_0_5_5 and discharging atoms segmentP(all_0_5_5, all_0_6_6) = all_35_1_12, ssList(all_0_5_5) = 0, app(all_143_3_49, all_369_1_117) = all_0_5_5, app(all_143_5_51, all_0_6_6) = all_143_3_49, yields:
% 121.46/83.79 | (596) all_35_1_12 = 0 | ? [v0] : (( ~ (v0 = 0) & ssList(all_369_1_117) = v0) | ( ~ (v0 = 0) & ssList(all_143_5_51) = v0) | ( ~ (v0 = 0) & ssList(all_0_6_6) = v0))
% 121.46/83.79 |
% 121.46/83.79 | Instantiating formula (91) with all_0_5_5, all_369_1_117, all_143_3_49 and discharging atoms ssList(all_143_3_49) = 0, app(all_143_3_49, all_369_1_117) = all_0_5_5, yields:
% 121.46/83.79 | (597) ? [v0] : ? [v1] : (ssList(all_369_1_117) = v0 & ssList(all_0_5_5) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 121.46/83.79 |
% 121.46/83.79 | Instantiating formula (91) with all_0_6_6, all_270_1_75, all_143_5_51 and discharging atoms ssList(all_143_5_51) = 0, app(all_143_5_51, all_270_1_75) = all_0_6_6, yields:
% 121.46/83.79 | (598) ? [v0] : ? [v1] : (ssList(all_270_1_75) = v0 & ssList(all_0_6_6) = v1 & ( ~ (v0 = 0) | v1 = 0))
% 121.46/83.79 |
% 121.46/83.79 | Instantiating (598) with all_860_0_149, all_860_1_150 yields:
% 121.46/83.79 | (599) ssList(all_270_1_75) = all_860_1_150 & ssList(all_0_6_6) = all_860_0_149 & ( ~ (all_860_1_150 = 0) | all_860_0_149 = 0)
% 121.46/83.79 |
% 121.46/83.79 | Applying alpha-rule on (599) yields:
% 121.46/83.79 | (600) ssList(all_270_1_75) = all_860_1_150
% 121.46/83.79 | (601) ssList(all_0_6_6) = all_860_0_149
% 121.46/83.79 | (602) ~ (all_860_1_150 = 0) | all_860_0_149 = 0
% 121.46/83.79 |
% 121.46/83.79 | Instantiating (597) with all_895_0_194, all_895_1_195 yields:
% 121.46/83.79 | (603) ssList(all_369_1_117) = all_895_1_195 & ssList(all_0_5_5) = all_895_0_194 & ( ~ (all_895_1_195 = 0) | all_895_0_194 = 0)
% 121.46/83.79 |
% 121.46/83.79 | Applying alpha-rule on (603) yields:
% 121.46/83.79 | (604) ssList(all_369_1_117) = all_895_1_195
% 121.46/83.79 | (605) ssList(all_0_5_5) = all_895_0_194
% 121.46/83.79 | (606) ~ (all_895_1_195 = 0) | all_895_0_194 = 0
% 121.46/83.79 |
% 121.46/83.79 | Instantiating (595) with all_903_0_206, all_903_1_207 yields:
% 121.46/83.79 | (607) ssList(all_369_1_117) = all_903_0_206 & ssList(all_72_2_22) = all_903_1_207 & ( ~ (all_903_1_207 = 0) | all_903_0_206 = 0)
% 121.46/83.79 |
% 121.46/83.79 | Applying alpha-rule on (607) yields:
% 121.46/83.79 | (608) ssList(all_369_1_117) = all_903_0_206
% 121.46/83.79 | (609) ssList(all_72_2_22) = all_903_1_207
% 121.46/83.79 | (610) ~ (all_903_1_207 = 0) | all_903_0_206 = 0
% 121.46/83.79 |
% 121.46/83.79 +-Applying beta-rule and splitting (596), into two cases.
% 121.46/83.79 |-Branch one:
% 121.46/83.79 | (611) all_35_1_12 = 0
% 121.46/83.79 |
% 121.46/83.79 | Equations (611) can reduce 259 to:
% 121.46/83.79 | (200) $false
% 121.46/83.79 |
% 121.46/83.79 |-The branch is then unsatisfiable
% 121.46/83.79 |-Branch two:
% 121.46/83.79 | (259) ~ (all_35_1_12 = 0)
% 121.46/83.79 | (614) ? [v0] : (( ~ (v0 = 0) & ssList(all_369_1_117) = v0) | ( ~ (v0 = 0) & ssList(all_143_5_51) = v0) | ( ~ (v0 = 0) & ssList(all_0_6_6) = v0))
% 121.46/83.79 |
% 121.46/83.79 | Instantiating (614) with all_924_0_243 yields:
% 121.46/83.79 | (615) ( ~ (all_924_0_243 = 0) & ssList(all_369_1_117) = all_924_0_243) | ( ~ (all_924_0_243 = 0) & ssList(all_143_5_51) = all_924_0_243) | ( ~ (all_924_0_243 = 0) & ssList(all_0_6_6) = all_924_0_243)
% 121.46/83.79 |
% 121.46/83.79 | Instantiating formula (76) with all_369_1_117, all_895_1_195, all_903_0_206 and discharging atoms ssList(all_369_1_117) = all_903_0_206, ssList(all_369_1_117) = all_895_1_195, yields:
% 121.46/83.79 | (616) all_903_0_206 = all_895_1_195
% 121.46/83.79 |
% 121.46/83.79 | Instantiating formula (76) with all_72_2_22, all_903_1_207, 0 and discharging atoms ssList(all_72_2_22) = all_903_1_207, ssList(all_72_2_22) = 0, yields:
% 121.46/83.79 | (617) all_903_1_207 = 0
% 121.46/83.79 |
% 121.46/83.79 | Instantiating formula (76) with all_0_6_6, all_860_0_149, 0 and discharging atoms ssList(all_0_6_6) = all_860_0_149, ssList(all_0_6_6) = 0, yields:
% 121.46/83.79 | (618) all_860_0_149 = 0
% 121.46/83.79 |
% 121.46/83.79 | From (616) and (608) follows:
% 121.46/83.79 | (604) ssList(all_369_1_117) = all_895_1_195
% 121.46/83.79 |
% 121.46/83.79 | From (618) and (601) follows:
% 121.46/83.79 | (3) ssList(all_0_6_6) = 0
% 121.46/83.79 |
% 121.46/83.79 +-Applying beta-rule and splitting (615), into two cases.
% 121.46/83.79 |-Branch one:
% 121.46/83.79 | (621) ( ~ (all_924_0_243 = 0) & ssList(all_369_1_117) = all_924_0_243) | ( ~ (all_924_0_243 = 0) & ssList(all_143_5_51) = all_924_0_243)
% 121.46/83.79 |
% 121.46/83.79 +-Applying beta-rule and splitting (621), into two cases.
% 121.46/83.79 |-Branch one:
% 121.46/83.79 | (622) ~ (all_924_0_243 = 0) & ssList(all_369_1_117) = all_924_0_243
% 121.46/83.79 |
% 121.46/83.79 | Applying alpha-rule on (622) yields:
% 121.46/83.79 | (623) ~ (all_924_0_243 = 0)
% 121.46/83.79 | (624) ssList(all_369_1_117) = all_924_0_243
% 121.46/83.79 |
% 121.46/83.79 +-Applying beta-rule and splitting (610), into two cases.
% 121.46/83.79 |-Branch one:
% 121.46/83.79 | (625) ~ (all_903_1_207 = 0)
% 121.46/83.79 |
% 121.46/83.79 | Equations (617) can reduce 625 to:
% 121.46/83.79 | (200) $false
% 121.46/83.79 |
% 121.46/83.79 |-The branch is then unsatisfiable
% 121.46/83.79 |-Branch two:
% 121.46/83.79 | (617) all_903_1_207 = 0
% 121.46/83.79 | (628) all_903_0_206 = 0
% 121.46/83.79 |
% 121.46/83.79 | Combining equations (616,628) yields a new equation:
% 121.46/83.79 | (629) all_895_1_195 = 0
% 121.46/83.79 |
% 121.46/83.79 | Simplifying 629 yields:
% 121.46/83.79 | (630) all_895_1_195 = 0
% 121.46/83.79 |
% 121.46/83.79 | From (630) and (604) follows:
% 121.46/83.79 | (631) ssList(all_369_1_117) = 0
% 121.46/83.79 |
% 121.46/83.79 | Instantiating formula (76) with all_369_1_117, all_924_0_243, 0 and discharging atoms ssList(all_369_1_117) = all_924_0_243, ssList(all_369_1_117) = 0, yields:
% 121.46/83.79 | (632) all_924_0_243 = 0
% 121.46/83.79 |
% 121.46/83.79 | Equations (632) can reduce 623 to:
% 121.46/83.79 | (200) $false
% 121.46/83.79 |
% 121.46/83.79 |-The branch is then unsatisfiable
% 121.46/83.80 |-Branch two:
% 121.46/83.80 | (634) ~ (all_924_0_243 = 0) & ssList(all_143_5_51) = all_924_0_243
% 121.46/83.80 |
% 121.46/83.80 | Applying alpha-rule on (634) yields:
% 121.46/83.80 | (623) ~ (all_924_0_243 = 0)
% 121.46/83.80 | (636) ssList(all_143_5_51) = all_924_0_243
% 121.46/83.80 |
% 121.46/83.80 | Instantiating formula (76) with all_143_5_51, all_924_0_243, 0 and discharging atoms ssList(all_143_5_51) = all_924_0_243, ssList(all_143_5_51) = 0, yields:
% 121.46/83.80 | (632) all_924_0_243 = 0
% 121.46/83.80 |
% 121.46/83.80 | Equations (632) can reduce 623 to:
% 121.46/83.80 | (200) $false
% 121.46/83.80 |
% 121.46/83.80 |-The branch is then unsatisfiable
% 121.46/83.80 |-Branch two:
% 121.46/83.80 | (639) ~ (all_924_0_243 = 0) & ssList(all_0_6_6) = all_924_0_243
% 121.46/83.80 |
% 121.46/83.80 | Applying alpha-rule on (639) yields:
% 121.46/83.80 | (623) ~ (all_924_0_243 = 0)
% 121.56/83.80 | (641) ssList(all_0_6_6) = all_924_0_243
% 121.56/83.80 |
% 121.56/83.80 | Instantiating formula (76) with all_0_6_6, all_924_0_243, 0 and discharging atoms ssList(all_0_6_6) = all_924_0_243, ssList(all_0_6_6) = 0, yields:
% 121.56/83.80 | (632) all_924_0_243 = 0
% 121.56/83.80 |
% 121.56/83.80 | Equations (632) can reduce 623 to:
% 121.56/83.80 | (200) $false
% 121.56/83.80 |
% 121.56/83.80 |-The branch is then unsatisfiable
% 121.56/83.80 |-Branch two:
% 121.56/83.80 | (644) ~ (all_143_5_51 = 0) & ssList(all_0_6_6) = all_143_5_51
% 121.56/83.80 |
% 121.56/83.80 | Applying alpha-rule on (644) yields:
% 121.56/83.80 | (645) ~ (all_143_5_51 = 0)
% 121.56/83.80 | (646) ssList(all_0_6_6) = all_143_5_51
% 121.56/83.80 |
% 121.56/83.80 | Instantiating formula (76) with all_0_6_6, all_143_5_51, 0 and discharging atoms ssList(all_0_6_6) = all_143_5_51, ssList(all_0_6_6) = 0, yields:
% 121.56/83.80 | (647) all_143_5_51 = 0
% 121.56/83.80 |
% 121.56/83.80 | Equations (647) can reduce 645 to:
% 121.56/83.80 | (200) $false
% 121.56/83.80 |
% 121.56/83.80 |-The branch is then unsatisfiable
% 121.56/83.80 |-Branch two:
% 121.56/83.80 | (649) segmentP(all_0_5_5, nil) = all_35_1_12
% 121.56/83.80 | (650) all_35_1_12 = 0 | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_5_5) = v0)
% 121.56/83.80 |
% 121.56/83.80 +-Applying beta-rule and splitting (650), into two cases.
% 121.56/83.80 |-Branch one:
% 121.56/83.80 | (611) all_35_1_12 = 0
% 121.56/83.80 |
% 121.56/83.80 | Equations (611) can reduce 259 to:
% 121.56/83.80 | (200) $false
% 121.56/83.80 |
% 121.56/83.80 |-The branch is then unsatisfiable
% 121.56/83.80 |-Branch two:
% 121.56/83.80 | (259) ~ (all_35_1_12 = 0)
% 121.56/83.80 | (654) ? [v0] : ( ~ (v0 = 0) & ssList(all_0_5_5) = v0)
% 121.56/83.80 |
% 121.56/83.80 | Instantiating (654) with all_123_0_319 yields:
% 121.56/83.80 | (655) ~ (all_123_0_319 = 0) & ssList(all_0_5_5) = all_123_0_319
% 121.56/83.80 |
% 121.56/83.80 | Applying alpha-rule on (655) yields:
% 121.56/83.80 | (656) ~ (all_123_0_319 = 0)
% 121.56/83.80 | (657) ssList(all_0_5_5) = all_123_0_319
% 121.56/83.80 |
% 121.56/83.80 | Instantiating formula (76) with all_0_5_5, all_123_0_319, 0 and discharging atoms ssList(all_0_5_5) = all_123_0_319, ssList(all_0_5_5) = 0, yields:
% 121.56/83.80 | (658) all_123_0_319 = 0
% 121.56/83.80 |
% 121.56/83.80 | Equations (658) can reduce 656 to:
% 121.56/83.80 | (200) $false
% 121.56/83.80 |
% 121.56/83.80 |-The branch is then unsatisfiable
% 121.56/83.80 |-Branch two:
% 121.56/83.80 | (611) all_35_1_12 = 0
% 121.56/83.80 | (661) ~ (all_35_2_13 = 0)
% 121.56/83.80 |
% 121.56/83.80 | Equations (192) can reduce 661 to:
% 121.56/83.80 | (200) $false
% 121.56/83.80 |
% 121.56/83.80 |-The branch is then unsatisfiable
% 121.56/83.80 |-Branch two:
% 121.56/83.80 | (255) ~ (all_35_0_11 = 0)
% 121.56/83.80 | (664) ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 121.56/83.80 |
% 121.56/83.80 | Instantiating (664) with all_99_0_320 yields:
% 121.56/83.80 | (665) ~ (all_99_0_320 = 0) & ssList(all_0_6_6) = all_99_0_320
% 121.56/83.80 |
% 121.56/83.80 | Applying alpha-rule on (665) yields:
% 121.56/83.80 | (666) ~ (all_99_0_320 = 0)
% 121.56/83.80 | (667) ssList(all_0_6_6) = all_99_0_320
% 121.56/83.80 |
% 121.56/83.80 | Instantiating formula (76) with all_0_6_6, all_99_0_320, 0 and discharging atoms ssList(all_0_6_6) = all_99_0_320, ssList(all_0_6_6) = 0, yields:
% 121.56/83.80 | (668) all_99_0_320 = 0
% 121.56/83.80 |
% 121.56/83.80 | Equations (668) can reduce 666 to:
% 121.56/83.80 | (200) $false
% 121.56/83.80 |
% 121.56/83.80 |-The branch is then unsatisfiable
% 121.56/83.80 |-Branch two:
% 121.56/83.80 | (670) ~ (all_73_5_28 = 0) & ssList(all_0_5_5) = all_73_5_28
% 121.56/83.80 |
% 121.56/83.80 | Applying alpha-rule on (670) yields:
% 121.56/83.80 | (671) ~ (all_73_5_28 = 0)
% 121.56/83.80 | (672) ssList(all_0_5_5) = all_73_5_28
% 121.56/83.80 |
% 121.56/83.80 | Instantiating formula (76) with all_0_5_5, all_73_5_28, 0 and discharging atoms ssList(all_0_5_5) = all_73_5_28, ssList(all_0_5_5) = 0, yields:
% 121.56/83.80 | (673) all_73_5_28 = 0
% 121.56/83.80 |
% 121.56/83.80 | Equations (673) can reduce 671 to:
% 121.56/83.80 | (200) $false
% 121.56/83.80 |
% 121.56/83.80 |-The branch is then unsatisfiable
% 121.56/83.80 |-Branch two:
% 121.56/83.80 | (675) ~ (all_72_2_22 = 0) & ssList(all_0_6_6) = all_72_2_22
% 121.56/83.80 |
% 121.56/83.80 | Applying alpha-rule on (675) yields:
% 121.56/83.80 | (676) ~ (all_72_2_22 = 0)
% 121.56/83.80 | (677) ssList(all_0_6_6) = all_72_2_22
% 121.56/83.80 |
% 121.56/83.80 +-Applying beta-rule and splitting (210), into two cases.
% 121.56/83.80 |-Branch one:
% 121.56/83.80 | (229) all_0_5_5 = all_0_6_6
% 121.56/83.80 |
% 121.56/83.80 | Equations (229) can reduce 197 to:
% 121.56/83.80 | (200) $false
% 121.56/83.80 |
% 121.56/83.80 |-The branch is then unsatisfiable
% 121.56/83.80 |-Branch two:
% 121.56/83.80 | (197) ~ (all_0_5_5 = all_0_6_6)
% 121.56/83.80 | (232) ? [v0] : ? [v1] : (frontsegP(all_0_6_6, all_0_5_5) = v1 & ssList(all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 121.56/83.80 |
% 121.56/83.80 | Instantiating (232) with all_81_0_321, all_81_1_322 yields:
% 121.56/83.80 | (682) frontsegP(all_0_6_6, all_0_5_5) = all_81_0_321 & ssList(all_0_6_6) = all_81_1_322 & ( ~ (all_81_0_321 = 0) | ~ (all_81_1_322 = 0))
% 121.56/83.80 |
% 121.56/83.80 | Applying alpha-rule on (682) yields:
% 121.56/83.80 | (683) frontsegP(all_0_6_6, all_0_5_5) = all_81_0_321
% 121.56/83.80 | (684) ssList(all_0_6_6) = all_81_1_322
% 121.56/83.80 | (685) ~ (all_81_0_321 = 0) | ~ (all_81_1_322 = 0)
% 121.56/83.80 |
% 121.56/83.80 | Instantiating formula (76) with all_0_6_6, all_81_1_322, 0 and discharging atoms ssList(all_0_6_6) = all_81_1_322, ssList(all_0_6_6) = 0, yields:
% 121.56/83.80 | (686) all_81_1_322 = 0
% 121.56/83.80 |
% 121.56/83.80 | Instantiating formula (76) with all_0_6_6, all_72_2_22, all_81_1_322 and discharging atoms ssList(all_0_6_6) = all_81_1_322, ssList(all_0_6_6) = all_72_2_22, yields:
% 121.56/83.81 | (687) all_81_1_322 = all_72_2_22
% 121.56/83.81 |
% 121.56/83.81 | Combining equations (686,687) yields a new equation:
% 121.56/83.81 | (688) all_72_2_22 = 0
% 121.56/83.81 |
% 121.56/83.81 | Equations (688) can reduce 676 to:
% 121.56/83.81 | (200) $false
% 121.56/83.81 |
% 121.56/83.81 |-The branch is then unsatisfiable
% 121.56/83.81 |-Branch two:
% 121.56/83.81 | (690) segmentP(all_0_6_6, all_0_6_6) = all_15_0_8
% 121.56/83.81 | (691) all_15_0_8 = 0 | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 121.56/83.81 |
% 121.56/83.81 +-Applying beta-rule and splitting (691), into two cases.
% 121.56/83.81 |-Branch one:
% 121.56/83.81 | (692) all_15_0_8 = 0
% 121.56/83.81 |
% 121.56/83.81 | Equations (692) can reduce 191 to:
% 121.56/83.81 | (200) $false
% 121.56/83.81 |
% 121.56/83.81 |-The branch is then unsatisfiable
% 121.56/83.81 |-Branch two:
% 121.56/83.81 | (191) ~ (all_15_0_8 = 0)
% 121.56/83.81 | (664) ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 121.56/83.81 |
% 121.56/83.81 | Instantiating (664) with all_61_0_323 yields:
% 121.56/83.81 | (696) ~ (all_61_0_323 = 0) & ssList(all_0_6_6) = all_61_0_323
% 121.56/83.81 |
% 121.56/83.81 | Applying alpha-rule on (696) yields:
% 121.56/83.81 | (697) ~ (all_61_0_323 = 0)
% 121.56/83.81 | (698) ssList(all_0_6_6) = all_61_0_323
% 121.56/83.81 |
% 121.56/83.81 | Instantiating formula (76) with all_0_6_6, all_61_0_323, 0 and discharging atoms ssList(all_0_6_6) = all_61_0_323, ssList(all_0_6_6) = 0, yields:
% 121.56/83.81 | (699) all_61_0_323 = 0
% 121.56/83.81 |
% 121.56/83.81 | Equations (699) can reduce 697 to:
% 121.56/83.81 | (200) $false
% 121.56/83.81 |
% 121.56/83.81 |-The branch is then unsatisfiable
% 121.56/83.81 |-Branch two:
% 121.56/83.81 | (701) segmentP(all_0_6_6, nil) = all_15_0_8
% 121.56/83.81 | (691) all_15_0_8 = 0 | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 121.56/83.81 |
% 121.56/83.81 +-Applying beta-rule and splitting (691), into two cases.
% 121.56/83.81 |-Branch one:
% 121.56/83.81 | (692) all_15_0_8 = 0
% 121.56/83.81 |
% 121.56/83.81 | Equations (692) can reduce 191 to:
% 121.56/83.81 | (200) $false
% 121.56/83.81 |
% 121.56/83.81 |-The branch is then unsatisfiable
% 121.56/83.81 |-Branch two:
% 121.56/83.81 | (191) ~ (all_15_0_8 = 0)
% 121.56/83.81 | (664) ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 121.56/83.81 |
% 121.56/83.81 | Instantiating (664) with all_57_0_324 yields:
% 121.56/83.81 | (707) ~ (all_57_0_324 = 0) & ssList(all_0_6_6) = all_57_0_324
% 121.56/83.81 |
% 121.56/83.81 | Applying alpha-rule on (707) yields:
% 121.56/83.81 | (708) ~ (all_57_0_324 = 0)
% 121.56/83.81 | (709) ssList(all_0_6_6) = all_57_0_324
% 121.56/83.81 |
% 121.56/83.81 | Instantiating formula (76) with all_0_6_6, all_57_0_324, 0 and discharging atoms ssList(all_0_6_6) = all_57_0_324, ssList(all_0_6_6) = 0, yields:
% 121.56/83.81 | (710) all_57_0_324 = 0
% 121.56/83.81 |
% 121.56/83.81 | Equations (710) can reduce 708 to:
% 121.56/83.81 | (200) $false
% 121.56/83.81 |
% 121.56/83.81 |-The branch is then unsatisfiable
% 121.56/83.81 |-Branch two:
% 121.56/83.81 | (692) all_15_0_8 = 0
% 121.56/83.81 | (713) ~ (all_15_1_9 = 0) | ~ (all_15_2_10 = 0)
% 121.56/83.81 |
% 121.56/83.81 +-Applying beta-rule and splitting (713), into two cases.
% 121.56/83.81 |-Branch one:
% 121.56/83.81 | (714) ~ (all_15_1_9 = 0)
% 121.56/83.81 |
% 121.56/83.81 | Equations (180) can reduce 714 to:
% 121.56/83.81 | (200) $false
% 121.56/83.81 |
% 121.56/83.81 |-The branch is then unsatisfiable
% 121.56/83.81 |-Branch two:
% 121.56/83.81 | (180) all_15_1_9 = 0
% 121.56/83.81 | (717) ~ (all_15_2_10 = 0)
% 121.56/83.81 |
% 121.56/83.81 | Equations (168) can reduce 717 to:
% 121.56/83.81 | (200) $false
% 121.56/83.81 |
% 121.56/83.81 |-The branch is then unsatisfiable
% 121.56/83.81 |-Branch two:
% 121.56/83.81 | (714) ~ (all_15_1_9 = 0)
% 121.56/83.81 | (654) ? [v0] : ( ~ (v0 = 0) & ssList(all_0_5_5) = v0)
% 121.56/83.81 |
% 121.56/83.81 | Instantiating (654) with all_32_0_325 yields:
% 121.56/83.81 | (721) ~ (all_32_0_325 = 0) & ssList(all_0_5_5) = all_32_0_325
% 121.56/83.81 |
% 121.56/83.81 | Applying alpha-rule on (721) yields:
% 121.56/83.81 | (722) ~ (all_32_0_325 = 0)
% 121.56/83.81 | (723) ssList(all_0_5_5) = all_32_0_325
% 121.56/83.81 |
% 121.56/83.81 | Instantiating formula (76) with all_0_5_5, all_32_0_325, 0 and discharging atoms ssList(all_0_5_5) = all_32_0_325, ssList(all_0_5_5) = 0, yields:
% 121.56/83.81 | (724) all_32_0_325 = 0
% 121.56/83.81 |
% 121.56/83.81 | Equations (724) can reduce 722 to:
% 121.56/83.81 | (200) $false
% 121.56/83.81 |
% 121.56/83.81 |-The branch is then unsatisfiable
% 121.56/83.81 |-Branch two:
% 121.56/83.81 | (726) all_0_5_5 = nil & all_0_6_6 = nil
% 121.56/83.81 |
% 121.56/83.81 | Applying alpha-rule on (726) yields:
% 121.56/83.81 | (199) all_0_5_5 = nil
% 121.56/83.81 | (267) all_0_6_6 = nil
% 121.56/83.81 |
% 121.56/83.81 | From (267) and (3) follows:
% 121.56/83.81 | (94) ssList(nil) = 0
% 121.56/83.81 |
% 121.56/83.81 | From (199) and (158) follows:
% 121.56/83.81 | (730) neq(nil, nil) = 0
% 121.56/83.81 |
% 121.56/83.81 | From (267) and (57) follows:
% 121.56/83.81 | (731) neq(nil, nil) = all_0_3_3
% 121.56/83.81 |
% 121.56/83.81 +-Applying beta-rule and splitting (150), into two cases.
% 121.56/83.81 |-Branch one:
% 121.56/83.81 | (732) ~ (neq(all_0_6_6, nil) = all_0_4_4)
% 121.56/83.81 |
% 121.56/83.81 | From (267)(154) and (732) follows:
% 121.56/83.81 | (733) ~ (neq(nil, nil) = 0)
% 121.56/83.81 |
% 121.56/83.81 | Using (730) and (733) yields:
% 121.56/83.81 | (160) $false
% 121.56/83.81 |
% 121.56/83.81 |-The branch is then unsatisfiable
% 121.56/83.81 |-Branch two:
% 121.56/83.81 | (735) neq(all_0_6_6, nil) = all_0_4_4
% 121.56/83.81 | (736) all_0_3_3 = all_0_4_4
% 121.56/83.81 |
% 121.56/83.81 | Combining equations (154,736) yields a new equation:
% 121.56/83.81 | (177) all_0_3_3 = 0
% 121.56/83.81 |
% 121.56/83.81 | From (177) and (731) follows:
% 121.56/83.81 | (730) neq(nil, nil) = 0
% 121.56/83.81 |
% 121.56/83.81 +-Applying beta-rule and splitting (157), into two cases.
% 121.56/83.81 |-Branch one:
% 121.56/83.81 | (182) ~ (neq(all_0_6_6, nil) = 0)
% 121.56/83.81 |
% 121.56/83.81 | From (267) and (182) follows:
% 121.56/83.81 | (733) ~ (neq(nil, nil) = 0)
% 121.56/83.81 |
% 121.56/83.81 | Using (730) and (733) yields:
% 121.56/83.81 | (160) $false
% 121.56/83.81 |
% 121.56/83.81 |-The branch is then unsatisfiable
% 121.56/83.81 |-Branch two:
% 121.56/83.81 | (179) neq(all_0_6_6, nil) = 0
% 121.56/83.81 | (185) ? [v0] : ? [v1] : ? [v2] : (segmentP(all_0_5_5, all_0_6_6) = v1 & segmentP(all_0_6_6, all_0_6_6) = v2 & ssList(all_0_6_6) = v0 & ( ~ (v2 = 0) | ~ (v1 = 0) | ~ (v0 = 0)))
% 121.56/83.81 |
% 121.56/83.81 | From (267) and (179) follows:
% 121.56/83.81 | (730) neq(nil, nil) = 0
% 121.56/83.81 |
% 121.56/83.81 | Instantiating formula (14) with nil and discharging atoms ssList(nil) = 0, neq(nil, nil) = 0, yields:
% 121.56/83.81 | (160) $false
% 121.56/83.81 |
% 121.56/83.81 |-The branch is then unsatisfiable
% 121.56/83.81 |-Branch two:
% 121.56/83.81 | (746) all_0_5_5 = nil & ~ (all_0_6_6 = nil)
% 121.56/83.81 |
% 121.56/83.81 | Applying alpha-rule on (746) yields:
% 121.56/83.81 | (199) all_0_5_5 = nil
% 121.56/83.81 | (266) ~ (all_0_6_6 = nil)
% 121.56/83.81 |
% 121.56/83.81 | From (199) and (19) follows:
% 121.56/83.81 | (749) frontsegP(nil, all_0_6_6) = all_0_2_2
% 121.56/83.81 |
% 121.56/83.81 | From (199) and (74) follows:
% 121.56/83.81 | (94) ssList(nil) = 0
% 121.56/83.81 |
% 121.56/83.81 +-Applying beta-rule and splitting (95), into two cases.
% 121.56/83.81 |-Branch one:
% 121.56/83.81 | (175) all_0_2_2 = 0 & all_0_3_3 = 0
% 121.56/83.81 |
% 121.56/83.81 | Applying alpha-rule on (175) yields:
% 121.56/83.81 | (176) all_0_2_2 = 0
% 121.56/83.81 | (177) all_0_3_3 = 0
% 121.56/83.81 |
% 121.56/83.81 | From (176) and (749) follows:
% 121.56/83.81 | (754) frontsegP(nil, all_0_6_6) = 0
% 121.56/83.81 |
% 121.56/83.81 +-Applying beta-rule and splitting (152), into two cases.
% 121.56/83.81 |-Branch one:
% 121.56/83.81 | (267) all_0_6_6 = nil
% 121.56/83.81 |
% 121.56/83.81 | Equations (267) can reduce 266 to:
% 121.56/83.81 | (200) $false
% 121.56/83.81 |
% 121.56/83.81 |-The branch is then unsatisfiable
% 121.56/83.81 |-Branch two:
% 121.56/83.81 | (266) ~ (all_0_6_6 = nil)
% 121.56/83.81 | (270) ? [v0] : ? [v1] : (ssList(v0) = 0 & cons(v1, v0) = all_0_6_6 & ssItem(v1) = 0)
% 121.56/83.81 |
% 121.56/83.81 | Instantiating formula (123) with all_0_6_6, nil and discharging atoms frontsegP(nil, all_0_6_6) = 0, ssList(nil) = 0, yields:
% 121.56/83.82 | (759) all_0_6_6 = nil | ? [v0] : ? [v1] : (frontsegP(all_0_6_6, nil) = v1 & ssList(all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 121.56/83.82 |
% 121.56/83.82 | Instantiating formula (99) with all_0_6_6 and discharging atoms frontsegP(nil, all_0_6_6) = 0, yields:
% 121.56/83.82 | (760) all_0_6_6 = nil | ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 121.56/83.82 |
% 121.56/83.82 +-Applying beta-rule and splitting (760), into two cases.
% 121.56/83.82 |-Branch one:
% 121.56/83.82 | (267) all_0_6_6 = nil
% 121.56/83.82 |
% 121.56/83.82 | Equations (267) can reduce 266 to:
% 121.56/83.82 | (200) $false
% 121.56/83.82 |
% 121.56/83.82 |-The branch is then unsatisfiable
% 121.56/83.82 |-Branch two:
% 121.56/83.82 | (266) ~ (all_0_6_6 = nil)
% 121.56/83.82 | (664) ? [v0] : ( ~ (v0 = 0) & ssList(all_0_6_6) = v0)
% 121.56/83.82 |
% 121.56/83.82 | Instantiating (664) with all_34_0_342 yields:
% 121.56/83.82 | (765) ~ (all_34_0_342 = 0) & ssList(all_0_6_6) = all_34_0_342
% 121.56/83.82 |
% 121.56/83.82 | Applying alpha-rule on (765) yields:
% 121.56/83.82 | (766) ~ (all_34_0_342 = 0)
% 121.56/83.82 | (767) ssList(all_0_6_6) = all_34_0_342
% 121.56/83.82 |
% 121.56/83.82 +-Applying beta-rule and splitting (759), into two cases.
% 121.56/83.82 |-Branch one:
% 121.56/83.82 | (267) all_0_6_6 = nil
% 121.56/83.82 |
% 121.56/83.82 | Equations (267) can reduce 266 to:
% 121.56/83.82 | (200) $false
% 121.56/83.82 |
% 121.56/83.82 |-The branch is then unsatisfiable
% 121.56/83.82 |-Branch two:
% 121.56/83.82 | (266) ~ (all_0_6_6 = nil)
% 121.56/83.82 | (771) ? [v0] : ? [v1] : (frontsegP(all_0_6_6, nil) = v1 & ssList(all_0_6_6) = v0 & ( ~ (v1 = 0) | ~ (v0 = 0)))
% 121.56/83.82 |
% 121.56/83.82 | Instantiating (771) with all_39_0_343, all_39_1_344 yields:
% 121.56/83.82 | (772) frontsegP(all_0_6_6, nil) = all_39_0_343 & ssList(all_0_6_6) = all_39_1_344 & ( ~ (all_39_0_343 = 0) | ~ (all_39_1_344 = 0))
% 121.56/83.82 |
% 121.56/83.82 | Applying alpha-rule on (772) yields:
% 121.56/83.82 | (773) frontsegP(all_0_6_6, nil) = all_39_0_343
% 121.56/83.82 | (774) ssList(all_0_6_6) = all_39_1_344
% 121.56/83.82 | (775) ~ (all_39_0_343 = 0) | ~ (all_39_1_344 = 0)
% 121.56/83.82 |
% 121.56/83.82 | Instantiating formula (76) with all_0_6_6, all_39_1_344, 0 and discharging atoms ssList(all_0_6_6) = all_39_1_344, ssList(all_0_6_6) = 0, yields:
% 121.56/83.82 | (776) all_39_1_344 = 0
% 121.56/83.82 |
% 121.56/83.82 | Instantiating formula (76) with all_0_6_6, all_34_0_342, all_39_1_344 and discharging atoms ssList(all_0_6_6) = all_39_1_344, ssList(all_0_6_6) = all_34_0_342, yields:
% 121.56/83.82 | (777) all_39_1_344 = all_34_0_342
% 121.56/83.82 |
% 121.56/83.82 | Combining equations (777,776) yields a new equation:
% 121.56/83.82 | (778) all_34_0_342 = 0
% 121.56/83.82 |
% 121.56/83.82 | Simplifying 778 yields:
% 121.56/83.82 | (779) all_34_0_342 = 0
% 121.56/83.82 |
% 121.56/83.82 | Equations (779) can reduce 766 to:
% 121.56/83.82 | (200) $false
% 121.56/83.82 |
% 121.56/83.82 |-The branch is then unsatisfiable
% 121.56/83.82 |-Branch two:
% 121.56/83.82 | (726) all_0_5_5 = nil & all_0_6_6 = nil
% 121.56/83.82 |
% 121.56/83.82 | Applying alpha-rule on (726) yields:
% 121.56/83.82 | (199) all_0_5_5 = nil
% 121.56/83.82 | (267) all_0_6_6 = nil
% 121.56/83.82 |
% 121.56/83.82 | Equations (267) can reduce 266 to:
% 121.56/83.82 | (200) $false
% 121.56/83.82 |
% 121.56/83.82 |-The branch is then unsatisfiable
% 121.56/83.82 % SZS output end Proof for theBenchmark
% 121.56/83.82
% 121.56/83.82 83233ms
%------------------------------------------------------------------------------